Generic safety documentation model
Mahn, J.A.
1994-04-01
This document is intended to be a resource for preparers of safety documentation for Sandia National Laboratories, New Mexico facilities. It provides standardized discussions of some topics that are generic to most, if not all, Sandia/NM facilities safety documents. The material provides a ``core`` upon which to develop facility-specific safety documentation. The use of the information in this document will reduce the cost of safety document preparation and improve consistency of information.
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Mathematical models of hysteresis
1998-08-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
[Mathematical models of hysteresis
Mayergoyz, I.D.
1991-01-01
The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories''. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.
Descriptive Model of Generic WAMS
Hauer, John F.; DeSteese, John G.
2007-06-01
The Department of Energy’s (DOE) Transmission Reliability Program is supporting the research, deployment, and demonstration of various wide area measurement system (WAMS) technologies to enhance the reliability of the Nation’s electrical power grid. Pacific Northwest National Laboratory (PNNL) was tasked by the DOE National SCADA Test Bed Program to conduct a study of WAMS security. This report represents achievement of the milestone to develop a generic WAMS model description that will provide a basis for the security analysis planned in the next phase of this study.
Generic magnetic fusion rocket model
Santarius, J.F.; Logan, B.G.
1993-06-01
A generic magnetic fusion rocket model is developed and used to explore the limits of fusion propulsion systems. Two fusion fuels are examined, D-T and D-(He-3), and the D-(He-3) fuel cycle is found to give a higher specific power in almost all parameter regimes. The key findings are that (1) magnetic fusion should ultimately be able to deliver specific powers of about 10 kW/kg and (2) specific powers of 15 kW/kg could be achieved with only modest extrapolations of present technology. 9 refs.
Generic domain models in software engineering
NASA Technical Reports Server (NTRS)
Maiden, Neil
1992-01-01
This paper outlines three research directions related to domain-specific software development: (1) reuse of generic models for domain-specific software development; (2) empirical evidence to determine these generic models, namely elicitation of mental knowledge schema possessed by expert software developers; and (3) exploitation of generic domain models to assist modelling of specific applications. It focuses on knowledge acquisition for domain-specific software development, with emphasis on tool support for the most important phases of software development.
Bayesian procedure for modeling dependence in generic estimates for component reliability
Lim, T.J.; Hwang, M.J.; Chung, W.D.
1997-12-01
This paper presents a mathematical model for aggregating component reliability data from dependent generic compendia. Our model postulates that generic data are sets of estimates for the parameters of the variability distribution, and the estimates are statistics of failure data from several plants. The same plant data may be utilized in some generic literature sources, which causes dependency among the generic estimates. We propose an estimation procedure based on a parametric empirical Bayesian framework. The proposed model accounts for the relative credibility as well as the dependence among generic estimates. Numerical examples are provided to show the characteristics of the model. 16 refs., 2 figs., 2 tabs.
Generic hypersonic vehicle performance model
NASA Technical Reports Server (NTRS)
Chavez, Frank R.; Schmidt, David K.
1993-01-01
An integrated computational model of a generic hypersonic vehicle was developed for the purpose of determining the vehicle's performance characteristics, which include the lift, drag, thrust, and moment acting on the vehicle at specified altitude, flight condition, and vehicular configuration. The lift, drag, thrust, and moment are developed for the body fixed coordinate system. These forces and moments arise from both aerodynamic and propulsive sources. SCRAMjet engine performance characteristics, such as fuel flow rate, can also be determined. The vehicle is assumed to be a lifting body with a single aerodynamic control surface. The body shape and control surface location are arbitrary and must be defined. The aerodynamics are calculated using either 2-dimensional Newtonian or modified Newtonian theory and approximate high-Mach-number Prandtl-Meyer expansion theory. Skin-friction drag was also accounted for. The skin-friction drag coefficient is a function of the freestream Mach number. The data for the skin-friction drag coefficient values were taken from NASA Technical Memorandum 102610. The modeling of the vehicle's SCRAMjet engine is based on quasi 1-dimensional gas dynamics for the engine diffuser, nozzle, and the combustor with heat addition. The engine has three variable inputs for control: the engine inlet diffuser area ratio, the total temperature rise through the combustor due to combustion of the fuel, and the engine internal expansion nozzle area ratio. The pressure distribution over the vehicle's lower aft body surface, which acts as an external nozzle, is calculated using a combination of quasi 1-dimensional gas dynamic theory and Newtonian or modified Newtonian theory. The exhaust plume shape is determined by matching the pressure inside the plume, calculated from the gas dynamic equations, with the freestream pressure, calculated from Newtonian or Modified Newtonian theory. In this manner, the pressure distribution along the vehicle after body
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
A Generic Biokinetic Model for C-14
Manger, Ryan P
2011-01-01
The generic biokinetic model currently recommended by the International Commission on Radiological Protection (ICRP) for the treatment of systemic radiocarbon assumes uniform distribution of activity in tissues and a biological half-time of 40 d. This model is intended to generate cautiously high estimates of dose per unit intake of C-14 and, in fact, generally predicts a much higher effective dose than systemic models that have been developed on the basis of biokinetic studies of specific carbon compounds. The simplistic model formulation precludes its application as a bioassay model or adjustment to fit case-specific bioassay data. This paper proposes a new generic biokinetic model for systemic radiocarbon that is less conservative than the current ICRP model but maintains sufficient conservatism to overestimate the effective dose coefficients generated by most radiocarbon-compound-specific models. The proposed model includes two systemic pools with different biological half-times representing an initial systemic form of absorbed radiocarbon, a submodel describing the behaviour of labelled carbon dioxide produced in vivo, and three excretion pathways: breath, urine and faeces. Generic excretion rates along each path are based on multi-phase excretion curves observed in experimental studies of radiocarbons. The generic model structure is designed so that the user may adjust the level of dosimetric conservatism to fit the information at hand and may adjust parameter values for consistency with subject-specific or site-specific bioassay data.
Baldrige Theory into Practice: A Generic Model
ERIC Educational Resources Information Center
Arif, Mohammed
2007-01-01
Purpose: The education system globally has moved from a push-based or producer-centric system to a pull-based or customer centric system. Malcolm Baldrige Quality Award (MBQA) model happens to be one of the latest additions to the pull based models. The purpose of this paper is to develop a generic framework for MBQA that can be used by…
Generic Model Host System Design
Chu, Chungming; Wu, Juhao; Qiang, Ji; Shen, Guobao; /Brookhaven
2012-06-22
There are many simulation codes for accelerator modelling; each one has some strength but not all. A platform which can host multiple modelling tools would be ideal for various purposes. The model platform along with infrastructure support can be used not only for online applications but also for offline purposes. Collaboration is formed for the effort of providing such a platform. In order to achieve such a platform, a set of common physics data structure has to be set. Application Programming Interface (API) for physics applications should also be defined within a model data provider. A preliminary platform design and prototype is discussed.
Mathematical Modelling: A New Approach to Teaching Applied Mathematics.
ERIC Educational Resources Information Center
Burghes, D. N.; Borrie, M. S.
1979-01-01
Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)
A Generic Nonlinear Aerodynamic Model for Aircraft
NASA Technical Reports Server (NTRS)
Grauer, Jared A.; Morelli, Eugene A.
2014-01-01
A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.
Mathematical Modeling: A Structured Process
ERIC Educational Resources Information Center
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Mathematical Modeling: Convoying Merchant Ships
ERIC Educational Resources Information Center
Mathews, Susann M.
2004-01-01
This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…
A Primer for Mathematical Modeling
ERIC Educational Resources Information Center
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
Space Generic Open Avionics Architecture (SGOAA) reference model technical guide
NASA Technical Reports Server (NTRS)
Wray, Richard B.; Stovall, John R.
1993-01-01
This report presents a full description of the Space Generic Open Avionics Architecture (SGOAA). The SGOAA consists of a generic system architecture for the entities in spacecraft avionics, a generic processing architecture, and a six class model of interfaces in a hardware/software system. The purpose of the SGOAA is to provide an umbrella set of requirements for applying the generic architecture interface model to the design of specific avionics hardware/software systems. The SGOAA defines a generic set of system interface points to facilitate identification of critical interfaces and establishes the requirements for applying appropriate low level detailed implementation standards to those interface points. The generic core avionics system and processing architecture models provided herein are robustly tailorable to specific system applications and provide a platform upon which the interface model is to be applied.
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
ERIC Educational Resources Information Center
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Modeling generic aspects of ideal fibril formation
NASA Astrophysics Data System (ADS)
Michel, D.
2016-01-01
Many different proteins self-aggregate into insoluble fibrils growing apically by reversible addition of elementary building blocks. But beyond this common principle, the modalities of fibril formation are very disparate, with various intermediate forms which can be reshuffled by minor modifications of physico-chemical conditions or amino-acid sequences. To bypass this complexity, the multifaceted phenomenon of fibril formation is reduced here to its most elementary principles defined for a linear prototype of fibril. Selected generic features, including nucleation, elongation, and conformational recruitment, are modeled using minimalist hypotheses and tools, by separating equilibrium from kinetic aspects and in vitro from in vivo conditions. These reductionist approaches allow to bring out known and new rudiments, including the kinetic and equilibrium effects of nucleation, the dual influence of elongation on nucleation, the kinetic limitations on nucleation and fibril numbers, and the accumulation of complexes in vivo by rescue from degradation. Overlooked aspects of these processes are also pointed: the exponential distribution of fibril lengths can be recovered using various models because it is attributable to randomness only. It is also suggested that the same term "critical concentration" is used for different things, involved in either nucleation or elongation.
Modeling generic aspects of ideal fibril formation.
Michel, D
2016-01-21
Many different proteins self-aggregate into insoluble fibrils growing apically by reversible addition of elementary building blocks. But beyond this common principle, the modalities of fibril formation are very disparate, with various intermediate forms which can be reshuffled by minor modifications of physico-chemical conditions or amino-acid sequences. To bypass this complexity, the multifaceted phenomenon of fibril formation is reduced here to its most elementary principles defined for a linear prototype of fibril. Selected generic features, including nucleation, elongation, and conformational recruitment, are modeled using minimalist hypotheses and tools, by separating equilibrium from kinetic aspects and in vitro from in vivo conditions. These reductionist approaches allow to bring out known and new rudiments, including the kinetic and equilibrium effects of nucleation, the dual influence of elongation on nucleation, the kinetic limitations on nucleation and fibril numbers, and the accumulation of complexes in vivo by rescue from degradation. Overlooked aspects of these processes are also pointed: the exponential distribution of fibril lengths can be recovered using various models because it is attributable to randomness only. It is also suggested that the same term "critical concentration" is used for different things, involved in either nucleation or elongation. PMID:26801045
A Generic Modeling Process to Support Functional Fault Model Development
NASA Technical Reports Server (NTRS)
Maul, William A.; Hemminger, Joseph A.; Oostdyk, Rebecca; Bis, Rachael A.
2016-01-01
Functional fault models (FFMs) are qualitative representations of a system's failure space that are used to provide a diagnostic of the modeled system. An FFM simulates the failure effect propagation paths within a system between failure modes and observation points. These models contain a significant amount of information about the system including the design, operation and off nominal behavior. The development and verification of the models can be costly in both time and resources. In addition, models depicting similar components can be distinct, both in appearance and function, when created individually, because there are numerous ways of representing the failure space within each component. Generic application of FFMs has the advantages of software code reuse: reduction of time and resources in both development and verification, and a standard set of component models from which future system models can be generated with common appearance and diagnostic performance. This paper outlines the motivation to develop a generic modeling process for FFMs at the component level and the effort to implement that process through modeling conventions and a software tool. The implementation of this generic modeling process within a fault isolation demonstration for NASA's Advanced Ground System Maintenance (AGSM) Integrated Health Management (IHM) project is presented and the impact discussed.
Explorations in Elementary Mathematical Modeling
ERIC Educational Resources Information Center
Shahin, Mazen
2010-01-01
In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
Unsteady Aerodynamic Modeling in Roll for the NASA Generic Transport Model
NASA Technical Reports Server (NTRS)
Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.
2012-01-01
Reducing the impact of loss-of-control conditions on commercial transport aircraft is a primary goal of the NASA Aviation Safety Program. One aspect in developing the supporting technologies is to improve the aerodynamic models that represent these adverse conditions. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. In this paper, a more general mathematical model is proposed for the subscale NASA Generic Transport Model (GTM) that covers both low and high angles of attack. Particular attention is devoted to the stall region where full-scale transports have demonstrated a tendency for roll instability. The complete aerodynamic model was estimated from dynamic wind-tunnel data. Advanced computational methods are used to improve understanding and visualize the flow physics within the region where roll instability is a factor.
Generic Sensor Modeling Using Pulse Method
NASA Technical Reports Server (NTRS)
Helder, Dennis L.; Choi, Taeyoung
2005-01-01
Recent development of high spatial resolution satellites such as IKONOS, Quickbird and Orbview enable observation of the Earth's surface with sub-meter resolution. Compared to the 30 meter resolution of Landsat 5 TM, the amount of information in the output image was dramatically increased. In this era of high spatial resolution, the estimation of spatial quality of images is gaining attention. Historically, the Modulation Transfer Function (MTF) concept has been used to estimate an imaging system's spatial quality. Sometimes classified by target shapes, various methods were developed in laboratory environment utilizing sinusoidal inputs, periodic bar patterns and narrow slits. On-orbit sensor MTF estimation was performed on 30-meter GSD Landsat4 Thematic Mapper (TM) data from the bridge pulse target as a pulse input . Because of a high resolution sensor s small Ground Sampling Distance (GSD), reasonably sized man-made edge, pulse, and impulse targets can be deployed on a uniform grassy area with accurate control of ground targets using tarps and convex mirrors. All the previous work cited calculated MTF without testing the MTF estimator's performance. In previous report, a numerical generic sensor model had been developed to simulate and improve the performance of on-orbit MTF estimating techniques. Results from the previous sensor modeling report that have been incorporated into standard MTF estimation work include Fermi edge detection and the newly developed 4th order modified Savitzky-Golay (MSG) interpolation technique. Noise sensitivity had been studied by performing simulations on known noise sources and a sensor model. Extensive investigation was done to characterize multi-resolution ground noise. Finally, angle simulation was tested by using synthetic pulse targets with angles from 2 to 15 degrees, several brightness levels, and different noise levels from both ground targets and imaging system. As a continuing research activity using the developed sensor
Students' Mathematical Modeling of Motion
ERIC Educational Resources Information Center
Marshall, Jill A.; Carrejo, David J.
2008-01-01
We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…
Mathematical Modeling of Diverse Phenomena
NASA Technical Reports Server (NTRS)
Howard, J. C.
1979-01-01
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
Generic CSP Performance Model for NREL's System Advisor Model: Preprint
Wagner, M. J.; Zhu, G.
2011-08-01
The suite of concentrating solar power (CSP) modeling tools in NREL's System Advisor Model (SAM) includes technology performance models for parabolic troughs, power towers, and dish-Stirling systems. Each model provides the user with unique capabilities that are catered to typical design considerations seen in each technology. Since the scope of the various models is generally limited to common plant configurations, new CSP technologies, component geometries, and subsystem combinations can be difficult to model directly in the existing SAM technology models. To overcome the limitations imposed by representative CSP technology models, NREL has developed a 'Generic Solar System' (GSS) performance model for use in SAM. This paper discusses the formulation and performance considerations included in this model and verifies the model by comparing its results with more detailed models.
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
ERIC Educational Resources Information Center
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
Mathematical Models for Doppler Measurements
NASA Technical Reports Server (NTRS)
Lear, William M.
1987-01-01
Error analysis increases precision of navigation. Report presents improved mathematical models of analysis of Doppler measurements and measurement errors of spacecraft navigation. To take advantage of potential navigational accuracy of Doppler measurements, precise equations relate measured cycle count to position and velocity. Drifts and random variations in transmitter and receiver oscillator frequencies taken into account. Mathematical models also adapted to aircraft navigation, radar, sonar, lidar, and interferometry.
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
ERIC Educational Resources Information Center
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
Generic element formulation for modelling bolted lap joints
NASA Astrophysics Data System (ADS)
Ahmadian, Hamid; Jalali, Hassan
2007-07-01
Joints have significant effects on the dynamic response of the assembled structures due to existence of two non-linear mechanisms in their interface, namely slipping and slapping. These mechanisms affect the structural response by adding considerable damping into the structure and lowering the natural frequencies due to the stiffness softening. Neglecting these effects in modelling of joints produces errors in predictions of the structure responses. In this paper, a non-linear generic element formulation is developed for modelling bolted lap joints. The generic element is formed by satisfying all conditions that are known for a joint interface and hence providing a non-linear parametric formulation for the families of allowable joint models. Dynamic response of the developed model for the assembled structure including the generic joint interface element is obtained using the incremental harmonic balance (IHB) method. The generic parameters of the joint are identified by minimising the difference between the model response obtained from IHB method and the observed behaviour of the structure. The procedure is demonstrated by modelling an actual structure containing a single lap bolted joint in the middle. The frequency responses of the structure around the first two resonance frequencies are measured by exciting the structure using a sinusoidal force at each individual frequency. The measured responses are compared with the predictions of the model containing a parametric generic joint element. The parameters of the joint interface model are successfully identified by minimising the difference between the measured responses and the model predictions.
