de Gracia, M; Grau, P; Huete, E; Gómez, J; García-Heras, J L; Ayesa, E
2009-10-01
This paper presents a new mathematical model developed to reproduce the performance of a generic sludge digester working either under aerobic or anaerobic operational conditions. The digester has been modelled as two completely mixed tanks associated with gaseous and liquid volumes. The conversion model has been developed based on a plant wide modelling methodology (PWM) and comprises biochemical transformations, physicochemical reactions and thermodynamic considerations. The model predicts the reactor temperature and the temporary evolution of an extensive vector of model components which are completely defined in terms of elemental mass fractions (C, H, O, N and P) and charge density. Thus, the comprehensive definition of the model components guarantees the continuity of elemental mass and charge in all the model transformations and between any two systems defined by the model. The aim of the generic digester model is to overcome the problems that arise when trying to connect aerobic and anaerobic digestion processes working in series or to connect water and sludge lines in a WWTP. The modelling methodology used has allowed the systematic construction of the biochemical model which acts as an initial illustrative example of an application that has been experimentally verified. The variation of the temperature is also predicted based on a thermal dynamic model. Real data from four different facilities and a straightforward calibration have been used to successfully verify the model predictions in the cases of mesophilic and thermophilic anaerobic digestion as well as autothermal thermophilic aerobic digestion (ATAD). The large amount of data from the full scale ATAD and the anaerobic digestion pilot plants, all of them working under different conditions, has allowed the validation of the model for that case study. PMID:19720390
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.
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 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.
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…
Generic data modeling for clinical repositories.
Johnson, S B
1996-01-01
OBJECTIVE: To construct a large-scale clinical repository that accurately captures a detailed understanding of the data vital to the process of health care and that provides highly efficient access to patient information for the users of a clinical information system. DESIGN: Conventional approaches to data modeling encourage the development of a highly specific data schema in order to capture as much information as possible about a given domain. In contrast, current database technology functions most effectively for clinical databases when a generic data schema is used. The technique of "generic data modeling" is presented as a method of reconciling these opposing views of clinical data, using formal operations to transform a detailed schema into a generic one. RESULTS: A complex schema consisting of hundreds of entities and representing a rich set of constraints about the patient care domain is transformed into a generic schema consisting of roughly two dozen tables. The resulting database design is efficient for patient-oriented queries and is highly flexible in adapting to the changing information needs of a health care institution, particularly changes involving the collection of new data elements. CONCLUSION: Conventional approaches to data modeling can be used to develop rich, complex models of clinical data that are useful for understanding and managing the process of patient care. Generic data modeling techniques can successfully transform a detailed design into an efficient generic design that is flexible enough to meet the needs of an operational clinical information system. PMID:8880680
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.
A generic biokinetic model for Carbon-14.
Manger, R 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. PMID:21075764
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.
A Proposal for Improving Students' Mathematical Attitude Based on Mathematical Modelling
ERIC Educational Resources Information Center
Falsetti, Marcela C.; Rodriguez, Mabel A.
2005-01-01
On the occasion of having to design an introductory course of mathematics for the University (UNGS, Buenos Aires, Argentina) we took into account the perspective of mathematical modelling. In this article we present the theoretical framework that we elaborated on to design our course. This framework allowed us to adapt the generic perspectives of…
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…
Mathematical model of sarcoidosis
Hao, Wenrui; Crouser, Elliott D.; Friedman, Avner
2014-01-01
Sarcoidosis is a disease involving abnormal collection of inflammatory cells forming nodules, called granulomas. Such granulomas occur in the lung and the mediastinal lymph nodes, in the heart, and in other vital and nonvital organs. The origin of the disease is unknown, and there are only limited clinical data on lung tissue of patients. No current model of sarcoidosis exists. In this paper we develop a mathematical model on the dynamics of the disease in the lung and use patients’ lung tissue data to validate the model. The model is used to explore potential treatments. PMID:25349384
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…
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…
Mathematical Modelling in European Education
ERIC Educational Resources Information Center
Ferri, Rita Borromeo
2013-01-01
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…
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…
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.
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.
Supporting Synchronous Collaborative Learning: A Generic, Multi-Dimensional Model
ERIC Educational Resources Information Center
Lonchamp, Jacques
2006-01-01
Future CSCL technologies are described by the community as flexible, tailorable, negotiable, and appropriate for various collaborative settings, conditions and contexts. This paper describes the key design issues of a generic synchronous collaborative learning environment, called Omega+. In this approach, model-based genericity is applied to the…
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.
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…
Mathematical Models for Elastic Structures
NASA Astrophysics Data System (ADS)
Villaggio, Piero
1997-10-01
During the seventeenth century, several useful theories of elastic structures emerged, with applications to civil and mechanical engineering problems. Recent and improved mathematical tools have extended applications into new areas such as mathematical physics, geomechanics, and biomechanics. This book offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures that are used to solve practical problems with particular emphasis on nonlinear problems.
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
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 Waiting Time.
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)
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.
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…
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…
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…
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 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…
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.
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…
Mathematical Modeling in the Undergraduate Curriculum
ERIC Educational Resources Information Center
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
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
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
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 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.
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…
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…
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.
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.
The Nature of Mathematical Modeling
NASA Astrophysics Data System (ADS)
Gershenfeld, Neil
2011-06-01
Preface; 1. Introduction; Part I. Analytical Models: 2. Ordinary differential and difference equations; 3. Partial differential equations; 4. Variational principles; 5. Random systems; Part II. Numerical Models: 6. Finite differences: ordinary difference equations; 7. Finite differences: partial differential equations; 8. Finite elements; 9. Cellular automata and lattice gases; Part III. Observational Models: 10. Function fitting; 11. Transforms; 12. Architectures; 13. Optimization and search; 14. Clustering and density estimation; 15. Filtering and state estimation; 16. Linear and nonlinear time series; Appendix 1. Graphical and mathematical software; Appendix 2. Network programming; Appendix 3. Benchmarking; Appendix 4. Problem solutions; Bibliography.
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…
Reconstruction of a generic metabolic network model of cancer cells.
Hadi, Mahdieh; Marashi, Sayed-Amir
2014-11-01
A promising strategy for finding new cancer drugs is to use metabolic network models to investigate the essential reactions or genes in cancer cells. In this study, we present a generic constraint-based model of cancer metabolism, which is able to successfully predict the metabolic phenotypes of cancer cells. This model is reconstructed by collecting the available data on tumor suppressor genes. Notably, we show that the activation of oncogene related reactions can be explained by the inactivation of tumor suppressor genes. We show that in a simulated growth medium similar to the body fluids, our model outperforms the previously proposed model of cancer metabolism in predicting expressed genes.
Mathematical modeling of kidney transport.
Layton, Anita T
2013-01-01
In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.
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 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 Model for Mapping Students' Cognitive Capability
ERIC Educational Resources Information Center
Tambunan, Hardi
2016-01-01
The quality mapping of educational unit program is important issue in education in Indonesia today in an effort to improve the quality of education. The objective of this study is to make a mathematical model to find out the map of students' capability in mathematics. It has been made a mathematical model to be used in the mapping of students'…
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).
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 Modeling in the Secondary School Curriculum.
ERIC Educational Resources Information Center
Swetz, Frank, Ed.; Hartzler, J. S., Ed.
Over the past 10 years, national conferences and committees investigating the state of American mathematics education have advocated an increased emphasis on problem solving and mathematical modeling situations in the secondary school curriculum. However, little effort has been made to prepare secondary school teachers to use mathematical modeling…
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 Modeling of Electronic Devices and Circuits
NASA Astrophysics Data System (ADS)
Singh, B. P.; Singh, Meena; Roy, Sanjay Kumar
2010-11-01
The necessity of modeling lies in the nature of technology and its advancement. The modeling minimizes time and cost of the process involved. The mathematical model provides an insight into the behavior of the physical system that reduces the problem to its essential characteristics. The floating admittance matrix (FAM) approach is an elegant method of mathematical modeling of electronic devices and circuits.
Bioequivalence of generic drugs.
Andrade, Chittaranjan
2015-09-01
Generic drugs are bioequivalent to the original brand; this is a prerequisite for marketing approval. It is theoretically possible that one generic drug may overestimate the pharmacokinetic (PK) parameters of the original and another generic may underestimate these PK parameters; in consequence, these 2 generics may not be bioequivalent between themselves. The result could be loss of efficacy or development of drug-related adverse effects if these generics are interchanged in stable patients. In a recent study involving 292 indirect comparisons of generic formulations of 9 different drugs, mathematical modeling showed that in most cases (87.0% for maximum concentration, 90.1% for area under the curve, and 80.5% for both) generic drugs are bioequivalent to each other. These reassuring findings notwithstanding, prudence dictates that, in stable patients, generic drugs should be interchanged only if there is a good reason for it. This is because bioequivalent brands of drugs may differ in their excipient content, and this can result in variations in safety profiles. PMID:26455677
Bioequivalence of generic drugs.