Generic Spacecraft Model for Real-Time Simulation
NASA Technical Reports Server (NTRS)
Kenney, Patrick S.; Ragsdale, William; Neuhaus, Jason R.
2008-01-01
Generic Spacecraft is the name of an evolving library of software that provides for simulation of a generic spacecraft that can orbit the Earth and land on the Moon (and, eventually, on Mars). This library is incorporated into the Langley Standard Realtime Simulation in C++ (LaSRS++) software framework. The generic-spacecraft simulation serves as a test bed for modeling spacecraft dynamics, propulsion, control systems, guidance, and displays. The Generic Spacecraft library supplements the LaSRS++ framework with an interface that facilitates the connection of new models into the LaSRS++ simulation by eliminating what would otherwise be the necessity of writing additional C++ classes to record data from the models and code to display values on graphical user interfaces (GUIs): The library includes routines for integrating new models into the LaSRS++ framework, identifying model inputs and outputs with full descriptions and units identified, recording data, and automatically generating graphical user interfaces (GUIs). The library is designed to be used in a manner similar to that of LaSRS++ software components for simulating vehicles other than the generic spacecraft. The user specifies (1) a spacecraft and individual models to be constructed and (2) connections between individual model inputs and outputs.
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
ERIC Educational Resources Information Center
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Mathematical Models of Gene Regulation
NASA Astrophysics Data System (ADS)
Mackey, Michael C.
2004-03-01
This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.
Using Covariation Reasoning to Support Mathematical Modeling
ERIC Educational Resources Information Center
Jacobson, Erik
2014-01-01
For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…
Mathematical circulatory system model
NASA Technical Reports Server (NTRS)
Lakin, William D. (Inventor); Stevens, Scott A. (Inventor)
2010-01-01
A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.
Mathematical Modeling: A Bridge to STEM Education
ERIC Educational Resources Information Center
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…
The 24-Hour Mathematical Modeling Challenge
ERIC Educational Resources Information Center
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
Mathematical modelling in nuclear medicine
Kuikka, Jyrki T.; Bassingthwaighte, James B.; Henrich, Michael M.; Feinendegen, Ludwig E.
2010-01-01
Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space. Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging. One formulates a model first by defining what it should represent: this is the hypothesis. When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. This is what one would like to test against data. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations. The former are known as distributed models and the latter as lumped compartmental or mixing chamber models. Since both are derived from the same ideas, the parameters are usually the same; their differences are in their ability to represent the hypothesis correctly, quantitatively, and sometimes in their computability. In this essay we review the philosophical and practical aspects of such modelling analysis for translating image sequences into physiological terms. PMID:1936044
Mathematical modeling of piezoresistive elements
NASA Astrophysics Data System (ADS)
Geremias, M.; Moreira, R. C.; Rasia, L. A.; Moi, A.
2015-10-01
This article presents the longitudinal piezoresistive coefficients for thin film amorphous semiconductor type a-C:H. Experimental data and mathematical models have been used in computer simulations. The results show that a reduction of the longitudinal piezoresistive coefficient occurs due to the increased concentration of impurities in the films analyzed.
Teachers' Conceptions of Mathematical Modeling
ERIC Educational Resources Information Center
Gould, Heather
2013-01-01
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
ERIC Educational Resources Information Center
Yilmaz, Suha; Tekin-Dede, Ayse
2016-01-01
Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…
Mathematical Models for Somite Formation
Baker, Ruth E.; Schnell, Santiago; Maini, Philip K.
2009-01-01
Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area. PMID:18023728
Quantum Entanglement in a Generic-Spin Model
NASA Astrophysics Data System (ADS)
Wang, Cui-Xia; Ding, Xiong; Huang, Guo-Qiang; Luo, Cui-Lan
2016-06-01
We investigate quantum entanglement in a generic-spin model with spin squeezing criterions based on squeezing inequalities. By analytically and numerically calculating the squeezing criterions, we show that the system is always entangled except at some special times and the stronger entanglement may be achieved by decreasing the coupling strength and increasing the number of particles.
Generic two-variable model of excitability
NASA Astrophysics Data System (ADS)
Ventura, A. C.; Mindlin, G. B.; Dawson, S. Ponce
2002-04-01
We present a simple model that displays all classes of two-dimensional excitable regimes. One of the variables of the model displays the usual spikes observed in excitable systems. Since the model is written in terms of a ``standard'' vector field, it is always possible to fit it to experimental data displaying spikes in an algorithmic way. In fact, we use it to fit a series of membrane potential recordings obtained in the medicinal leech and time series generated with the FitzHugh-Nagumo equations and the excitability model of Eguía et al. [Phys. Rev. E 58, 2636 (1998)]. In each case, we determine the excitability class of the corresponding system.
Physical and mathematical cochlear models
NASA Astrophysics Data System (ADS)
Lim, Kian-Meng
2000-10-01
The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity
A Generic Model of Dyadic Social Relationships
Favre, Maroussia; Sornette, Didier
2015-01-01
We introduce a model of dyadic social interactions and establish its correspondence with relational models theory (RMT), a theory of human social relationships. RMT posits four elementary models of relationships governing human interactions, singly or in combination: Communal Sharing, Authority Ranking, Equality Matching, and Market Pricing. To these are added the limiting cases of asocial and null interactions, whereby people do not coordinate with reference to any shared principle. Our model is rooted in the observation that each individual in a dyadic interaction can do either the same thing as the other individual, a different thing or nothing at all. To represent these three possibilities, we consider two individuals that can each act in one out of three ways toward the other: perform a social action X or Y, or alternatively do nothing. We demonstrate that the relationships generated by this model aggregate into six exhaustive and disjoint categories. We propose that four of these categories match the four relational models, while the remaining two correspond to the asocial and null interactions defined in RMT. We generalize our results to the presence of N social actions. We infer that the four relational models form an exhaustive set of all possible dyadic relationships based on social coordination. Hence, we contribute to RMT by offering an answer to the question of why there could exist just four relational models. In addition, we discuss how to use our representation to analyze data sets of dyadic social interactions, and how social actions may be valued and matched by the agents. PMID:25826403
A generic model of dyadic social relationships.
Favre, Maroussia; Sornette, Didier
2015-01-01
We introduce a model of dyadic social interactions and establish its correspondence with relational models theory (RMT), a theory of human social relationships. RMT posits four elementary models of relationships governing human interactions, singly or in combination: Communal Sharing, Authority Ranking, Equality Matching, and Market Pricing. To these are added the limiting cases of asocial and null interactions, whereby people do not coordinate with reference to any shared principle. Our model is rooted in the observation that each individual in a dyadic interaction can do either the same thing as the other individual, a different thing or nothing at all. To represent these three possibilities, we consider two individuals that can each act in one out of three ways toward the other: perform a social action X or Y, or alternatively do nothing. We demonstrate that the relationships generated by this model aggregate into six exhaustive and disjoint categories. We propose that four of these categories match the four relational models, while the remaining two correspond to the asocial and null interactions defined in RMT. We generalize our results to the presence of N social actions. We infer that the four relational models form an exhaustive set of all possible dyadic relationships based on social coordination. Hence, we contribute to RMT by offering an answer to the question of why there could exist just four relational models. In addition, we discuss how to use our representation to analyze data sets of dyadic social interactions, and how social actions may be valued and matched by the agents. PMID:25826403
Strategies to Support Students' Mathematical Modeling
ERIC Educational Resources Information Center
Jung, Hyunyi
2015-01-01
An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…
A Generic Multibody Parachute Simulation Model
NASA Technical Reports Server (NTRS)
Neuhaus, Jason Richard; Kenney, Patrick Sean
2006-01-01
Flight simulation of dynamic atmospheric vehicles with parachute systems is a complex task that is not easily modeled in many simulation frameworks. In the past, the performance of vehicles with parachutes was analyzed by simulations dedicated to parachute operations and were generally not used for any other portion of the vehicle flight trajectory. This approach required multiple simulation resources to completely analyze the performance of the vehicle. Recently, improved software engineering practices and increased computational power have allowed a single simulation to model the entire flight profile of a vehicle employing a parachute.
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
ERIC Educational Resources Information Center
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Mathematical modeling of genome replication
NASA Astrophysics Data System (ADS)
Retkute, Renata; Nieduszynski, Conrad A.; de Moura, Alessandro
2012-09-01
Eukaryotic DNA replication is initiated from multiple sites on the chromosome, but little is known about the global and local regulation of replication. We present a mathematical model for the spatial dynamics of DNA replication, which offers insight into the kinetics of replication in different types of organisms. Most biological experiments involve average quantities over large cell populations (typically >107 cells) and therefore can mask the cell-to-cell variability present in the system. Although the model is formulated in terms of a population of cells, using mathematical analysis we show that one can obtain signatures of stochasticity in individual cells from averaged quantities. This work generalizes the result by Retkute [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.068103 107, 068103 (2011)] to a broader set of parameter regimes.
Mathematical models of diabetes progression.
De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels
2008-12-01
Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page. PMID:18780774
Mathematical modelling in MHD technology
Scheindlin, A.E.; Medin, S.A. )
1990-01-01
The technological scheme and the general parameters of the commercial scale pilot MHD power plant are described. The characteristics of the flow train components and the electrical equipment are discussed. The basic ideas of the mathematical modelling of the processes and the devices operation in MHD systems are considered. The application of different description levels in computer simulation is analyzed and the examples of typical solutions are presented.
Developing Generic Dynamic Models for the 2030 Eastern Interconnection Grid
Kou, Gefei; Hadley, Stanton W; Markham, Penn N; Liu, Yilu
2013-12-01
The Eastern Interconnection Planning Collaborative (EIPC) has built three major power flow cases for the 2030 Eastern Interconnection (EI) based on various levels of energy/environmental policy conditions, technology advances, and load growth. Using the power flow cases, this report documents the process of developing the generic 2030 dynamic models using typical dynamic parameters. The constructed model was validated indirectly using the synchronized phasor measurements by removing the wind generation temporarily.
Application of Generic Disposal System Models
Mariner, Paul; Hammond, Glenn Edward; Sevougian, S. David; Stein, Emily
2015-11-01
This report describes specific GDSA activities in fiscal year 2015 (FY2015) toward the development of the enhanced disposal system modeling and analysis capability for geologic disposal of nuclear waste. The GDSA framework employs the PFLOTRAN thermal-hydrologic-chemical multi-physics code (Hammond et al., 2011) and the Dakota uncertainty sampling and propagation code (Adams et al., 2013). Each code is designed for massively-parallel processing in a high-performance computing (HPC) environment. Multi-physics representations in PFLOTRAN are used to simulate various coupled processes including heat flow, fluid flow, waste dissolution, radionuclide release, radionuclide decay and ingrowth, precipitation and dissolution of secondary phases, and radionuclide transport through the engineered barriers and natural geologic barriers to a well location in an overlying or underlying aquifer. Dakota is used to generate sets of representative realizations and to analyze parameter sensitivity.
Summer Camp of Mathematical Modeling in China
ERIC Educational Resources Information Center
Tian, Xiaoxi; Xie, Jinxing
2013-01-01
The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…
[Mathematical model of mental time].
Glasko, A V; Sadykhova, L G
2014-01-01
On the basis of Ernst Mach's ideas and developed before the mathematical theory of mental processes, mathematical definition of duration of an interval of mental time, all over again for perception (experience) of separate event, and then--generally, i.e. for perception (experience) of sequence of events is entered. Its dependence on duration of an appropriating interval of physical time is investigated. Communication of mental time with perception of time (for two cases: "greater" and "small" intervals) is investigated. Comparison of theoretical formulas with results of experimental measurements is spent. Is defined process time which can be used, in particular, as a measure of work. The effect of the inverse of the psychological time, described in works of the Mach is analyzed and modelled. PMID:25723024
Mathematical models of bipolar disorder
NASA Astrophysics Data System (ADS)
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
Mathematical modeling of a class of multibody flexible spacecraft structures
NASA Technical Reports Server (NTRS)
Kelkar, Atul, G.
1994-01-01
A mathematical model for a general multibody flexible spacecraft is obtained. The generic spacecraft considered consists of a flexible central body to which a number of flexible multibody structures are attached. The coordinate systems used in the derivation allow effective decoupling of the translational motion of the entire spacecraft from its rotational motion about its center of mass. The derivation assumes that the deformations in the bodies are only due to elastic motions. The dynamic model derived is a closed-form vector-matrix differential equation. The model developed can be used for analysis and simulation of many realistic spacecraft configurations.
Mathematical models in medicine: Diseases and epidemics
Witten, M.
1987-01-01
This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling.
Mathematical modeling of glycerol biotransformation
NASA Astrophysics Data System (ADS)
Popova-Krumova, Petya; Yankova, Sofia; Ilieva, Biliana
2013-12-01
A method for mathematical modeling of glycerol biotransformation by Klebsiella oxytoca is presented. Glycerol is a renewable resource for it is formed as a by-product during biodiesel production. Because of its large volume production, it seems to be a good idea to develop a technology that converts this waste into products of high value (1, 3-Propanediol; 2, 3-Butanediol). The kinetic model of this process consists of many equations and parameters. The minimization of the least square function will be used for model parameters identification. In cases of parameters identification in multiparameter models the minimization of the least square function is very difficult because it is multiextremal. This is the main problem in the multiextremal function minimization which will be solved on the base a hierarchical approach, using a polynomial approximation of the experimental data.
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).
A generic efficient adaptive grid scheme for rocket propulsion modeling
NASA Technical Reports Server (NTRS)
Mo, J. D.; Chow, Alan S.
1993-01-01
The objective of this research is to develop an efficient, time-accurate numerical algorithm to discretize the Navier-Stokes equations for the predictions of internal one-, two-dimensional and axisymmetric flows. A generic, efficient, elliptic adaptive grid generator is implicitly coupled with the Lower-Upper factorization scheme in the development of ALUNS computer code. The calculations of one-dimensional shock tube wave propagation and two-dimensional shock wave capture, wave-wave interactions, shock wave-boundary interactions show that the developed scheme is stable, accurate and extremely robust. The adaptive grid generator produced a very favorable grid network by a grid speed technique. This generic adaptive grid generator is also applied in the PARC and FDNS codes and the computational results for solid rocket nozzle flowfield and crystal growth modeling by those codes will be presented in the conference, too. This research work is being supported by NASA/MSFC.
Mathematical modeling of cold cap
Pokorny, Richard; Hrma, Pavel R.
2012-10-13
The ultimate goal of studies of cold cap behavior in glass melters is to increase the rate of glass processing in an energy-efficient manner. Regrettably, mathematical models, which are ideal tools for assessing the responses of melters to process parameters, have not paid adequate attention to the cold cap. In this study, we consider a cold cap resting on a pool of molten glass from which it receives a steady heat flux while temperature, velocity, and extent of conversion are functions of the position along the vertical coordinate. A one-dimensional (1D) mathematical model simulates this process by solving the differential equations for mass and energy balances with appropriate boundary conditions and constitutive relationships for material properties. The sensitivity analyses on the effects of incoming heat fluxes to the cold cap through its lower and upper boundaries show that the cold cap thickness increases as the heat flux from above increases, and decreases as the total heat flux increases. We also discuss the effects of foam, originating from batch reactions and from redox reactions in molten glass and argue that models must represent the foam layer to achieve a reliable prediction of the melting rate as a function of feed properties and melter conditions.
A Generative Model of Mathematics Learning
ERIC Educational Resources Information Center
Wittrock, M. C.
1974-01-01
The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…
On Fences, Forms and Mathematical Modeling
ERIC Educational Resources Information Center
Lege, Jerry
2009-01-01
The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…
Mathematical model for classification of EEG signals
NASA Astrophysics Data System (ADS)
Ortiz, Victor H.; Tapia, Juan J.
2015-09-01
A mathematical model to filter and classify brain signals from a brain machine interface is developed. The mathematical model classifies the signals from the different lobes of the brain to differentiate the signals: alpha, beta, gamma and theta, besides the signals from vision, speech, and orientation. The model to develop further eliminates noise signals that occur in the process of signal acquisition. This mathematical model can be used on different platforms interfaces for rehabilitation of physically handicapped persons.
Mathematical model for alopecia areata.
Dobreva, Atanaska; Paus, Ralf; Cogan, N G
2015-09-01
Alopecia areata (AA) is an autoimmune disease, and its clinical phenotype is characterized by the formation of distinct hairless patterns on the scalp or other parts of the body. In most cases hair falls out in round patches. A well-established hypothesis for the pathogenesis of AA states that collapse of hair follicle immune privilege is one of the essential elements in disease development. To investigate the dynamics of alopecia areata, we develop a mathematical model that incorporates immune system components and hair follicle immune privilege agents whose involvement in AA has been confirmed in clinical studies and experimentally. We perform parameter sensitivity analysis in order to determine which inputs have the greatest effect on outcome variables. Our findings suggest that, among all processes reflected in the model, immune privilege guardians and the pro-inflammatory cytokine interferon-γ govern disease dynamics. These results agree with the immune privilege collapse hypothesis for the development of AA. PMID:26047853
Computational oncology - mathematical modelling of drug regimens for precision medicine.
Barbolosi, Dominique; Ciccolini, Joseph; Lacarelle, Bruno; Barlési, Fabrice; André, Nicolas
2016-04-01
Computational oncology is a generic term that encompasses any form of computer-based modelling relating to tumour biology and cancer therapy. Mathematical modelling can be used to probe the pharmacokinetics and pharmacodynamics relationships of the available anticancer agents in order to improve treatment. As a result of the ever-growing numbers of druggable molecular targets and possible drug combinations, obtaining an optimal toxicity-efficacy balance is an increasingly complex task. Consequently, standard empirical approaches to optimizing drug dosing and scheduling in patients are now of limited utility; mathematical modelling can substantially advance this practice through improved rationalization of therapeutic strategies. The implementation of mathematical modelling tools is an emerging trend, but remains largely insufficient to meet clinical needs; at the bedside, anticancer drugs continue to be prescribed and administered according to standard schedules. To shift the therapeutic paradigm towards personalized care, precision medicine in oncology requires powerful new resources for both researchers and clinicians. Mathematical modelling is an attractive approach that could help to refine treatment modalities at all phases of research and development, and in routine patient care. Reviewing preclinical and clinical examples, we highlight the current achievements and limitations with regard to computational modelling of drug regimens, and discuss the potential future implementation of this strategy to achieve precision medicine in oncology. PMID:26598946
FOSSIL2 energy policy model documentation: generic structures of the FOSSIL2 model
1980-10-01
This report discusses the structure, derivations, assumptions, and mathematical formulation of the FOSSIL2 model. Each major facet of the model - supply/demand interactions, industry financing, and production - has been designed to parallel closely the actual cause/effect relationships determining the behavior of the United States energy system. The data base for the FOSSIL2 program is large. When possible, all data were obtained from sources well known to experts in the energy field. Cost and resource estimates are based on DOE data whenever possible. This report presents the FOSSIL2 model at several levels. In Volume I, an overview of the basic structures, assumptions, and behavior of the FOSSIL2 model is presented so that the reader can understand the results of various policy tests. The discussion covers the three major building blocks, or generic structures, used to construct the model: supply/demand balance; finance and capital formation; and energy production. These structures reflect the components and interactions of the major processes within each energy industry that directly affect the dynamics of fuel supply, demand, and price within the energy system as a whole.
Mathematical model for bone mineralization
Komarova, Svetlana V.; Safranek, Lee; Gopalakrishnan, Jay; Ou, Miao-jung Yvonne; McKee, Marc D.; Murshed, Monzur; Rauch, Frank; Zuhr, Erica
2015-01-01
Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly nonlinear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology. PMID:26347868
Generic solar photovoltaic system dynamic simulation model specification.
Ellis, Abraham; Behnke, Michael Robert; Elliott, Ryan Thomas
2013-10-01
This document is intended to serve as a specification for generic solar photovoltaic (PV) system positive-sequence dynamic models to be implemented by software developers and approved by the WECC MVWG for use in bulk system dynamic simulations in accordance with NERC MOD standards. Two specific dynamic models are included in the scope of this document. The first, a Central Station PV System model, is intended to capture the most important dynamic characteristics of large scale (> 10 MW) PV systems with a central Point of Interconnection (POI) at the transmission level. The second, a Distributed PV System model, is intended to represent an aggregation of smaller, distribution-connected systems that comprise a portion of a composite load that might be modeled at a transmission load bus.
Mathematical Modeling Of Life-Support Systems
NASA Technical Reports Server (NTRS)
Seshan, Panchalam K.; Ganapathi, Balasubramanian; Jan, Darrell L.; Ferrall, Joseph F.; Rohatgi, Naresh K.
1994-01-01
Generic hierarchical model of life-support system developed to facilitate comparisons of options in design of system. Model represents combinations of interdependent subsystems supporting microbes, plants, fish, and land animals (including humans). Generic model enables rapid configuration of variety of specific life support component models for tradeoff studies culminating in single system design. Enables rapid evaluation of effects of substituting alternate technologies and even entire groups of technologies and subsystems. Used to synthesize and analyze life-support systems ranging from relatively simple, nonregenerative units like aquariums to complex closed-loop systems aboard submarines or spacecraft. Model, called Generic Modular Flow Schematic (GMFS), coded in such chemical-process-simulation languages as Aspen Plus and expressed as three-dimensional spreadsheet.
Analysis of Physiological Systems via Mathematical Models.
ERIC Educational Resources Information Center
Hazelrig, Jane B.
1983-01-01
Discusses steps to be executed when studying physiological systems with theoretical mathematical models. Steps considered include: (1) definition of goals; (2) model formulation; (3) mathematical description; (4) qualitative evaluation; (5) parameter estimation; (6) model fitting; (7) evaluation; and (8) design of new experiments based on the…
Exact Solution of Two-Site Bose-Hubbard Model with Generic Open Boundaries
NASA Astrophysics Data System (ADS)
Xin, Zhi-Rong; Yang, Tao; Hao, Kun; Yang, Wen-Li
2015-12-01
The Bose-Hubbard model is a paradigm for the study of strongly correlated bosonic systems. We study the two-site Bose-Hubbard model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices. Besides the inhomogeneous parameters, the model itself has three free boundary parameters, which break the U(1)-symmetry, in other words, break the particle number conservation. The Hamiltonian H under these circumstances is constructed. With the help of the off-diagonal Bethe Ansatz method, we successfully obtain the corresponding Bethe Ansatz equations as well as the eigenvalues. Supported by the National Natural Science Foundation of China under Grant Nos. 11375141, 11425522, 11434013, 11347025, 11447239, and Beijing Center for Mathematics and Information Interdisciplinary Sciences are gratefully acknowledged.
Generic Business Model Types for Enterprise Mashup Intermediaries
NASA Astrophysics Data System (ADS)
Hoyer, Volker; Stanoevska-Slabeva, Katarina
The huge demand for situational and ad-hoc applications desired by the mass of business end users led to a new kind of Web applications, well-known as Enterprise Mashups. Users with no or limited programming skills are empowered to leverage in a collaborative manner existing Mashup components by combining and reusing company internal and external resources within minutes to new value added applications. Thereby, Enterprise Mashup environments interact as intermediaries to match the supply of providers and demand of consumers. By following the design science approach, we propose an interaction phase model artefact based on market transaction phases to structure required intermediary features. By means of five case studies, we demonstrate the application of the designed model and identify three generic business model types for Enterprise Mashups intermediaries (directory, broker, and marketplace). So far, intermediaries following a real marketplace business model don’t exist in context of Enterprise Mashups and require further research for this emerging paradigm.
GENERIC MODEL FOR MAGNETIC EXPLOSIONS APPLIED TO SOLAR FLARES
Melrose, D. B.
2012-04-10
An accepted model for magnetospheric substorms is proposed as the basis for a generic model for magnetic explosions and is applied to solar flares. The model involves widely separated energy-release and particle-acceleration regions, with energy transported Alfvenically between them. On a global scale, these regions are coupled by a large-scale current that is set up during the explosion by redirection of pre-existing current associated with the stored magnetic energy. The explosion-related current is driven by an electromotive force (EMF) due to the changing magnetic flux enclosed by this current. The current path and the EMF are identified for an idealized quadrupolar model for a flare.
Mathematical models for exotic wakes
NASA Astrophysics Data System (ADS)
Basu, Saikat; Stremler, Mark
2014-11-01
Vortex wakes are a common occurrence in the environment around us; the most famous example being the von Kármán vortex street with two vortices being shed by the bluff body in each cycle. However, frequently there can be many other more exotic wake configurations with different vortex arrangements, based on the flow parameters and the bluff body dimensions and/or its oscillation characteristics. Some examples include wakes with periodic shedding of three vortices (`P+S' mode) and four vortices (symmetric `2P' mode, staggered `2P' mode, `2C' mode). We present mathematical models for such wakes assuming two-dimensional potential flows with embedded point vortices. The spatial alignment of the vortices is inspired by the experimentally observed wakes. The idealized system follows a Hamiltonian formalism. Model-based analysis reveals a rich dynamics pertaining to the relative vortex motion in the mid-wake region. Downstream evolution of the vortices, as predicted from the model results, also show good correspondence with wake-shedding experiments performed on flowing soap films.
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
2016-01-01
Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research. PMID:27557541
Scaffolding Mathematical Modelling with a Solution Plan
ERIC Educational Resources Information Center
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
Constructing a Model of Mathematical Literacy.
ERIC Educational Resources Information Center
Pugalee, David K.
1999-01-01
Discusses briefly the call for mathematical literacy and the need for a model that articulates the fluid and dynamic nature of this form of literacy. Presents such a model which uses two concentric circles, one depicting the four processes of mathematical literacy (representing, manipulating, reasoning, and problem solving) and enablers that…
Mathematical Modelling as a Professional Task
ERIC Educational Resources Information Center
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Mathematical Modelling and New Theories of Learning.
ERIC Educational Resources Information Center
Boaler, Jo
2001-01-01
Demonstrates the importance of expanding notions of learning beyond knowledge to the practices in mathematics classrooms. Considers a three-year study of students who learned through mathematical modeling. Shows that a modeling approach encouraged the development of a range of important practices in addition to knowledge that were useful in real…
Modelling and Optimizing Mathematics Learning in Children
ERIC Educational Resources Information Center
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
Kolden, G G
1996-06-01
The generic model of psychotherapy is offered as a transtheoretical model of universal change processes. Session 3 change processes are examined in a naturalistic study of dynamic therapy guided by the generic model. Findings replicate and extend earlier work addressing propositions of the generic model in dynamic therapy. Openness and bond contributed to in-session realizations, whereas bond and realizations fostered session progress. Session progress, bond, use of experiential operations, and less frequent use of dynamic interventions contributed to change between Sessions 2 and 4. Discussion outlines a model of change in early dynamic therapy and highlights the usefulness of the generic model for the evaluation of change processes. PMID:8698941
Mathematical modeling in soil science
NASA Astrophysics Data System (ADS)
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
Rival approaches to mathematical modelling in immunology
NASA Astrophysics Data System (ADS)
Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.
2007-08-01
In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.
ERIC Educational Resources Information Center
Andrews, Paul
2009-01-01
An increasingly common approach to comparative education research, particularly with respect to mathematics education, has been the exploitation of video technology, not least because the use of video cameras offers several advantages over traditional methods such as direct observation. It is important to acknowledge, however, that video…
ERIC Educational Resources Information Center
Horton, Robert M.; Leonard, William H.
2005-01-01
In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…
A Seminar in Mathematical Model-Building.
ERIC Educational Resources Information Center
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
A mathematical model of the UH-60 helicopter
NASA Technical Reports Server (NTRS)
Hilbert, K. B.
1984-01-01
This report documents the revisions made to a ten-degree-of-freedom, full-flight envelope, generic helicopter mathematical model to represent the UH-60 helicopter accurately. The major modifications to the model include fuselage aerodynamic force and moment equations specific to the UH-60, a canted tail rotor, a horizontal stabilator with variable incidence, and a pitch bias actuator (PBA). In addition, this report presents a full set of parameters and numerical values which describe the helicopter configuration and physical characteristics. Model validation was accomplished by comparison of trim and stability derivative data generated from the UH-60 math model with data generated from a similar total force and moment math model.
The mathematics of cancer: integrating quantitative models.
Altrock, Philipp M; Liu, Lin L; Michor, Franziska
2015-12-01
Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology. PMID:26597528
Mathematical Models for Library Systems Analysis.
ERIC Educational Resources Information Center
Leimkuhler, F. F.
1967-01-01
The paper reviews the research on design and operation of research libraries sponsored by the Purdue University Libraries and the Purdue School of Industrial Engineering. The use of mathematical models in library operations research is discussed. Among the mathematical methods discussed are marginal analysis or cost minimization, computer…
Mathematical Modelling in the Early School Years
ERIC Educational Resources Information Center
English, Lyn D.; Watters, James J.
2005-01-01
In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…
Mathematical modeling of ligaments and tendons.
Woo, S L; Johnson, G A; Smith, B A
1993-11-01
Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model. PMID:8302027
Aerodynamics model for a generic ASTOVL lift-fan aircraft
NASA Technical Reports Server (NTRS)
Birckelbaw, Lourdes G.; Mcneil, Walter E.; Wardwell, Douglas A.
1995-01-01
This report describes the aerodynamics model used in a simulation model of an advanced short takeoff and vertical landing (ASTOVL) lift-fan fighter aircraft. The simulation model was developed for use in piloted evaluations of transition and hover flight regimes, so that only low speed (M approximately 0.2) aerodynamics are included in the mathematical model. The aerodynamic model includes the power-off aerodynamic forces and moments and the propulsion system induced aerodynamic effects, including ground effects. The power-off aerodynamics data were generated using the U.S. Air Force Stability and Control Digital DATCOM program and a NASA Ames in-house graphics program called VORVIEW which allows the user to easily analyze arbitrary conceptual aircraft configurations using the VORLAX program. The jet-induced data were generated using the prediction methods of R. E. Kuhn et al., as referenced in this report.
Expressing Generic Concepts with and without a Language Model
ERIC Educational Resources Information Center
Goldin-Meadow, S.; Gelman, S.A.; Mylander, C.
2005-01-01
Utterances expressing generic kinds (''birds fly'') highlight qualities of a category that are stable and enduring, and thus provide insight into conceptual organization. To explore the role that linguistic input plays in children's production of generic nouns, we observed American and Chinese deaf children whose hearing losses prevented them from…
A generic biokinetic model for carbon-14 labelled compounds
NASA Astrophysics Data System (ADS)
Manger, Ryan Paul
Carbon-14, a radioactive nuclide, is used in many industrial applications. Due to its wide range of uses in industry, many workers are at risk of accidental internal exposure to 14C. Being a low energy beta emitter, 14C is not a significant external radiation hazard, but the internal consequences posed by 14C are important, especially because of its long half life of 5730 years [46]. The current biokinetic model recommended by the International Commission on Radiological Protection (ICRP) is a conservative estimate of how radiocarbon is treated by the human body. The ICRP generic radiocarbon model consists of a single compartment representing the entire human body. This compartment has a biological half life of 40 days yielding an effective dose coefficient of 5.8x10-10 Sv B q-1 [44, 45, 49, 53, 54]. This overestimates the dose of all radiocarbon compounds that have been studied [96]. An improved model has been developed that includes and alimentary tract, a urinary bladder, CO2 model, and an "Other" compartment used to model systemic tissues. The model can be adapted to replicate any excretion curve and excretion pattern. In addition, the effective dose coefficient produced by the updated model is near the mean effective dose coefficient of carbon compounds that have been considered in this research. The major areas of improvement are: more anatomically significant, a less conservative dose coefficient, and the ability to manipulate the model for known excretion data. Due to the wide variety of carbon compounds, it is suggested that specific biokinetic models be implemented for known radiocarbon substances. If the source of radiocarbon is dietary, then the physiologically based model proposed by Whillans [102] that splits all ingested radiocarbon compounds into carbohydrates, fats, and proteins should be used.
ERIC Educational Resources Information Center
Peretz, Dvora
2005-01-01
This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…
Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.