Andrade, Chittaranjan
2015-09-01
Generic drugs are bioequivalent to the original brand; this is a prerequisite for marketing approval. It is theoretically possible that one generic drug may overestimate the pharmacokinetic (PK) parameters of the original and another generic may underestimate these PK parameters; in consequence, these 2 generics may not be bioequivalent between themselves. The result could be loss of efficacy or development of drug-related adverse effects if these generics are interchanged in stable patients. In a recent study involving 292 indirect comparisons of generic formulations of 9 different drugs, mathematical modeling showed that in most cases (87.0% for maximum concentration, 90.1% for area under the curve, and 80.5% for both) generic drugs are bioequivalent to each other. These reassuring findings notwithstanding, prudence dictates that, in stable patients, generic drugs should be interchanged only if there is a good reason for it. This is because bioequivalent brands of drugs may differ in their excipient content, and this can result in variations in safety profiles.
A Model for Teaching College Remedial Mathematics.
ERIC Educational Resources Information Center
Friedman, Mordechai
1986-01-01
A model for teaching college remedial mathematics is presented, with information on the background, the development of the model, and the model itself, as well as a discussion of how the model is used. (MNS)
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 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
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.
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.
The Activity System of School-Teaching Mathematics and Mathematical Modelling.
ERIC Educational Resources Information Center
Julie, Cyril
2002-01-01
Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…
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
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.
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…
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…
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…
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.
Mathematical modeling of radio systems and devices
NASA Astrophysics Data System (ADS)
Borisov, Iu. P.; Tsvetnov, V. V.
Methods for developing mathematical models of radio systems and devices are presented with emphasis on the functional approach to the modeling of radio systems. In particular, attention is given to the formal description of radio systems, computer-aided modeling of radio systems, a classification of methods of radio system modeling, and methods of mathematical description of signals and noise. Specific methods discussed include the carrier method, the complex envelope method, the method of statistical equivalents, and the information parameter method.
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.
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 Programming Models in Educational Planning.
ERIC Educational Resources Information Center
McNamara, James F.
This document begins by defining and discussing educational planning. A brief overview of mathematical programing with an explanation of the general linear programing model is then provided. Some recent applications of mathematical programing techniques to educational planning problems are reviewed, and their implications for educational research…
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,…
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 Receiver Tracking Model for GPS Ionospheric Amplitude Scintillation
NASA Astrophysics Data System (ADS)
Paula, E. R.; Moraes, A. D.; Perrella, W. J.; Galera Monico, J. F.
2012-12-01
Ionospheric scintillations result in rapid variations in phase and amplitude of the radio signal, which propagates through the ionosphere. Depending on the temporal and spatial situation, the scintillation can represent a problem in the availability and precision of the Global Navigation Satellite Systems (GNSS). Scintillations affect the receiver performance, specially the tracking loop level. Depending on the scintillation level, the receiver might increase the measurement errors or even can lead to a loss of lock of the carrier and code loops. In extreme cases, the scintillation can result in full disrupting of the receiver. In this work we introduce a generic model to evaluate the effects of ionospheric amplitude scintillation on GPS receiver tracking loops. This model is based on α-μ distribution, which can be seen as a generalized fading model, that includes a variety of distributions such as Gamma, Nakagami-m, Exponential, Weibull, one-sided Gaussian and Rayleigh. Differently from the model based only on Nakagami-m, this one is not limited to S4< 0,71 which allows using it to predict amplitude scintillation effects for stronger scenarios. The estimation of α-μ coefficients, the empirical parameterization based on field measurements and the typical values estimated based on observations made during the last solar maximum are presented and discussed.
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 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…
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 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.
Cooking Potatoes: Experimentation and Mathematical Modeling.
ERIC Educational Resources Information Center
Chen, Xiao Dong
2002-01-01
Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)
Mathematical models of behavior of individual animals.
Tsibulsky, Vladimir L; Norman, Andrew B
2007-01-01
This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.
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.
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.
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.
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.
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.
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).
Tutorial: Mathematical Modeling of Library Systems.
ERIC Educational Resources Information Center
Rouse, William B.
1979-01-01
Discusses the purpose of mathematical models and reviews the phases of the modeling process--defining performance, representing the problem, predicting performance, estimating parameters, defining optimization criterion, determining solution, and implementing results. Reviews of book-use, resource allocation, and library network models are…
Mathematical Modelling with 9-Year-Olds
ERIC Educational Resources Information Center
English, Lyn D.; Watters, James J.