Clément, Frédérique
2016-07-01
Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of
Mathematical Modeling of Chemical Stoichiometry
ERIC Educational Resources Information Center
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Whether generic model works for rapid ERP-based BCI calibration
Jin, Jing; Sellers, Eric W.; Zhang, Yu; Daly, Ian; Wang, Xingyu; Cichocki, Andrzej
2013-01-01
Event-related potential (ERP)-based brain–computer interfacing (BCI) is an effective method of basic communication. However, collecting calibration data, and classifier training, detracts from the amount of time allocated for online communication. Decreasing calibration time can reduce preparation time thereby allowing for additional online use, potentially lower fatigue, and improved performance. Previous studies, using generic online training models which avoid offline calibration, afford more time for online spelling. Such studies have not examined the direct effects of the model on individual performance, and the training sequence exceeded the time reported here. The first goal of this work is to survey whether one generic model works for all subjects and the second goal is to show the performance of a generic model using an online training strategy when participants could use the generic model. The generic model was derived from 10 participant’s data. An additional 11 participants were recruited for the current study. Seven of the participants were able to use the generic model during online training. Moreover, the generic model performed as well as models obtained from participant specific offline data with a mean training time of less than 2 min. However, four of the participants could not use this generic model, which shows that one generic mode is not generic for all subjects. More research on ERPs of subjects with different characteristics should be done, which would be helpful to build generic models for subject groups. This result shows a potential valuable direction for improving the BCI system. PMID:23032116
Building generic anatomical models using virtual model cutting and iterative registration
2010-01-01
Background Using 3D generic models to statistically analyze trends in biological structure changes is an important tool in morphometrics research. Therefore, 3D generic models built for a range of populations are in high demand. However, due to the complexity of biological structures and the limited views of them that medical images can offer, it is still an exceptionally difficult task to quickly and accurately create 3D generic models (a model is a 3D graphical representation of a biological structure) based on medical image stacks (a stack is an ordered collection of 2D images). We show that the creation of a generic model that captures spatial information exploitable in statistical analyses is facilitated by coupling our generalized segmentation method to existing automatic image registration algorithms. Methods The method of creating generic 3D models consists of the following processing steps: (i) scanning subjects to obtain image stacks; (ii) creating individual 3D models from the stacks; (iii) interactively extracting sub-volume by cutting each model to generate the sub-model of interest; (iv) creating image stacks that contain only the information pertaining to the sub-models; (v) iteratively registering the corresponding new 2D image stacks; (vi) averaging the newly created sub-models based on intensity to produce the generic model from all the individual sub-models. Results After several registration procedures are applied to the image stacks, we can create averaged image stacks with sharp boundaries. The averaged 3D model created from those image stacks is very close to the average representation of the population. The image registration time varies depending on the image size and the desired accuracy of the registration. Both volumetric data and surface model for the generic 3D model are created at the final step. Conclusions Our method is very flexible and easy to use such that anyone can use image stacks to create models and retrieve a sub
A generic hydroeconomic model to assess future water scarcity
NASA Astrophysics Data System (ADS)
Neverre, Noémie; Dumas, Patrice
2015-04-01
We developed a generic hydroeconomic model able to confront future water supply and demand on a large scale, taking into account man-made reservoirs. The assessment is done at the scale of river basins, using only globally available data; the methodology can thus be generalized. On the supply side, we evaluate the impacts of climate change on water resources. The available quantity of water at each site is computed using the following information: runoff is taken from the outputs of CNRM climate model (Dubois et al., 2010), reservoirs are located using Aquastat, and the sub-basin flow-accumulation area of each reservoir is determined based on a Digital Elevation Model (HYDRO1k). On the demand side, agricultural and domestic demands are projected in terms of both quantity and economic value. For the agricultural sector, globally available data on irrigated areas and crops are combined in order to determine irrigated crops localization. Then, crops irrigation requirements are computed for the different stages of the growing season using Allen (1998) method with Hargreaves potential evapotranspiration. Irrigation water economic value is based on a yield comparison approach between rainfed and irrigated crops. Potential irrigated and rainfed yields are taken from LPJmL (Blondeau et al., 2007), or from FAOSTAT by making simple assumptions on yield ratios. For the domestic sector, we project the combined effects of demographic growth, economic development and water cost evolution on future demands. The method consists in building three-blocks inverse demand functions where volume limits of the blocks evolve with the level of GDP per capita. The value of water along the demand curve is determined from price-elasticity, price and demand data from the literature, using the point-expansion method, and from water costs data. Then projected demands are confronted to future water availability. Operating rules of the reservoirs and water allocation between demands are based on
Mathematical modelling of cucumber (cucumis sativus) drying
NASA Astrophysics Data System (ADS)
Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.
2014-07-01
This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.
Mathematical Modeling and the Presidential Election.
ERIC Educational Resources Information Center
Witkowski, Joseph C.
1992-01-01
Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)
Mathematical Model Development and Simulation Support
NASA Technical Reports Server (NTRS)
Francis, Ronald C.; Tobbe, Patrick A.
2000-01-01
This report summarizes the work performed in support of the Contact Dynamics 6DOF Facility and the Flight Robotics Lab at NASA/ MSFC in the areas of Mathematical Model Development and Simulation Support.
Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms
ERIC Educational Resources Information Center
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
Generic model for smart-sensor-based data acquisition system
NASA Astrophysics Data System (ADS)
Ehrlich, Jacques; Zerrouki, Amal; Galisson, Arnaud; Demassieux, Nicolas
1996-05-01
Smart sensor is a recent concept presenting numerous advantages such as versatility, strong electromagnetic immunity, reduction of the connectivity, high computation power, etc. In civil engineering smart sensor based systems are well suited due to the large amount of spatially distant transducers and the need of large computational power. However, such systems require long development time, especially in their software part, and beside the multitude of instrumentation problems encountered, the need of a generic model is strong. The aim of the model is the design of a software generator for distributed data acquisition system. The key of our system is in the description of an instrumentation plane under the form of a data dependence graph (DDG). The goal of the generator is to map and 'execute' that DDG on the physical architecture according to the number of transducers, their affectation to the smart sensors and a PC based system controller. In this paper, after an outline of the smart sensor concept, we describe the DDG based representation of the instrumentation plan. An example of bridge monitoring is then described. Finally, the smart sensor, the system controller and the network modelization are outlined and their ability to allow the DDG mapping with the help of local or remote variable is shown.
Automatic mathematical modeling for space application
NASA Technical Reports Server (NTRS)
Wang, Caroline K.
1987-01-01
A methodology for automatic mathematical modeling is described. The major objective is to create a very friendly environment for engineers to design, maintain and verify their model and also automatically convert the mathematical model into FORTRAN code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine simulation mathematical model called Propulsion System Automatic Modeling (PSAM). PSAM provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. PSAM contains an initial set of component process elements for the Space Shuttle Main Engine simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. PSAM is then able to automatically generate the model and the FORTRAN code. A future goal is to download the FORTRAN code to the VAX/VMS system for conventional computation.
Unsteady pressure loads in a generic high speed engine model
NASA Technical Reports Server (NTRS)
Parrott, Tony L.; Jones, Michael G.; Thurlow, Ernie M.
1992-01-01
Unsteady pressure loads were measured along the top interior wall of a generic high-speed engine (GHSE) model undergoing performance tests in the combustion-Heated Scramjet Test Facility at the Langley Research Center. Flow to the model inlet was simulated at 72000 ft and a flight Mach number of 4. The inlet Mach number was 3.5 with a total temperature and pressure of 1640 R and 92 psia. The unsteady pressure loads were measured with 5 piezoresistive gages, recessed into the wall 4 to 12 gage diameters to reduce incident heat flux to the diaphragms, and distributed from the inlet to the combustor. Contributors to the unsteady pressure loads included boundary layer turbulence, combustion noise, and transients generated by unstart loads. Typical turbulent boundary layer rms pressures in the inlet ranged from 133 dB in the inlet to 181 dB in the combustor over the frequency range from 0 to 5 kHz. Downstream of the inlet exist, combustion noise was shown to dominate boundary layer turbulence noise at increased heat release rates. Noise levels in the isolator section increased by 15 dB when the fuel-air ratio was increased from 0.37 to 0.57 of the stoichiometric ratio. Transient pressure disturbances associated with engine unstarts were measured in the inlet and have an upstream propagation speed of about 7 ft/sec and pressure jumps of at least 3 psia.
ERIC Educational Resources Information Center
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
ERIC Educational Resources Information Center
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
Mathematical biodynamic feedthrough model applied to rotorcraft.
Venrooij, Joost; Mulder, Mark; Abbink, David A; van Paassen, Marinus M; Mulder, Max; van der Helm, Frans C T; Bulthoff, Heinrich H
2014-07-01
Biodynamic feedthrough (BDFT) occurs when vehicle accelerations feed through the human body and cause involuntary control inputs. This paper proposes a model to quantitatively predict this effect in rotorcraft. This mathematical BDFT model aims to fill the gap between the currently existing black box BDFT models and physical BDFT models. The model structure was systematically constructed using asymptote modeling, a procedure described in detail in this paper. The resulting model can easily be implemented in many typical rotorcraft BDFT studies, using the provided model parameters. The model's performance was validated in both the frequency and time domain. Furthermore, it was compared with several recent BDFT models. The results show that the proposed mathematical model performs better than typical black box models and is easier to parameterize and implement than a recent physical model. PMID:24013832
Dorn, Sebastian; Enßlin, Torsten A.; Ramirez, Erandy; Kunze, Kerstin E.
2014-06-01
We present a generic inference method for inflation models from observational data by the usage of higher-order statistics of the curvature perturbation on uniform density hypersurfaces. This method is based on the calculation of the posterior for the primordial non-Gaussianity parameters f{sub NL} and g{sub NL}, which in general depend on specific parameters of inflation and reheating models, and enables to discriminate among the still viable inflation models. To keep analyticity as far as possible to dispense with numerically expensive sampling techniques a saddle-point approximation is introduced, whose precision is validated for a numerical toy example. The mathematical formulation is done in a generic way so that the approach remains applicable to cosmic microwave background data as well as to large scale structure data. Additionally, we review a few currently interesting inflation models and present numerical toy examples thereof in two and three dimensions to demonstrate the efficiency of the higher-order statistics method. A second quantity of interest is the primordial power spectrum. Here, we present two Bayesian methods to infer it from observational data, the so called critical filter and an extension thereof with smoothness prior, both allowing for a non-parametric spectrum reconstruction. These methods are able to reconstruct the spectra of the observed perturbations and the primordial ones of curvature perturbation even in case of non-Gaussianity and partial sky coverage. We argue that observables like T- and B-modes permit to measure both spectra. This also allows to infer the level of non-Gaussianity generated since inflation.
NASA Technical Reports Server (NTRS)
Campbell, Stefan F.; Kaneshige, John T.
2010-01-01
Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).
Montefusco, Alberto; Consonni, Francesco; Beretta, Gian Paolo
2015-04-01
By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves. PMID:25974469
NASA Astrophysics Data System (ADS)
Montefusco, Alberto; Consonni, Francesco; Beretta, Gian Paolo
2015-04-01
By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves.
Mathematical Models of Tuberculosis Reactivation and Relapse
Wallis, Robert S.
2016-01-01
The natural history of human infection with Mycobacterium tuberculosis (Mtb) is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiologic mechanism of tuberculosis in patients treated with tumor necrosis factor blockers, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic. PMID:27242697
ERIC Educational Resources Information Center
Ciltas, Alper; Isik, Ahmet
2013-01-01
The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…
Comparison of thermal modeling and experimental results of a generic model for ground vehicle
NASA Astrophysics Data System (ADS)
Bushlin, Y.; Lessin, A.; Reinov, A.
2006-05-01
Accurate thermal modeling requires verification and validation of the model and software being used. For basic evaluation of thermal prediction models and software tools, a generic model - CUBI was build. The model was designed to have simple geometry yet, consisted of similar characteristics as of a ground vehicle. The model was equipped with thermocouples for measuring its temperature variations and was placed in a typical desert environment for field testing. The experimental setup also included a meteorological station. The data collected was used for the thermal behavior analysis of the generic model and for comparison with the thermal calculations predictions. Comparison of the results shows sufficient compliance but yet reviles some issues in the modeling that should be addressed.
Comprehensive Mathematical Model Of Real Fluids
NASA Technical Reports Server (NTRS)
Anderson, Peter G.
1996-01-01
Mathematical model of thermodynamic properties of water, steam, and liquid and gaseous hydrogen and oxygen developed for use in computational simulations of flows of mass and heat in main engine of space shuttle. Similar models developed for other fluids and applications. Based on HBMS equation of state.
Mathematical Modeling of Viral Zoonoses in Wildlife
Allen, L. J. S.; Brown, V. L.; Jonsson, C. B.; Klein, S. L.; Laverty, S. M.; Magwedere, K.; Owen, J. C.; van den Driessche, P.
2011-01-01
Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed. PMID:22639490
Mathematical Model For Scattering From Mirrors
NASA Technical Reports Server (NTRS)
Wang, Yaujen
1988-01-01
Additional terms account for effects of particulate contamination. Semiempirical mathematical model of scattering of light from surface of mirror gives improved account of effects of particulate contamination. Models that treated only scattering by microscopic irregularities in surface gave bidirectional reflectance distribution functions differing from measured scattering intensities over some ranges of angles.
Mathematical model for predicting human vertebral fracture
NASA Technical Reports Server (NTRS)
Benedict, J. V.
1973-01-01
Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.
Mathematical modeling relevant to closed artificial ecosystems
DeAngelis, D.L.
2003-01-01
The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.
Generic Engineering Competencies: A Review and Modelling Approach
ERIC Educational Resources Information Center
Male, Sally A.
2010-01-01
This paper puts forward the view that engineering educators have a responsibility to prepare graduates for engineering work and careers. The current literature reveals gaps between the competencies required for engineering work and those developed in engineering education. Generic competencies feature in these competency gaps. Literature suggests…
Mathematical modeling of molecular diffusion through mucus
Cu, Yen; Saltzman, W. Mark
2008-01-01
The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488
Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling
ERIC Educational Resources Information Center
Karali, Diren; Durmus, Soner
2015-01-01
The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…
Lepton-flavor violating B decays in generic Z' models
NASA Astrophysics Data System (ADS)
Crivellin, Andreas; Hofer, Lars; Matias, Joaquim; Nierste, Ulrich; Pokorski, Stefan; Rosiek, Janusz
2015-09-01
LHCb has reported deviations from the Standard Model in b →s μ+μ- transitions for which a new neutral gauge boson is a prime candidate for an explanation. As this gauge boson has to couple in a flavor nonuniversal way to muons and electrons in order to explain RK, it is interesting to examine the possibility that also lepton flavor is violated, especially in the light of the CMS excess in h →τ±μ∓. In this article, we investigate the perspectives to discover the lepton-flavor violating modes B →K(*)τ±μ∓ , Bs→τ±μ∓ and B →K(*)μ±e∓, Bs→μ±e∓. For this purpose we consider a simplified model in which new-physics effects originate from an additional neutral gauge boson (Z') with generic couplings to quarks and leptons. The constraints from τ →3 μ , τ →μ ν ν ¯, μ →e γ , gμ-2 , semileptonic b →s μ+μ- decays, B →K(*)ν ν ¯ and Bs-B¯s mixing are examined. From these decays, we determine upper bounds on the decay rates of lepton-flavor violating B decays. Br (B →K ν ν ¯) limits the branching ratios of lepton-flavor violating B decays to be smaller than 8 ×10-5(2 ×10-5) for vectorial (left-handed) lepton couplings. However, much stronger bounds can be obtained by a combined analysis of Bs-B¯s, τ →3 μ , τ →μ ν ν ¯ and other rare decays. The bounds depend on the amount of fine-tuning among the contributions to Bs-B¯s mixing. Allowing for a fine-tuning at the percent level we find upper bounds of the order of 10-6 for branching ratios into τ μ final states, while Bs→μ±e∓ is strongly suppressed and only B →K(*)μ±e∓ can be experimentally accessible (with a branching ratio of order 10-7).
The (Mathematical) Modeling Process in Biosciences
Torres, Nestor V.; Santos, Guido
2015-01-01
In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology. PMID:26734063
Two Mathematical Models of Nonlinear Vibrations
NASA Technical Reports Server (NTRS)
Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William
2007-01-01
Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.
Mathematical model of self-cycling fermentation
Wincure, B.M.; Cooper, D.G.; Rey, A.
1995-04-20
This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation.
Cooperative Monitoring Center Occasional Paper/7: A Generic Model for Cooperative Border Security
Netzer, Colonel Gideon
1999-03-01
This paper presents a generic model for dealing with security problems along borders between countries. It presents descriptions and characteristics of various borders and identifies the threats to border security, while emphasizing cooperative monitoring solutions.
Identification of the noise using mathematical modelling
NASA Astrophysics Data System (ADS)
Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav
2016-03-01
In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today's computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.
Establishing an Explanatory Model for Mathematics Identity
ERIC Educational Resources Information Center
Cribbs, Jennifer D.; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M.
2015-01-01
This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…
Mathematical Model Of Nerve/Muscle Interaction
NASA Technical Reports Server (NTRS)
Hannaford, Blake
1990-01-01
Phasic Excitation/Activation (PEA) mathematical model simulates short-term nonlinear dynamics of activation and control of muscle by nerve. Includes electronic and mechanical elements. Is homeomorphic at level of its three major building blocks, which represent motoneuron, dynamics of activation of muscle, and mechanics of muscle.
Mathematical and physical modelling of materials processing
NASA Technical Reports Server (NTRS)
1982-01-01
Mathematical and physical modeling of turbulence phenomena in metals processing, electromagnetically driven flows in materials processing, gas-solid reactions, rapid solidification processes, the electroslag casting process, the role of cathodic depolarizers in the corrosion of aluminum in sea water, and predicting viscoelastic flows are described.
Introduction to mathematical models and methods
Siddiqi, A. H.; Manchanda, P.
2012-07-17
Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.
A generic crystallization-like model that describes the kinetics of amyloid fibril formation.
Crespo, Rosa; Rocha, Fernando A; Damas, Ana M; Martins, Pedro M
2012-08-31
Associated with neurodegenerative disorders such as Alzheimer, Parkinson, or prion diseases, the conversion of soluble proteins into amyloid fibrils remains poorly understood. Extensive "in vitro" measurements of protein aggregation kinetics have been reported, but no consensus mechanism has emerged until now. This contribution aims at overcoming this gap by proposing a theoretically consistent crystallization-like model (CLM) that is able to describe the classic types of amyloid fibrillization kinetics identified in our literature survey. Amyloid conversion represented as a function of time is shown to follow different curve shapes, ranging from sigmoidal to hyperbolic, according to the relative importance of the nucleation and growth steps. Using the CLM, apparently unrelated data are deconvoluted into generic mechanistic information integrating the combined influence of seeding, nucleation, growth, and fibril breakage events. It is notable that this complex assembly of interdependent events is ultimately reduced to a mathematically simple model, whose two parameters can be determined by little more than visual inspection. The good fitting results obtained for all cases confirm the CLM as a good approximation to the generalized underlying principle governing amyloid fibrillization. A perspective is presented on possible applications of the CLM during the development of new targets for amyloid disease therapeutics. PMID:22767606
A Generic Crystallization-like Model That Describes the Kinetics of Amyloid Fibril Formation*♦
Crespo, Rosa; Rocha, Fernando A.; Damas, Ana M.; Martins, Pedro M.
2012-01-01
Associated with neurodegenerative disorders such as Alzheimer, Parkinson, or prion diseases, the conversion of soluble proteins into amyloid fibrils remains poorly understood. Extensive “in vitro” measurements of protein aggregation kinetics have been reported, but no consensus mechanism has emerged until now. This contribution aims at overcoming this gap by proposing a theoretically consistent crystallization-like model (CLM) that is able to describe the classic types of amyloid fibrillization kinetics identified in our literature survey. Amyloid conversion represented as a function of time is shown to follow different curve shapes, ranging from sigmoidal to hyperbolic, according to the relative importance of the nucleation and growth steps. Using the CLM, apparently unrelated data are deconvoluted into generic mechanistic information integrating the combined influence of seeding, nucleation, growth, and fibril breakage events. It is notable that this complex assembly of interdependent events is ultimately reduced to a mathematically simple model, whose two parameters can be determined by little more than visual inspection. The good fitting results obtained for all cases confirm the CLM as a good approximation to the generalized underlying principle governing amyloid fibrillization. A perspective is presented on possible applications of the CLM during the development of new targets for amyloid disease therapeutics. PMID:22767606
Mathematical Modeling of Loop Heat Pipes
NASA Technical Reports Server (NTRS)
Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.
1998-01-01
The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.
NASA Technical Reports Server (NTRS)
Hoffler, Keith D.; Fears, Scott P.; Carzoo, Susan W.
1997-01-01
A generic airplane model concept was developed to allow configurations with various agility, performance, handling qualities, and pilot vehicle interface to be generated rapidly for piloted simulation studies. The simple concept allows stick shaping and various stick command types or modes to drive an airplane with both linear and nonlinear components. Output from the stick shaping goes to linear models or a series of linear models that can represent an entire flight envelope. The generic model also has provisions for control power limitations, a nonlinear feature. Therefore, departures from controlled flight are possible. Note that only loss of control is modeled, the generic airplane does not accurately model post departure phenomenon. The model concept is presented herein, along with four example airplanes. Agility was varied across the four example airplanes without altering specific excess energy or significantly altering handling qualities. A new feedback scheme to provide angle-of-attack cueing to the pilot, while using a pitch rate command system, was implemented and tested.
Some mathematical tools for a modeller's workbench
NASA Technical Reports Server (NTRS)
Cohen, E.
1984-01-01
The development of a mathematical software tools in workbench environment to model related objects more straightforward is outlined. A computer model from informal drawings and a plastic model of a helicopter is discussed. Lofting was the predominant, characteristic modelling technique. Ships and airplane designs use lofting as a technique because they have defined surfaces, (hulls and fuselages) from vertical station cuts perpendicular to the vertical center plane defining the major axis of reflective symmetry. A turbine blade from a jet engine was modelled in this way. The aerodynamic portion and the root comes from different paradigms. The union of these two parts into a coherent model is shown.
Mathematical challenges in glacier modeling (Invited)
NASA Astrophysics Data System (ADS)
jouvet, G.
2013-12-01
Many of Earth's glaciers are currently shrinking and it is expected that this trend will continue as global warming progresses. To virtually reproduce the evolution of glaciers and finally to predict their future, one needs to couple models of different disciplines and scales. Indeed, the slow motion of ice is described by fluid mechanics equations while the daily snow precipitations and melting are described by hydrological and climatic models. Less visible, applied mathematics are essential to run such a coupling at two different levels: by solving numerically the underlying equations and by seeking parameters using optimisation methods. This talk aims to make visible the role of mathematics in this area. I will first present a short educational film I have made for the "Mathematics of Planet Earth 2013", which is an introduction to the topic. To go further, solving the mechanical model of ice poses several mathematical challenges due to the complexity of the equations and geometries of glaciers. Then, I will describe some strategies to deal with such difficulties and design robust simulation tools. Finally, I will present some simulations of the largest glacier of the European Alps, the Aletsch glacier. As a less unexpected application, I will show how these results allowed us to make a major advance in a police investigation started in 1926.
Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling
ERIC Educational Resources Information Center
Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan
2012-01-01
The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…
ERIC Educational Resources Information Center
Bukova-Guzel, Esra
2011-01-01
This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…
NASA Astrophysics Data System (ADS)
Smith, Erick; Haarer, Shawn; Confrey, Jere
Although reform efforts in mathematics education have called for more diverse views of mathematics, there have been few studies of how mathematics is used and takes form in practices outside of mathematics itself. Thus legitimate diverse models have largely been missing in education. This study attempts to broaden our understanding of mathematics by investigating how applied mathematicians and biologists, working together to construct dynamic population models, understand these models within the framework of their perspective practices, that is how these models take on a role as ''boundary objects'' between the two practices. By coming to understand how these models function within the practice of biology, the paper suggests that mathematics educators have the opportunity both to reevaluate their own assumptions about modeling and to build an understanding of the dialectic process necessary for these models to develop an epistemological basis that is shared across practices. Investigating this dialectic process is both important and missing in most mathematical classrooms.1
Voters' Fickleness:. a Mathematical Model
NASA Astrophysics Data System (ADS)
Boccara, Nino
This paper presents a spatial agent-based model in order to study the evolution of voters' choice during the campaign of a two-candidate election. Each agent, represented by a point inside a two-dimensional square, is under the influence of its neighboring agents, located at a Euclidean distance less than or equal to d, and under the equal influence of both candidates seeking to win its support. Moreover, each agent located at time t at a given point moves at the next timestep to a randomly selected neighboring location distributed normally around its position at time t. Besides their location in space, agents are characterized by their level of awareness, a real a ∈ [0, 1], and their opinion ω ∈ {-1, 0, +1}, where -1 and +1 represent the respective intentions to cast a ballot in favor of one of the two candidates while 0 indicates either disinterest or refusal to vote. The essential purpose of the paper is qualitative; its aim is to show that voters' fickleness is strongly correlated to the level of voters' awareness and the efficiency of candidates' propaganda.
Mathematical models of malaria - a review
2011-01-01
Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease PMID:21777413
The stability of colorectal cancer mathematical models
NASA Astrophysics Data System (ADS)
Khairudin, Nur Izzati; Abdullah, Farah Aini
2013-04-01
Colorectal cancer is one of the most common types of cancer. To better understand about the kinetics of cancer growth, mathematical models are used to provide insight into the progression of this natural process which enables physicians and oncologists to determine optimal radiation and chemotherapy schedules and develop a prognosis, both of which are indispensable for treating cancer. This thesis investigates the stability of colorectal cancer mathematical models. We found that continuous saturating feedback is the best available model of colorectal cancer growth. We also performed stability analysis. The result shows that cancer progress in sequence of genetic mutations or epigenetic which lead to a very large number of cells population until become unbounded. The cell population growth initiate and its saturating feedback is overcome when mutation changes causing the net per-capita growth rate of stem or transit cells exceed critical threshold.
Computing Linear Mathematical Models Of Aircraft
NASA Technical Reports Server (NTRS)
Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.
1991-01-01
Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.
Performance Assessment Modeling and Sensitivity Analyses of Generic Disposal System Concepts.
Sevougian, S. David; Freeze, Geoffrey A.; Gardner, William Payton; Hammond, Glenn Edward; Mariner, Paul
2014-09-01
directly, rather than through simplified abstractions. It also a llows for complex representations of the source term, e.g., the explicit representation of many individual waste packages (i.e., meter - scale detail of an entire waste emplacement drift). This report fulfills the Generic Disposal System Analysis Work Packa ge Level 3 Milestone - Performance Assessment Modeling and Sensitivity Analyses of Generic Disposal System Concepts (M 3 FT - 1 4 SN08080 3 2 ).
Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology.
ERIC Educational Resources Information Center
Lingefjard, Thomas
2002-01-01
Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…
An Experimental Approach to Mathematical Modeling in Biology
ERIC Educational Resources Information Center
Ledder, Glenn
2008-01-01
The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…
Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum.
ERIC Educational Resources Information Center
Swetz, Frank
1991-01-01
Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)
Mathematical modeling of vertebrate limb development.
Zhang, Yong-Tao; Alber, Mark S; Newman, Stuart A
2013-05-01
In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton. PMID:23219575
Editorial: Mathematical modelling of infectious diseases.
Fenton, Andy
2016-06-01
The field of disease ecology - the study of the spread and impact of parasites and pathogens within their host populations and communities - has a long history of using mathematical models. Dating back over 100 years, researchers have used mathematics to describe the spread of disease-causing agents, understand the relationship between host density and transmission and plan control strategies. The use of mathematical modelling in disease ecology exploded in the late 1970s and early 1980s through the work of Anderson and May (Anderson and May, 1978, 1981, 1992; May and Anderson, 1978), who developed the fundamental frameworks for studying microparasite (e.g. viruses, bacteria and protozoa) and macroparasite (e.g. helminth) dynamics, emphasizing the importance of understanding features such as the parasite's basic reproduction number (R 0) and critical community size that form the basis of disease ecology research to this day. Since the initial models of disease population dynamics, which primarily focused on human diseases, theoretical disease research has expanded hugely to encompass livestock and wildlife disease systems, and also to explore evolutionary questions such as the evolution of parasite virulence or drug resistance. More recently there have been efforts to broaden the field still further, to move beyond the standard 'one-host-one-parasite' paradigm of the original models, to incorporate many aspects of complexity of natural systems, including multiple potential host species and interactions among multiple parasite species. PMID:27027318
A mathematical model of collagen lattice contraction
Dallon, J. C.; Evans, E. J.; Ehrlich, H. Paul
2014-01-01
Two mathematical models for fibroblast–collagen interaction are proposed which reproduce qualitative features of fibroblast-populated collagen lattice contraction. Both models are force based and model the cells as individual entities with discrete attachment sites; however, the collagen lattice is modelled differently in each model. In the collagen lattice model, the lattice is more interconnected and formed by triangulating nodes to form the fibrous structure. In the collagen fibre model, the nodes are not triangulated, are less interconnected, and the collagen fibres are modelled as a string of nodes. Both models suggest that the overall increase in stress of the lattice as it contracts is not the cause of the reduced rate of contraction, but that the reduced rate of contraction is due to inactivation of the fibroblasts. PMID:25142520
Building Mathematical Models of Simple Harmonic and Damped Motion.
ERIC Educational Resources Information Center
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
Mathematical Models for HIV Transmission Dynamics
Cassels, Susan; Clark, Samuel J.; Morris, Martina
2012-01-01
Summary HIV researchers have long appreciated the need to understand the social and behavioral determinants of HIV-related risk behavior, but the cumulative impact of individual behaviors on population-level HIV outcomes can be subtle and counterintuitive, and the methods for studying this are rarely part of a traditional social science or epidemiology training program. Mathematical models provide a way to examine the potential effects of the proximate biologic and behavioral determinants of HIV transmission dynamics, alone and in combination. The purpose of this article is to show how mathematical modeling studies have contributed to our understanding of the dynamics and disparities in the global spread of HIV. Our aims are to demonstrate the value that these analytic tools have for social and behavioral sciences in HIV prevention research, to identify gaps in the current literature, and to suggest directions for future research. PMID:18301132
ERIC Educational Resources Information Center
Jurow, A. Susan
2004-01-01
Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The…
ERIC Educational Resources Information Center
Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard
2008-01-01
This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…
ERIC Educational Resources Information Center
Lim, L. L.; Tso, T. -Y.; Lin, F. L.
2009-01-01
This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a…
Mathematical modelling of leprosy and its control.
Blok, David J; de Vlas, Sake J; Fischer, Egil A J; Richardus, Jan Hendrik
2015-03-01
Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital. PMID:25765193
On mathematical modelling of flameless combustion
Mancini, Marco; Schwoeppe, Patrick; Weber, Roman; Orsino, Stefano
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)
Mathematical Model For Deposition Of Soot
NASA Technical Reports Server (NTRS)
Makel, Darby B.
1991-01-01
Semiempirical mathematical model predicts deposition of soot in tubular gas generator in which hydrocarbon fuel burned in very-fuel-rich mixture with pure oxygen. Developed in response to concern over deposition of soot in gas generators and turbomachinery of rocket engines. Also of interest in terrestrial applications involving fuel-rich combustion or analogous process; e.g., purposeful deposition of soot to manufacture carbon black pigments.
Basic Perforator Flap Hemodynamic Mathematical Model
Tao, Youlun; Ding, Maochao; Wang, Aiguo; Zhuang, Yuehong; Chang, Shi-Min; Mei, Jin; Hallock, Geoffrey G.
2016-01-01
Background: A mathematical model to help explain the hemodynamic characteristics of perforator flaps based on blood flow resistance systems within the flap will serve as a theoretical guide for the future study and clinical applications of these flaps. Methods: There are 3 major blood flow resistance network systems of a perforator flap. These were defined as the blood flow resistance of an anastomosis between artery and artery of adjacent perforasomes, between artery and vein within a perforasome, and then between vein and vein corresponding to the outflow of that perforasome. From this, a calculation could be made of the number of such blood flow resistance network systems that must be crossed for all perforasomes within a perforator flap to predict whether that arrangement would be viable. Results: The summation of blood flow resistance networks from each perforasome in a given perforator flap could predict which portions would likely survive. This mathematical model shows how this is directly dependent on the location of the vascular pedicle to the flap and whether supercharging or superdrainage maneuvers have been added. These configurations will give an estimate of the hemodynamic characteristics for the given flap design. Conclusions: This basic mathematical model can (1) conveniently determine the degree of difficulty for each perforasome within a perforator flap to survive; (2) semiquantitatively allow the calculation of basic hemodynamic parameters; and (3) allow the assessment of the pros and cons expected for each pattern of perforasomes encountered clinically based on predictable hemodynamic observations.
Mathematical Models and the Experimental Analysis of Behavior
ERIC Educational Resources Information Center
Mazur, James E.
2006-01-01
The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make…
Mathematical models of breast and ovarian cancers.
Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron
2016-07-01
Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review, we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, as answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. WIREs Syst Biol Med 2016, 8:337-362. doi: 10.1002/wsbm.1343 For further resources related to this article, please visit the WIREs website. PMID:27259061
ERIC Educational Resources Information Center
Jess, Gillian; Torr, Jennifer; Cooper, Sally-Ann; Lennox, Nicholas; Edwards, Nicole; Galea, Jennifer; O'Brien, Gregory
2008-01-01
Background: Models of service provision and professional training differ between countries. This study aims to investigate a specialist intellectual disabilities model and a generic mental health model, specifically comparing psychiatrists' knowledge and competencies, and service quality and accessibility in meeting the mental health needs of…
Mathematical modeling of deformation during hot rolling
Jin, D.; Stachowiak, R.G.; Samarasekera, I.V.; Brimacombe, J.K.
1994-12-31
The deformation that occurs in the roll bite during the hot rolling of steel, particularly the strain-rate and strain distribution, has been mathematically modeled using finite-element analysis. In this paper three different finite-element models are compared with one another and with industrial measurements. The first model is an Eulerian analysis based on the flow formulation method, while the second utilizes an Updated Lagrangian approach. The third model is based on a commercially available program DEFORM which also utilizes a Lagrangian reference frame. Model predictions of strain and strain-rate distribution, particularly near the surface of the slab, are strongly influenced by the treatment of friction at the boundary and the magnitude of the friction coefficient or shear factor. Roll forces predicted by the model have been compared with industrial rolling loads from a seven-stand hot-strip mill.
NASA Technical Reports Server (NTRS)
Stovall, John R.; Wray, Richard B.