2005-01-01
This paper reports on the mathematical modelling of four classes of 4th-grade children as they worked on a modelling problem involving the selection of an Australian swimming team for the 2004 Olympics. The problem was implemented during the second year of the children's participation in a 3-year longitudinal program of modelling experiences…
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…
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 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
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).
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…
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.
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.
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.
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.
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.
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.
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.
Application of a generic biosphere model for dose assessments to five European sites.
Chen, Q; Kowe, R; Mobbs, S F; Pröhl, G; Olyslaegers, G; Zeevaert, T; Kanyar, B; Pinedo, P; Simón, I; Bergström, U; Hallberg, B; Jones, J A; Oatway, W B; Watson, S J
2006-06-01
The BIOMOSA (BIOsphere MOdels for Safety Assessment of radioactive waste disposal) project was part of the EC fifth framework research programme. The main goal of this project was to improve the scientific basis for the application of biosphere models in the framework of long-term safety studies of radioactive waste disposal facilities and to enhance the confidence in using biosphere models for performance assessments. The study focused on the development and application of a generic biosphere tool BIOGEM (BIOsphere GEneric Model) using the IAEA BIOMASS reference biosphere methodology, and the comparison between BIOGEM and five site-specific biosphere models. The site-specific models and the generic model were applied to five typical locations in Europe, resulting in estimates of the annual effective individual doses to the critical groups and the ranking of the importance of the exposure pathways for each of the sites. Uncertainty in the results was also estimated by means of stochastic calculations based on variation of the site-specific parameter values. This paper describes the generic model and the deterministic and stochastic results obtained when it was applied to the five sites. Details of the site-specific models and the corresponding results are described in two companion papers. This paper also presents a comparison of the results between the generic model and site-specific models. In general, there was an acceptable agreement of the BIOGEM for both the deterministic and stochastic results with the results from the site-specific models.
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…
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.
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
Mathematical model for citric acid fermentation.
Hu, J; Wu, P
1993-01-01
The kinetics for biomass proliferation, medium consumption and citric acid production in the course of citric acid fermentation were studied, and the mathematical models describing the course of citric acid fermentation were obtained in this paper. Based on the statistical data of experiment, the model was verified, and the model parameters were estimated with the results of the experiment. The results showed that the curves obtained by model calculation fitted with the ones determined by the experiments well, and the models described correctly the course of the citric acid fermentation. This is important for computer application to control the course of fermentation and realize the optimum of fermentation process.
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
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 Modelling of Turbidity Currents
NASA Astrophysics Data System (ADS)
Fay, G. L.; Fowler, A.; Howell, P.
2011-12-01
A turbidity current is a submarine sediment flow which propagates downslope through the ocean into the deep sea. Turbidity currents can occur randomly and without much warning and consequently are hard to observe and measure. The driving force in a turbidity current is the presence of sediment in the current - gravity acts on the sediment in suspension, causing it to move downstream through the ocean water. A phenomenon known as ignition or autosuspension has been observed in turbidity currents in submarine canyons, and it occurs when a current travelling downslope gathers speed as it erodes sediment from the sea floor in a self-reinforcing cycle. Using the turbidity current model of Parker et al. (Journal of Fluid Mechanics, 1986) we investigate the evolution of a 1-D turbidity current as it moves downstream. To seek a better understanding of the dynamics of flow as the current evolves in space and time, we present analytical results alongside computed numerical solutions, incorporating entrainment of water and erosion and deposition of sediment. We consider varying slope functions and inlet conditions and attempt to predict when the current will become extinct. We examine currents which are in both supercritical and subcritical flow regimes and consider the dynamics of the flow as the current switches regime.
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.
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.
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 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.…
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.
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
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)
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…
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
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…
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
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. PMID:27579238
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
Optimisation of a generic ionic model of cardiac myocyte electrical activity.