1994-01-01
This paper presents a description of a model for a space vehicle operational scenario and the commands for avionics. This model will be used in developing a dynamic architecture simulation model using the Statemate CASE tool for validation of the Space Generic Open Avionics Architecture (SGOAA). The SGOAA has been proposed as an avionics architecture standard to NASA through its Strategic Avionics Technology Working Group (SATWG) and has been accepted by the Society of Automotive Engineers (SAE) for conversion into an SAE Avionics Standard. This architecture was developed for the Flight Data Systems Division (FDSD) of the NASA Johnson Space Center (JSC) by the Lockheed Engineering and Sciences Company (LESC), Houston, Texas. This SGOAA includes a generic system architecture for the entities in spacecraft avionics, a generic processing external and internal hardware architecture, and a nine class model of interfaces. The SGOAA is both scalable and recursive and can be applied to any hierarchical level of hardware/software processing systems.
Mathematical and computational models of plasma flows
NASA Astrophysics Data System (ADS)
Brushlinsky, K. V.
Investigations of plasma flows are of interest, firstly, due to numerous applications, and secondly, because of their general principles, which form a special branch of physics: the plasma dynamics. Numerical simulation and computation, together with theoretic and experimental methods, play an important part in these investigations. Speaking on flows, a relatively dense plasma is mentioned, so its mathematical models appertain to the fluid mechanics, i.e., they are based on the magnetohydrodynamic description of plasma. Time dependent two dimensional models of plasma flows of two wide-spread types are considered: the flows across the magnetic field and those in the magnetic field plane.
Aircraft engine mathematical model - linear system approach
NASA Astrophysics Data System (ADS)
Rotaru, Constantin; Roateşi, Simona; Cîrciu, Ionicǎ
2016-06-01
This paper examines a simplified mathematical model of the aircraft engine, based on the theory of linear and nonlinear systems. The dynamics of the engine was represented by a linear, time variant model, near a nominal operating point within a finite time interval. The linearized equations were expressed in a matrix form, suitable for the incorporation in the MAPLE program solver. The behavior of the engine was included in terms of variation of the rotational speed following a deflection of the throttle. The engine inlet parameters can cover a wide range of altitude and Mach numbers.
Mathematical Modeling of Ultraporous Nonmetallic Reticulated Materials
NASA Astrophysics Data System (ADS)
Alifanov, O. M.; Cherepanov, V. V.; Morzhukhina, A. V.
2015-01-01
We have developed an imitation statistical mathematical model reflecting the structure and the thermal, electrophysical, and optical properties of nonmetallic ultraporous reticulated materials. This model, in combination with a nonstationary thermal experiment and methods of the theory of inverse heat transfer problems, permits determining the little-studied characteristics of the above materials such as the radiative and conductive heat conductivities, the spectral scattering and absorption coefficients, the scattering indicatrix, and the dielectric constants, which are of great practical interest but are difficult to investigate.
A mathematical model of 'Pride and Prejudice'.
Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro
2014-04-01
A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations. PMID:24560011
A mathematical model of adult subventricular neurogenesis
Ashbourn, J. M. A.; Miller, J. J.; Reumers, V.; Baekelandt, V.; Geris, L.
2012-01-01
Neurogenesis has been the subject of active research in recent years and many authors have explored the phenomenology of the process, its regulation and its purported purpose. Recent developments in bioluminescent imaging (BLI) allow direct in vivo imaging of neurogenesis, and in order to interpret the experimental results, mathematical models are necessary. This study proposes such a mathematical model that describes adult mammalian neurogenesis occurring in the subventricular zone and the subsequent migration of cells through the rostral migratory stream to the olfactory bulb (OB). This model assumes that a single chemoattractant is responsible for cell migration, secreted both by the OB and in an endocrine fashion by the cells involved in neurogenesis. The solutions to the system of partial differential equations are compared with the physiological rodent process, as previously documented in the literature and quantified through the use of BLI, and a parameter space is described, the corresponding solution to which matches that of the rodent model. A sensitivity analysis shows that this parameter space is stable to perturbation and furthermore that the system as a whole is sloppy. A large number of parameter sets are stochastically generated, and it is found that parameter spaces corresponding to physiologically plausible solutions generally obey constraints similar to the conditions reported in vivo. This further corroborates the model and its underlying assumptions based on the current understanding of the investigated phenomenon. Concomitantly, this leaves room for further quantitative predictions pertinent to the design of future proposed experiments. PMID:22572029
Generic data modeling for home telemonitoring of chronically ill patients.
Cai, J.; Johnson, S.; Hripcsak, G.
2000-01-01
Management of many types of chronic diseases such as diabetes and asthma relies heavily on patients' self-monitoring of their disease conditions. In recent years, internet-based home telemonitoring systems that allow transmission of patient data to a central database and offer immediate access to the data by the care providers have become available. However, these systems often work with only one or a few types of medical devices and thus are limited in the types of diseases they can monitor. For example, a system designed to collect spirometry data from asthmatic patients cannot be easily adapted to collect blood glucose data from diabetic patients. This is because different medical devices produce different types of data and the existing telemonitoring systems are generally built around a proprietary data schema specific for the device used. In this paper, we describe a generic data schema for a telemonitoring system that is applicable to different types of medical devices and different diseases, and show an implementation of the schema in a relational database suitable for a variety of telemonitoring activities. PMID:11079856
Assessment of Primary 5 Students' Mathematical Modelling Competencies
ERIC Educational Resources Information Center
Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia
2012-01-01
Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
ERIC Educational Resources Information Center
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond
2010-01-01
This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…
Development of a Multidisciplinary Middle School Mathematics Infusion Model
ERIC Educational Resources Information Center
Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura
2011-01-01
The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…
Mathematical modelling of submarine landslide motion
NASA Astrophysics Data System (ADS)
Burminskij, A.
2012-04-01
Mathematical modelling of submarine landslide motion The paper presents a mathematical model to calculate dynamic parameters of a submarine landslide. The problem of estimation possible submarine landslides dynamic parameters and run-out distances as well as their effect on submarine structures becomes more and more actual because they can have significant impacts on infrastructure such as the rupture of submarine cables and pipelines, damage to offshore drilling platforms, cause a tsunami. In this paper a landslide is considered as a viscoplastic flow and is described by continuum mechanics equations, averaged over the flow depth. The model takes into account friction at the bottom and at the landslide-water boundary, as well as the involvement of bottom material in motion. A software was created and series of test calculations were performed. Calculations permitted to estimate the contribution of various model coefficients and initial conditions. Motion down inclined bottom was studied both for constant and variable slope angle. Examples of typical distributions of the flow velocity, thickness and density along the landslide body at different stages of motion are given.
Mathematical model to predict drivers' reaction speeds.
Long, Benjamin L; Gillespie, A Isabella; Tanaka, Martin L
2012-02-01
Mental distractions and physical impairments can increase the risk of accidents by affecting a driver's ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers' performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers' reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers' reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions. PMID:22431214
Mathematical Modeling of Extinction of Inhomogeneous Populations.
Karev, G P; Kareva, I
2016-04-01
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed of clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the "unobserved heterogeneity," i.e., the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of "internal population time" is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117
Mathematical Modeling of Extinction of Inhomogeneous Populations
Karev, G.P.; Kareva, I.
2016-01-01
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117
Martinez-Moyano, I. J.; Samsa, M. E.; Burke, J. F.; Akcam, B. K.; Decision and Information Sciences; Rockefeller Coll. at the State Univ. of New York at Albany
2008-01-01
This paper presents a generic model for information security implementation in organizations. The model presented here is part of an ongoing research stream related to critical infrastructure protection and insider threat and attack analysis. This paper discusses the information security implementation case.
ERIC Educational Resources Information Center
Tynjälä, Päivi; Virtanen, Anne; Klemola, Ulla; Kostiainen, Emma; Rasku-Puttonen, Helena
2016-01-01
The purpose of the study was to examine how social competence and other generic skills can be developed in teacher education using a pedagogical model called Integrative Pedagogy. This model is based on the idea of integrating the four basic components of expertise: Theoretical knowledge, practical knowledge, self-regulative knowledge, and…
Mathematical Models of Continuous Flow Electrophoresis
NASA Technical Reports Server (NTRS)
Saville, D. A.; Snyder, R. S.
1985-01-01
Development of high resolution continuous flow electrophoresis devices ultimately requires comprehensive understanding of the ways various phenomena and processes facilitate or hinder separation. A comprehensive model of the actual three dimensional flow, temperature and electric fields was developed to provide guidance in the design of electrophoresis chambers for specific tasks and means of interpreting test data on a given chamber. Part of the process of model development includes experimental and theoretical studies of hydrodynamic stability. This is necessary to understand the origin of mixing flows observed with wide gap gravitational effects. To insure that the model accurately reflects the flow field and particle motion requires extensive experimental work. Another part of the investigation is concerned with the behavior of concentrated sample suspensions with regard to sample stream stability particle-particle interactions which might affect separation in an electric field, especially at high field strengths. Mathematical models will be developed and tested to establish the roles of the various interactions.
Mathematical modeling of diesel fuel hydrotreating
NASA Astrophysics Data System (ADS)
Tataurshikov, A.; Ivanchina, E.; Krivtcova, N.; Krivtsov, E.; Syskina, A.
2015-11-01
Hydrotreating of the diesel fraction with the high initial sulfur content of 1,4 mass% is carried out in the flow-through laboratory setup with the industrial GKD-202 catalyst at various process temperature. On the basis of the experimental data the regularities of the hydrogenation reactions are revealed, and the formalized scheme of sulfur-containing components (sulfides, benzothiophenes, and dibenzothiophenes) transformations is made. The mathematical model of hydrotreating process is developed, the constant values for the reaction rate of hydrodesulfurization of the specified components are calculated.
Mathematical model of laser PUVA psoriasis treatment
NASA Astrophysics Data System (ADS)
Medvedev, Boris A.; Tuchin, Valery V.; Yaroslavsky, Ilya V.
1991-05-01
In order to optimize laser PUVA psoriasis treatment we develop the mathematical model of the dynamics of cell processes within epidermis. We consider epidermis as a structure consisting of N cell monolayers. There are four kinds of cells that correspond to four epidermal strata. The different kinds of cells can exist within a given monolayer. We assume that the following cell processes take place: division, death and transition from one stratum to the following. Discrete transition of cells from stratum j to j + 1 approximates to real differentiation.
Mathematical modeling of infectious disease dynamics
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
Generic Kalman Filter Software
NASA Technical Reports Server (NTRS)
Lisano, Michael E., II; Crues, Edwin Z.
2005-01-01
The Generic Kalman Filter (GKF) software provides a standard basis for the development of application-specific Kalman-filter programs. Historically, Kalman filters have been implemented by customized programs that must be written, coded, and debugged anew for each unique application, then tested and tuned with simulated or actual measurement data. Total development times for typical Kalman-filter application programs have ranged from months to weeks. The GKF software can simplify the development process and reduce the development time by eliminating the need to re-create the fundamental implementation of the Kalman filter for each new application. The GKF software is written in the ANSI C programming language. It contains a generic Kalman-filter-development directory that, in turn, contains a code for a generic Kalman filter function; more specifically, it contains a generically designed and generically coded implementation of linear, linearized, and extended Kalman filtering algorithms, including algorithms for state- and covariance-update and -propagation functions. The mathematical theory that underlies the algorithms is well known and has been reported extensively in the open technical literature. Also contained in the directory are a header file that defines generic Kalman-filter data structures and prototype functions and template versions of application-specific subfunction and calling navigation/estimation routine code and headers. Once the user has provided a calling routine and the required application-specific subfunctions, the application-specific Kalman-filter software can be compiled and executed immediately. During execution, the generic Kalman-filter function is called from a higher-level navigation or estimation routine that preprocesses measurement data and post-processes output data. The generic Kalman-filter function uses the aforementioned data structures and five implementation- specific subfunctions, which have been developed by the user on
A Mathematical Model of Idiopathic Pulmonary Fibrosis
Hao, Wenrui; Marsh, Clay; Friedman, Avner
2015-01-01
Idiopathic pulmonary fibrosis (IPF) is a disease of unknown etiology, and life expectancy of 3-5 years after diagnosis. The incidence rate in the United States is estimated as high as 15 per 100,000 persons per year. The disease is characterized by repeated injury to the alveolar epithelium, resulting in inflammation and deregulated repair, leading to scarring of the lung tissue, resulting in progressive dyspnea and hypoxemia. The disease has no cure, although new drugs are in clinical trials and two agents have been approved for use by the FDA. In the present paper we develop a mathematical model based on the interactions among cells and proteins that are involved in the progression of the disease. The model simulations are shown to be in agreement with available lung tissue data of human patients. The model can be used to explore the efficacy of potential drugs. PMID:26348490
A deformable generic 3D model of haptoral anchor of Monogenean.
Teo, Bee Guan; Dhillon, Sarinder Kaur; Lim, Lee Hong Susan
2013-01-01
In this paper, a digital 3D model which allows for visualisation in three dimensions and interactive manipulation is explored as a tool to help us understand the structural morphology and elucidate the functions of morphological structures of fragile microorganisms which defy live studies. We developed a deformable generic 3D model of haptoral anchor of dactylogyridean monogeneans that can subsequently be deformed into different desired anchor shapes by using direct manipulation deformation technique. We used point primitives to construct the rectangular building blocks to develop our deformable 3D model. Point primitives are manually marked on a 2D illustration of an anchor on a Cartesian graph paper and a set of Cartesian coordinates for each point primitive is manually extracted from the graph paper. A Python script is then written in Blender to construct 3D rectangular building blocks based on the Cartesian coordinates. The rectangular building blocks are stacked on top or by the side of each other following their respective Cartesian coordinates of point primitive. More point primitives are added at the sites in the 3D model where more structural variations are likely to occur, in order to generate complex anchor structures. We used Catmull-Clark subdivision surface modifier to smoothen the surface and edge of the generic 3D model to obtain a smoother and more natural 3D shape and antialiasing option to reduce the jagged edges of the 3D model. This deformable generic 3D model can be deformed into different desired 3D anchor shapes through direct manipulation deformation technique by aligning the vertices (pilot points) of the newly developed deformable generic 3D model onto the 2D illustrations of the desired shapes and moving the vertices until the desire 3D shapes are formed. In this generic 3D model all the vertices present are deployed for displacement during deformation. PMID:24204903
A Deformable Generic 3D Model of Haptoral Anchor of Monogenean
Teo, Bee Guan; Dhillon, Sarinder Kaur; Lim, Lee Hong Susan
2013-01-01
In this paper, a digital 3D model which allows for visualisation in three dimensions and interactive manipulation is explored as a tool to help us understand the structural morphology and elucidate the functions of morphological structures of fragile microorganisms which defy live studies. We developed a deformable generic 3D model of haptoral anchor of dactylogyridean monogeneans that can subsequently be deformed into different desired anchor shapes by using direct manipulation deformation technique. We used point primitives to construct the rectangular building blocks to develop our deformable 3D model. Point primitives are manually marked on a 2D illustration of an anchor on a Cartesian graph paper and a set of Cartesian coordinates for each point primitive is manually extracted from the graph paper. A Python script is then written in Blender to construct 3D rectangular building blocks based on the Cartesian coordinates. The rectangular building blocks are stacked on top or by the side of each other following their respective Cartesian coordinates of point primitive. More point primitives are added at the sites in the 3D model where more structural variations are likely to occur, in order to generate complex anchor structures. We used Catmull-Clark subdivision surface modifier to smoothen the surface and edge of the generic 3D model to obtain a smoother and more natural 3D shape and antialiasing option to reduce the jagged edges of the 3D model. This deformable generic 3D model can be deformed into different desired 3D anchor shapes through direct manipulation deformation technique by aligning the vertices (pilot points) of the newly developed deformable generic 3D model onto the 2D illustrations of the desired shapes and moving the vertices until the desire 3D shapes are formed. In this generic 3D model all the vertices present are deployed for displacement during deformation. PMID:24204903
Mathematical modelling of eukaryotic DNA replication.
Hyrien, Olivier; Goldar, Arach
2010-01-01
Eukaryotic DNA replication is a complex process. Replication starts at thousand origins that are activated at different times in S phase and terminates when converging replication forks meet. Potential origins are much more abundant than actually fire within a given S phase. The choice of replication origins and their time of activation is never exactly the same in any two cells. Individual origins show different efficiencies and different firing time probability distributions, conferring stochasticity to the DNA replication process. High-throughput microarray and sequencing techniques are providing increasingly huge datasets on the population-averaged spatiotemporal patterns of DNA replication in several organisms. On the other hand, single-molecule replication mapping techniques such as DNA combing provide unique information about cell-to-cell variability in DNA replication patterns. Mathematical modelling is required to fully comprehend the complexity of the chromosome replication process and to correctly interpret these data. Mathematical analysis and computer simulations have been recently used to model and interpret genome-wide replication data in the yeast Saccharomyces cerevisiae and Schizosaccharomyces pombe, in Xenopus egg extracts and in mammalian cells. These works reveal how stochasticity in origin usage confers robustness and reliability to the DNA replication process. PMID:20205354
Mathematical Modelling: Transitions between the Real World and the Mathematical Model
ERIC Educational Resources Information Center
Crouch, Rosalind; Haines, Christopher
2004-01-01
Applications in engineering, science and technology within undergraduate programmes can be difficult for students to understand. In this paper, new results are presented which go some way to demonstrate and explain the problems faced by students in linking mathematical models to real-world applications. The study is based on student responses to…
Experimentation with GRACE, the Generic Model of Emotions For Computational Applications
NASA Astrophysics Data System (ADS)
Dang, Thi-Hai-Ha; Duhaut, Dominique
2009-03-01
In this paper, we present a model of emotions that we proposed in EmotiRob project. First of all, we make a comparison of recent models of emotions and show that our model is generic in basing on the theories of emotions of Ortony et al., of Lazarus, of Scherer and then the personality theory of Meyers-Brigg and Meyers. Then, we present our experimentation with the first instance of the model and its result to validate our work.
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
ERIC Educational Resources Information Center
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Building Mathematics Achievement Models in Four Countries Using TIMSS 2003
ERIC Educational Resources Information Center
Wang, Ze; Osterlind, Steven J.; Bergin, David A.
2012-01-01
Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries…
Experimental and analytical generic space station dynamic models
NASA Technical Reports Server (NTRS)
Belvin, W. K.; Edighoffer, H. H.
1986-01-01
A dynamic model used for verification of analytical and experimental methods is documented. The model consists of five substructures to simulate the multibody, low frequency nature of large space structures. Design considerations which led to a fundamental vibration frequency of less than one Hz are described. Finite element analysis used to predict the vibration modes and frequencies of the experimental model is presented. In addition, modeling of cable suspension effects using prestressed vibration analysis is described. Details of the expermental and analytical models are included to permit replication of the study. Results of the modal vibration tests and analysis are presented in a separate document.
Mathematical modeling of a thermovoltaic cell
NASA Technical Reports Server (NTRS)
White, Ralph E.; Kawanami, Makoto
1992-01-01
A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.
Mathematical modeling of a rotary hearth calciner
Meisingset, H.C.; Balchen, J.G.; Fernandez, R.
1996-10-01
Calcination of petroleum coke is a thermal process where green petroleum coke is heat-treated to a pre-determined temperature. During heat treatment the associated moisture is removed and the volatile combustible matter (VCM) is released. The VCM is burned in the gas phase giving the energy to sustain the process. In addition, structural changes take place. The combination of the final calcination temperature and the residence time determine the final real density of the calcined coke. Depending on its further use, different real density requirements may arise. It is important to control the dynamics of the calcination process so that the specified final quality is achieved. A dynamic mathematical model of a Rotary Hearth Calciner is presented. The model is based on physicochemical laws involving the most important phenomena taking place and the relevant calcination parameters. The temperature profile in the coke bed is predicted which in terms is related to the real density of the coke.
Mathematics Teacher Education: A Model from Crimea.
ERIC Educational Resources Information Center
Ferrucci, Beverly J.; Evans, Richard C.
1993-01-01
Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)
Missing the Promise of Mathematical Modeling
ERIC Educational Resources Information Center
Meyer, Dan
2015-01-01
The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…
Mathematical modeling of acid-base physiology
Occhipinti, Rossana; Boron, Walter F.
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3− , NH4+) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cell–which to our knowledge is the first one capable of handling a multitude of buffer reaction–that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3− influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. PMID:25617697
NASA Astrophysics Data System (ADS)
Honkonen, I.
2015-03-01
I present a method for developing extensible and modular computational models without sacrificing serial or parallel performance or source code readability. By using a generic simulation cell method I show that it is possible to combine several distinct computational models to run in the same computational grid without requiring modification of existing code. This is an advantage for the development and testing of, e.g., geoscientific software as each submodel can be developed and tested independently and subsequently used without modification in a more complex coupled program. An implementation of the generic simulation cell method presented here, generic simulation cell class (gensimcell), also includes support for parallel programming by allowing model developers to select which simulation variables of, e.g., a domain-decomposed model to transfer between processes via a Message Passing Interface (MPI) library. This allows the communication strategy of a program to be formalized by explicitly stating which variables must be transferred between processes for the correct functionality of each submodel and the entire program. The generic simulation cell class requires a C++ compiler that supports a version of the language standardized in 2011 (C++11). The code is available at https://github.com/nasailja/gensimcell for everyone to use, study, modify and redistribute; those who do are kindly requested to acknowledge and cite this work.
Exact solution of the XXX Gaudin model with generic open boundaries
NASA Astrophysics Data System (ADS)
Hao, Kun; Cao, Junpeng; Yang, Tao; Yang, Wen-Li
2015-03-01
The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U(1) -symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.
Fang, Yilin; Huang, Maoyi; Liu, Chongxuan; Li, Hongyi; Leung, Lai-Yung R.
2013-11-13
Physical and biogeochemical processes regulate soil carbon dynamics and CO2 flux to and from atmosphere, influencing global climate changes. Integration of these processes into earth system models (e.g., community land models (CLM)), however, currently faces three major challenges: 1) extensive efforts are required to modify modeling structures and to rewrite computer programs to incorporate new or updated processes as new knowledge is being generated, 2) computational cost is prohibitively expensive to simulate biogeochemical processes in land models due to large variations in the rates of biogeochemical processes, and 3) various mathematical representations of biogeochemical processes exist to incorporate different aspects of fundamental mechanisms, but systematic evaluation of the different mathematical representations is difficult, if not possible. To address these challenges, we propose a new computational framework to easily incorporate physical and biogeochemical processes into land models. The new framework consists of a new biogeochemical module with a generic algorithm and reaction database so that new and updated processes can be incorporated into land models without the need to manually set up the ordinary differential equations to be solved numerically. The reaction database consists of processes of nutrient flow through the terrestrial ecosystems in plants, litter and soil. This framework facilitates effective comparison studies of biogeochemical cycles in an ecosystem using different conceptual models under the same land modeling framework. The approach was first implemented in CLM and benchmarked against simulations from the original CLM-CN code. A case study was then provided to demonstrate the advantages of using the new approach to incorporate a phosphorus cycle into the CLM model. To our knowledge, the phosphorus-incorporated CLM is a new model that can be used to simulate phosphorus limitation on the productivity of terrestrial ecosystems.
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.
2014-01-01
Background Current terminology systems for structured reporting in pathology are more or less focused on tumor pathology. They have not been compiled in a systematic approach, therefore they gather terms of very different granularity. Generic models for terminology development could help in establishing reference terminologies for all fields of anatomic pathology. The core principle of those models is the ontological structure of native speaking terminology. By analyzing the PathLex interface a generic terminology model will be derived. Methods For each element template of PathLex its possible generic nature and its value set was analyzed, looking for the uniqueness or multiplicity of the values in the value sets. The generic terms were mapped to SNOMED-CT terms using "ArtDecor". Results The 488 PathLex element templates for Anatomic Pathology (AP) observations can be reduced to 53 generic templates, leaving out only 17 templates very specific for organ and/or disease. Among those 53 templates 28 are describing UICC-TNM staging, ICD-O-classification, and grading. Further 15 templates describe the results from marker investigations. Almost all of the terms, used in those templates could be mapped to SNOMED CT. All of the generic elements have their "organ specific" counterparts by assigning them to one of 20 organs and invasive or noninvasive cancer, respectively. Studying the structure of generic and specific terms it becomes obvious that any AP observation - occurs always in a context - consists of three basic elements (target of observation, property of observation, additional qualifiers, added by value sets for coded data). Conclusions If a machine-readable terminology is aimed to preserve all the information of native speaking, then two principal solutions exist: - ystematic consideration of all the aspects mentioned above in each single term - ocusing on the generic elements of terms and combining this with the structure of communication, reflecting the non
Teaching Mathematical Modelling for Earth Sciences via Case Studies
NASA Astrophysics Data System (ADS)
Yang, Xin-She
2010-05-01
Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).
Peng, Henry T; Edginton, Andrea N; Cheung, Bob
2013-10-01
Physiologically based pharmacokinetic models were developed using MATLAB Simulink® and PK-Sim®. We compared the capability and usefulness of these two models by simulating pharmacokinetic changes of midazolam under exercise and heat stress to verify the usefulness of MATLAB Simulink® as a generic PBPK modeling software. Although both models show good agreement with experimental data obtained under resting condition, their predictions of pharmacokinetics changes are less accurate in the stressful conditions. However, MATLAB Simulink® may be more flexible to include physiologically based processes such as oral absorption and simulate various stress parameters such as stress intensity, duration and timing of drug administration to improve model performance. Further work will be conducted to modify algorithms in our generic model developed using MATLAB Simulink® and to investigate pharmacokinetics under other physiological stress such as trauma. PMID:23852614
NASA Astrophysics Data System (ADS)
Kelka, Ulrich; Veveakis, Manolis; Beaudoin, Nicolas; Poulet, Thomas; Koehn, Daniel; Regenauer-Lieb, Klaus; Chung, Peter; Berndt, Jasper
2016-04-01
Rhythmically banded dolomites (zebra dolomite) are found worldwide, and are frequently associated with mineralization of the Mississippi Valley-Type (MVT). These rocks consist of dark fine grained and impurity-rich layers alternating with light coarse grained and virtually impurity-free layers. The texture of the light layers is similar to the one of tectonic syntaxial veins where crystals grow towards a median line. We present petrographic and chemical analysis of zebra dolomite samples from the San Vicente mine, Central Peru. The applied methods are petrographic microscopy, SEM, EBSD, EMP and LA-ICP-MS. The findings influence the development of a generic model of pattern formation. We found the density and the distribution of second-phase material to be one striking feature. The impurities are accumulated in the dark layers, which show an even higher density of second-phase material than the surrounding impurity-rich dolomite. With CL, it was possible to detect a luminescent structure in the center of the light bands which seems to be present independent of the thickness and spacing of the respective layers. This structure was analysed in more detail with EMP. We further found that the dolomite crystals in the dark and light layers are chemically similar but show a variation in some trace elements. Based on the analytical findings, we put forward a mathematical model of zebra dolomite formation based on Cnoidal waves. We believe that the light coarse grained layers represent hydromechanical instabilities arising during the diagenetic compaction of a fluid saturated, impurity-rich dolomite. Our approach is based on the extension of the classical compaction bands theory to a viscose, non-linear rheology. In the model, the spacing between two light coarse grained layers is linked to the compaction length during the pattern formation. With the formulation of a 1D steady-state solution we can relate the genesis of the structure to physical parameter, such as
Mathematical model of tumor-immune surveillance.
Mahasa, Khaphetsi Joseph; Ouifki, Rachid; Eladdadi, Amina; Pillis, Lisette de
2016-09-01
We present a novel mathematical model involving various immune cell populations and tumor cell populations. The model describes how tumor cells evolve and survive the brief encounter with the immune system mediated by natural killer (NK) cells and the activated CD8(+) cytotoxic T lymphocytes (CTLs). The model is composed of ordinary differential equations describing the interactions between these important immune lymphocytes and various tumor cell populations. Based on up-to-date knowledge of immune evasion and rational considerations, the model is designed to illustrate how tumors evade both arms of host immunity (i.e. innate and adaptive immunity). The model predicts that (a) an influx of an external source of NK cells might play a crucial role in enhancing NK-cell immune surveillance; (b) the host immune system alone is not fully effective against progression of tumor cells; (c) the development of immunoresistance by tumor cells is inevitable in tumor immune surveillance. Our model also supports the importance of infiltrating NK cells in tumor immune surveillance, which can be enhanced by NK cell-based immunotherapeutic approaches. PMID:27317864
Mathematical Model of Evolution of Brain Parcellation.
Ferrante, Daniel D; Wei, Yi; Koulakov, Alexei A
2016-01-01
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals. PMID:27378859
Mathematical Model of Evolution of Brain Parcellation
Ferrante, Daniel D.; Wei, Yi; Koulakov, Alexei A.
2016-01-01
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals. PMID:27378859
Mathematical modeling of electrocardiograms: a numerical study.
Boulakia, Muriel; Cazeau, Serge; Fernández, Miguel A; Gerbeau, Jean-Frédéric; Zemzemi, Nejib
2010-03-01
This paper deals with the numerical simulation of electrocardiograms (ECG). Our aim is to devise a mathematical model, based on partial differential equations, which is able to provide realistic 12-lead ECGs. The main ingredients of this model are classical: the bidomain equations coupled to a phenomenological ionic model in the heart, and a generalized Laplace equation in the torso. The obtention of realistic ECGs relies on other important features--including heart-torso transmission conditions, anisotropy, cell heterogeneity and His bundle modeling--that are discussed in detail. The numerical implementation is based on state-of-the-art numerical methods: domain decomposition techniques and second order semi-implicit time marching schemes, offering a good compromise between accuracy, stability and efficiency. The numerical ECGs obtained with this approach show correct amplitudes, shapes and polarities, in all the 12 standard leads. The relevance of every modeling choice is carefully discussed and the numerical ECG sensitivity to the model parameters investigated. PMID:20033779
How to incorporate generic refraction models into multistatic tracking algorithms
NASA Astrophysics Data System (ADS)
Crouse, D. F.
The vast majority of literature published on target tracking ignores the effects of atmospheric refraction. When refraction is considered, the solutions are generally tailored to a simple exponential atmospheric refraction model. This paper discusses how arbitrary refraction models can be incorporated into tracking algorithms. Attention is paid to multistatic tracking problems, where uncorrected refractive effects can worsen track accuracy and consistency in centralized tracking algorithms, and can lead to difficulties in track-to-track association in distributed tracking filters. Monostatic and bistatic track initialization using refraction-corrupted measurements is discussed. The results are demonstrated using an exponential refractive model, though an arbitrary refraction profile can be substituted.
A Generic Microdisturbanace Transmissibility Model For Reaction Wheels
NASA Astrophysics Data System (ADS)
Penate Castro, Jose; Seiler, Rene
2012-07-01
The increasing demand for space missions with high- precision pointing requirements for their payload instruments is underlining the importance of studying the impact of micro-level disturbances on the overall performance of spacecraft. For example, a satellite with an optical telescope taking high-resolution images might be very sensitive to perturbations, generated by moving equipment and amplified by the structure of the equipment itself as well as that of the host spacecraft that is accommodating both, the sources of mechanical disturbances and sensitive payload instruments. One of the major sources of mechanical disturbances inside a satellite may be found with reaction wheels. For investigation of their disturbance generation and propagation characteristics, a finite element model with parametric geometry definition has been developed. The model covers the main structural features of typical reaction wheel assemblies and can be used for a transmissibility representation of the equipment. With the parametric geometry definition approach, a wide range of different reaction wheel types and sizes can be analysed, without the need for (re-)defining an individual reaction wheel configuration from scratch. The reaction wheel model can be combined with a finite element model of the spacecraft structure and the payload for an end-to-end modelling and simulation of the microdisturbance generation and propagation. The finite element model has been generated in Patran® Command Language (PCL), which provides a powerful and time-efficient way to change parameters in the model, for creating a new or modifying an existing geometry, without requiring comprehensive manual interactions in the modelling pre-processor. As part of the overall modelling approach, a tailored structural model of the mechanical ball bearings has been implemented, which is one of the more complex problems to deal with, among others, due to the anisotropic stiffness and damping characteristics
Mathematical modelling of the anaerobic hybrid reactor.
Soroa, S; Gomez, J; Ayesa, E; Garcia-Heras, J L
2006-01-01
This paper presents a new mathematical model for the anaerobic hybrid reactor (AHR) (a UASB reactor and an anaerobic filter in series) and its experimental calibration and verification. The model includes a biochemical part and a mass transport one, which considers the AHR as two contact reactors in series. The anaerobic process transformations are described by the model developed by Siegrist et al. The fraction (F) of solids in the clarification zone of the UASB reactor that leaves this first reactor is the key physical parameter to be estimated. The main parameters of the model were calibrated using experimental results from a bench-scale AHR fed with real slaughterhouse wastewater. The fraction of inert particulate COD in the influent and the factor F were estimated by a trial and error procedure comparing experimental and simulated results of the mass of solids in the lower tank and the VSS concentration in the AHR effluent. A good fit was obtained. The final verification was carried out by comparing a set of experiments with simulated data. The model's capability to predict the process performance was thus proved. PMID:16939085
Mathematical model for contemplative amoeboid locomotion
NASA Astrophysics Data System (ADS)
Ueda, Kei-Ichi; Takagi, Seiji; Nishiura, Yasumasa; Nakagaki, Toshiyuki
2011-02-01
It has recently been reported that even single-celled organisms appear to be “indecisive” or “contemplative” when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously. Here, we develop a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). The biological justification of the model is tested by comparing with experimentally measured spatiotemporal profiles of the cell thickness. The experimentally observed types of behavior are reproduced in simulations based on our model, and the core logic of the modeled behavior is clarified by means of nonlinear dynamics. An on-off transition between the refractory and activated states of the chemical reactivity that takes place at the leading edge of the plasmodium plays a key role in the emergence of contemplative behavior.
Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors
ERIC Educational Resources Information Center
Rash, Agnes M.; Zurbach, E. Peter
2004-01-01
The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…
ERIC Educational Resources Information Center
Akgün, Levent
2015-01-01
The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…
Development of a Generic Tubular Tree Structure for the Modeling of Orbital Cranial Nerves.
Kaltofen, Thomas; Ivcevic, Sara; Kogler, Mathias; Priglinger, Siegfried
2016-01-01
We developed a generic approach for modeling tubular tree structures as triangle meshes for the extension of our biomechanical eye model SEE-KID with a visualization of the orbital cranial nerves. Since three of the orbital nerves innervate extraocular eye muscles and move together with them, the structure must also support the partial translation and rotation of the nerves. For the SEE-KID model, this extension allows a better parameterization as well as an easier simulation of innervational disorders. Moreover, it makes the model even more useful for education and training purposes in contrast to other anatomical models. Due to its generic nature, the developed data structure and the associated algorithms can be used for any tubular tree structures, even in non-medical application areas. PMID:27046571
Mathematical analysis of epidemiological models with heterogeneity
Van Ark, J.W.
1992-01-01
For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.
Mathematical Modeling of the Origins of Life
NASA Technical Reports Server (NTRS)
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Towards a generic rainfall-runoff model for green roofs.
Kasmin, H; Stovin, V R; Hathway, E A
2010-01-01
A simple conceptual model for green roof hydrological processes is shown to reproduce monitored data, both during a storm event, and over a longer continuous simulation period. The model comprises a substrate moisture storage component and a transient storage component. Storage within the substrate represents the roof's overall stormwater retention capacity (or initial losses). Following a storm event the retention capacity is restored by evapotranspiration (ET). However, standard methods for quantifying ET do not exist. Monthly ET values are identified using four different approaches: analysis of storm event antecedent dry weather period and initial losses data; calibration of the ET parameter in a continuous simulation model; use of the Thornthwaite ET formula; and direct laboratory measurement of evaporation. There appears to be potential to adapt the Thornthwaite ET formula to provide monthly ET estimates from local temperature data. The development of a standardized laboratory test for ET will enable differences resulting from substrate characteristics to be quantified. PMID:20729594
Non-generic couplings in supersymmetric standard models
NASA Astrophysics Data System (ADS)
Buchbinder, Evgeny I.; Constantin, Andrei; Lukas, Andre
2015-09-01
We study two phases of a heterotic standard model, obtained from a Calabi-Yau compactification of the E8 ×E8 heterotic string, in the context of the associated four-dimensional effective theories. In the first phase we have a standard model gauge group, an MSSM spectrum, four additional U (1) symmetries and singlet fields. In the second phase, obtained from the first by continuing along the singlet directions, three of the additional U (1) symmetries are spontaneously broken and the remaining one is a B-L symmetry. In this second phase, dimension five operators inducing proton decay are consistent with all symmetries and as such, they are expected to be present. We show that, contrary to this expectation, these operators are forbidden due to the additional U (1) symmetries present in the first phase of the model. We emphasise that such "unexpected" absences of operators, due to symmetry enhancement at specific loci in the moduli space, can be phenomenologically relevant and, in the present case, protect the model from fast proton decay.
Mathematical modeling of endovenous laser treatment (ELT)
Mordon, Serge R; Wassmer, Benjamin; Zemmouri, Jaouad
2006-01-01
Background and objectives Endovenous laser treatment (ELT) has been recently proposed as an alternative in the treatment of reflux of the Great Saphenous Vein (GSV) and Small Saphenous Vein (SSV). Successful ELT depends on the selection of optimal parameters required to achieve an optimal vein damage while avoiding side effects. Mathematical modeling of ELT could provide a better understanding of the ELT process and could determine the optimal dosage as a function of vein diameter. Study design/materials and methods The model is based on calculations describing the light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma Inc., Arlington, MA, USA). Damage to the vein wall for CW and single shot energy was calculated for 3 and 5 mm vein diameters. In pulsed mode, the pullback distance (3, 5 and 7 mm) was considered. For CW mode simulation, the pullback speed (1, 2, 3 mm/s) was the variable. The total dose was expressed as joules per centimeter in order to perform comparison to results already reported in clinical studies. Results In pulsed mode, for a 3 mm vein diameter, irrespective of the pullback distance (2, 5 or 7 mm), a minimum fluence of 15 J/cm is required to obtain a permanent damage of the intima. For a 5 mm vein diameter, 50 J/cm (15W-2s) is required. In continuous mode, for a 3 mm and 5 mm vein diameter, respectively 65 J/cm and 100 J/cm are required to obtain a permanent damage of the vessel wall. Finally, the use of different wavelengths (810 nm or 980 nm) played only a minor influence on these results. Discussion and conclusion The parameters determined by
Gonzalez, Javier M; Rodriguez, Carlos A; Zuluaga, Andres F; Agudelo, Maria; Vesga, Omar
2015-01-01
Some generics of antibacterials fail therapeutic equivalence despite being pharmaceutical equivalents of their innovators, but data are scarce with antifungals. We used the neutropenic mice model of disseminated candidiasis to challenge the therapeutic equivalence of three generic products of fluconazole compared with the innovator in terms of concentration of the active pharmaceutical ingredient, analytical chemistry (liquid chromatography/mass spectrometry), in vitro susceptibility testing, single-dose serum pharmacokinetics in infected mice, and in vivo pharmacodynamics. Neutropenic, five week-old, murine pathogen free male mice of the strain Udea:ICR(CD-2) were injected in the tail vein with Candida albicans GRP-0144 (MIC = 0.25 mg/L) or Candida albicans CIB-19177 (MIC = 4 mg/L). Subcutaneous therapy with fluconazole (generics or innovator) and sterile saline (untreated controls) started 2 h after infection and ended 24 h later, with doses ranging from no effect to maximal effect (1 to 128 mg/kg per day) divided every 3 or 6 hours. The Hill's model was fitted to the data by nonlinear regression, and results from each group compared by curve fitting analysis. All products were identical in terms of concentration, chromatographic and spectrographic profiles, MICs, mouse pharmacokinetics, and in vivo pharmacodynamic parameters. In conclusion, the generic products studied were pharmaceutically and therapeutically equivalent to the innovator of fluconazole. PMID:26536105
Performance degradation of a model helicopter rotor with a generic ice shape
NASA Technical Reports Server (NTRS)
Korkan, K. D.; Cross, E. J., Jr.; Miller, T. L.
1984-01-01
An experimental program using a commercially available remotely controlled model helicopter in the Texas A&M University (TAMU) subsonic wind tunnel has been conducted to investigate the performance degradation resulting from the simulated formation of ice on the leading edge of the main rotor blades in both hover and forward flight. The rotor blades utilized a NACA 0012 airfoil with a 2.5-in. constant chord. A generic ice shape derived from a predetermined natural ice condition was applied to the 53.375-in.-diameter main rotor, and thrust and torque coefficients were measured for the main rotor as functions of velocity, main rotor rpm, fuselage angle of incidence, collective pitch angle, and spanwise extent of icing. The model helicopter test exhibited significant performance degradation of the main rotor when generic ice was added. An increase of approximately 150 percent in torque coefficient to maintain a constant thrust coefficient was noted when generic ice had been applied to the 85 percent rotor radial location. Also, considerable additional degradation occurred when generic ice was applied to the 100 percent rotor radial location, as compared with the 85 percent simulated ice performance values, indicating the sensitivity of the rotor tip region.
Gonzalez, Javier M.; Rodriguez, Carlos A.; Zuluaga, Andres F.; Agudelo, Maria; Vesga, Omar
2015-01-01
Some generics of antibacterials fail therapeutic equivalence despite being pharmaceutical equivalents of their innovators, but data are scarce with antifungals. We used the neutropenic mice model of disseminated candidiasis to challenge the therapeutic equivalence of three generic products of fluconazole compared with the innovator in terms of concentration of the active pharmaceutical ingredient, analytical chemistry (liquid chromatography/mass spectrometry), in vitro susceptibility testing, single-dose serum pharmacokinetics in infected mice, and in vivo pharmacodynamics. Neutropenic, five week-old, murine pathogen free male mice of the strain Udea:ICR(CD-2) were injected in the tail vein with Candida albicans GRP-0144 (MIC = 0.25 mg/L) or Candida albicans CIB-19177 (MIC = 4 mg/L). Subcutaneous therapy with fluconazole (generics or innovator) and sterile saline (untreated controls) started 2 h after infection and ended 24 h later, with doses ranging from no effect to maximal effect (1 to 128 mg/kg per day) divided every 3 or 6 hours. The Hill’s model was fitted to the data by nonlinear regression, and results from each group compared by curve fitting analysis. All products were identical in terms of concentration, chromatographic and spectrographic profiles, MICs, mouse pharmacokinetics, and in vivo pharmacodynamic parameters. In conclusion, the generic products studied were pharmaceutically and therapeutically equivalent to the innovator of fluconazole. PMID:26536105
Mathematical modeling of human secondary osteons.
Ascenzi, Maria-Grazia; Andreuzzi, Marta; Kabo, J Michael
2004-01-01
This investigation explores the structural dimensions and patterns within single secondary osteons, with consideration of their biological variation. New data from images obtained previously of osteons observed through linearly polarized light, electron microscopy, and micro-x-ray, combined with recent findings on lamellae by circularly polarized light, confocal microscopy, synchrotron x-ray diffraction, and micro-x-ray, provide the basis for novel computerized models of single osteons and single lamellae. The novelty of such models is the concurrent representation of (1) collagen-hydroxyapatite orientation, (2) relative hydroxyapatite percentage, (3) distributions of osteocytes' lacunae and canaliculae, and (4) biological variations in dimensions of the relevant structures. The mathematical software Maple realizes the computerized models. While the parts of the models are constructed on a personal computer, the voluminous data associated with the representation of lacunar and canalicular distributions require a supercomputer for assembly of the models and final analysis. The programming used to define the models affords the option to randomize the dimensional specifications of osteons, lamellae, lacunae, and canaliculae within the experimentally observed numeric ranges and distributions. Through this option, the program can operate so that each run of the file produces a unique random model within the observed biological variations. The program can also be run to implement specific dimensional requirements. The modeling has applications in the microstructural study of fracture propagation and remodeling, as well as in the simulation of mechanical testing. The approach taken here is of wide application and could be of value in other areas of microscopy such as scanning electron microscopy, microcomputerized tomography scan, and magnetic resonance imaging on cancellous bone structures. PMID:15000289
Mathematical modeling plasma transport in tokamaks
Quiang, Ji
1995-12-31
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10{sup 20}/m{sup 3} with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%.
Mathematical modelling of animate and intentional motion.
Rittscher, Jens; Blake, Andrew; Hoogs, Anthony; Stein, Gees
2003-01-01
Our aim is to enable a machine to observe and interpret the behaviour of others. Mathematical models are employed to describe certain biological motions. The main challenge is to design models that are both tractable and meaningful. In the first part we will describe how computer vision techniques, in particular visual tracking, can be applied to recognize a small vocabulary of human actions in a constrained scenario. Mainly the problems of viewpoint and scale invariance need to be overcome to formalize a general framework. Hence the second part of the article is devoted to the question whether a particular human action should be captured in a single complex model or whether it is more promising to make extensive use of semantic knowledge and a collection of low-level models that encode certain motion primitives. Scene context plays a crucial role if we intend to give a higher-level interpretation rather than a low-level physical description of the observed motion. A semantic knowledge base is used to establish the scene context. This approach consists of three main components: visual analysis, the mapping from vision to language and the search of the semantic database. A small number of robust visual detectors is used to generate a higher-level description of the scene. The approach together with a number of results is presented in the third part of this article. PMID:12689374
Mathematical Model for the Mineralization of Bone
NASA Technical Reports Server (NTRS)
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
Mathematical Model for the Mineralization of Bone
NASA Technical Reports Server (NTRS)
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. The model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse. PMID:20030966
Chaos in Temperature in Generic 2p-Spin Models
NASA Astrophysics Data System (ADS)
Panchenko, Dmitry
2016-02-01
We prove chaos in temperature for even p-spin models which include sufficiently many p-spin interaction terms. Our approach is based on a new invariance property for coupled asymptotic Gibbs measures, similar in spirit to the invariance property that appeared in the proof of ultrametricity in Panchenko (Ann Math (2) 177(1):383-393, 2013), used in combination with Talagrand's analogue of Guerra's replica symmetry breaking bound for coupled systems.
Review and verification of CARE 3 mathematical model and code
NASA Technical Reports Server (NTRS)
Rose, D. M.; Altschul, R. E.; Manke, J. W.; Nelson, D. L.
1983-01-01
The CARE-III mathematical model and code verification performed by Boeing Computer Services were documented. The mathematical model was verified for permanent and intermittent faults. The transient fault model was not addressed. The code verification was performed on CARE-III, Version 3. A CARE III Version 4, which corrects deficiencies identified in Version 3, is being developed.
Generic Coarse-Grained Model for Protein Folding and Aggregation
NASA Astrophysics Data System (ADS)
Bereau, Tristan; Deserno, Markus
2009-03-01
The complexity involved in protein structure is not only due to the rich variety of amino acids, but also the inherent weak interactions, comparable to thermal energy, and important cooperative phenomena. This presents a challenge in atomistic simulations, as it is associated with high-dimensionality and ruggedness of the energy landscape as well as long equilibration times. We have recently developed a coarse-grained (CG) implicit solvent peptide model which has been designed to reproduce key consequences of the abovementioned weak interactions. Its intermediate level of resolution, four beads per amino acid, allows for accurate sampling of local conformations by designing a force field that relies on simple interactions. A realistic ratio of α-helix to β-sheet content is achieved by mimicking a nearest-neighbor dipole interaction. We tune the model in order to fold helical proteins while systematically comparing the structure with NMR data. Very good agreement is achieved for proteins that have simple tertiary structures. We further probe the effects of cooperativity between amino acids by looking at peptide aggregation, where hydrophobic peptide fragments cooperatively form large-scale β-sheet structures. The model is able to reproduce features from atomistic simulations on a qualitative basis.
Development of a Generic Creep-Fatigue Life Prediction Model
NASA Technical Reports Server (NTRS)
Goswami, Tarun
2002-01-01
The objective of this research proposal is to further compile creep-fatigue data of steel alloys and superalloys used in military aircraft engines and/or rocket engines and to develop a statistical multivariate equation. The newly derived model will be a probabilistic fit to all the data compiled from various sources. Attempts will be made to procure the creep-fatigue data from NASA Glenn Research Center and other sources to further develop life prediction models for specific alloy groups. In a previous effort [1-3], a bank of creep-fatigue data has been compiled and tabulated under a range of known test parameters. These test parameters are called independent variables, namely; total strain range, strain rate, hold time, and temperature. The present research attempts to use these variables to develop a multivariate equation, which will be a probabilistic equation fitting a large database. The data predicted by the new model will be analyzed using the normal distribution fits, the closer the predicted lives are with the experimental lives (normal line 1 to 1 fit) the better the prediction. This will be evaluated in terms of a coefficient of correlation, R 2 as well. A multivariate equation developed earlier [3] has the following form, where S, R, T, and H have specific meaning discussed later.
Turbulent motion of mass flows. Mathematical modeling
NASA Astrophysics Data System (ADS)
Eglit, Margarita; Yakubenko, Alexander; Yakubenko, Tatiana
2016-04-01
New mathematical models for unsteady turbulent mass flows, e.g., dense snow avalanches and landslides, are presented. Such models are important since most of large scale flows are turbulent. In addition to turbulence, the two other important points are taken into account: the entrainment of the underlying material by the flow and the nonlinear rheology of moving material. The majority of existing models are based on the depth-averaged equations and the turbulent character of the flow is accounted by inclusion of drag proportional to the velocity squared. In this paper full (not depth-averaged) equations are used. It is assumed that basal entrainment takes place if the bed friction equals the shear strength of the underlying layer (Issler D, M. Pastor Peréz. 2011). The turbulent characteristics of the flow are calculated using a three-parameter differential model (Lushchik et al., 1978). The rheological properties of moving material are modeled by one of the three types of equations: 1) Newtonian fluid with high viscosity, 2) power-law fluid and 3) Bingham fluid. Unsteady turbulent flows down long homogeneous slope are considered. The flow dynamical parameters and entrainment rate behavior in time as well as their dependence on properties of moving and underlying materials are studied numerically. REFERENCES M.E. Eglit and A.E. Yakubenko, 2014. Numerical modeling of slope flows entraining bottom material. Cold Reg. Sci. Technol., 108, 139-148 Margarita E. Eglit and Alexander E. Yakubenko, 2016. The effect of bed material entrainment and non-Newtonian rheology on dynamics of turbulent slope flows. Fluid Dynamics, 51(3) Issler D, M. Pastor Peréz. 2011. Interplay of entrainment and rheology in snow avalanches; a numerical study. Annals of Glaciology, 52(58), 143-147 Lushchik, V.G., Paveliev, A.A. , and Yakubenko, A.E., 1978. Three-parameter model of shear turbulence. Fluid Dynamics, 13, (3), 350-362