Guo, Tianruo; Al Abed, Amr; Lovell, Nigel H; Dokos, Socrates
2013-01-01
A generic cardiomyocyte ionic model, whose complexity lies between a simple phenomenological formulation and a biophysically detailed ionic membrane current description, is presented. The model provides a user-defined number of ionic currents, employing two-gate Hodgkin-Huxley type kinetics. Its generic nature allows accurate reconstruction of action potential waveforms recorded experimentally from a range of cardiac myocytes. Using a multiobjective optimisation approach, the generic ionic model was optimised to accurately reproduce multiple action potential waveforms recorded from central and peripheral sinoatrial nodes and right atrial and left atrial myocytes from rabbit cardiac tissue preparations, under different electrical stimulus protocols and pharmacological conditions. When fitted simultaneously to multiple datasets, the time course of several physiologically realistic ionic currents could be reconstructed. Model behaviours tend to be well identified when extra experimental information is incorporated into the optimisation.
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 analysis of a muscle architecture model.
Navallas, Javier; Malanda, Armando; Gila, Luis; Rodríguez, Javier; Rodríguez, Ignacio
2009-01-01
Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area; and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition, a considerable 'edge effect' is present in the outer zone of the muscle cross-section, making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size.
A Review of Mathematical Models for Leukemia and Lymphoma
Clapp, Geoffrey; Levy, Doron
2014-01-01
Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598
Mathematical models of human african trypanosomiasis epidemiology.
Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul
2015-03-01
Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.
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.
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 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.
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.
Mathematical model on a desalination process
Al-Samawi, A.A. )
1994-05-01
Mathematical models on the desalination of brackish water using EDR process are formulated. The product desalinated water variable is hypothesized as being dependent upon the following independent variables: total dissolved solids of the feed water, total dissolved solids of the product water, the rate of feed water, the temperature of feed water, the number of stages of membranes, and the energy consumption. The final model which is selected on statistical basis is considered appropriated for both prediction purposes and for the purpose of quantifying the separate effects of each significant variable upon the rate of production of desalted water variable. Results of the analysis are reported herein. 6 refs., 4 figs., 5 tabs.
ERIC Educational Resources Information Center
Smith, Erick; Haarer, Shawn; Confrey, Jere
1997-01-01
Provides details of a study that attempts to broaden the understanding of mathematics by investigating how applied mathematicians and biologists collaborate in developing dynamic population models. (DDR)
Generic camera model and its calibration for computational integral imaging and 3D reconstruction.
Li, Weiming; Li, Youfu
2011-03-01
Integral imaging (II) is an important 3D imaging technology. To reconstruct 3D information of the viewed objects, modeling and calibrating the optical pickup process of II are necessary. This work focuses on the modeling and calibration of an II system consisting of a lenslet array, an imaging lens, and a charge-coupled device camera. Most existing work on such systems assumes a pinhole array model (PAM). In this work, we explore a generic camera model that accommodates more generality. This model is an empirical model based on measurements, and we constructed a setup for its calibration. Experimental results show a significant difference between the generic camera model and the PAM. Images of planar patterns and 3D objects were computationally reconstructed with the generic camera model. Compared with the images reconstructed using the PAM, the images present higher fidelity and preserve more high spatial frequency components. To the best of our knowledge, this is the first attempt in applying a generic camera model to an II system.
Declarative representation of uncertainty in mathematical models.
Miller, Andrew K; Britten, Randall D; Nielsen, Poul M F
2012-01-01
An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
Declarative Representation of Uncertainty in Mathematical Models
Miller, Andrew K.; Britten, Randall D.; Nielsen, Poul M. F.
2012-01-01
An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form. PMID:22802941
A Generic Length-scale Equation For Second-order Turbulence Models of Oceanic Boundary Layers
NASA Astrophysics Data System (ADS)
Umlauf, L.; Burchard, H.
A generic transport equation for a generalized length-scale in second-order turbulence closure models for geophysical boundary layers is suggested. This variable consists of the products of powers of the turbulent kinetic energy, k, and the integral length-scale, l. The new approach generalizes traditional second-order models used in geophysical boundary layer modelling, e.g. the Mellor-Yamada model and the k- model, which, however, can be recovered as special cases. It is demonstrated how this new model can be calibrated with measurements in some typical geophysical boundary layer flows. As an example, the generic model is applied to the uppermost oceanic boundary layer directly influenced by the effects of breaking surface waves. Recent measurements show that in this layer the classical law of the wall is invalid, since there turbulence is dominated by turbulent transport of TKE from above, and not by shear-production. A widely accepted approach to describe the wave-affected layer with a one-equation turbulence model was suggested by Craig and Banner (1994). Here, some deficien- cies of their solutions are pointed out and a generalization of their ideas for the case of two-equation models is suggested. Direct comparison with very recently obtained measurements of the dissipation rate, , in the wave-affected boundary layer with com- puted results clearly demonstrate that only the generic two-equation model yields cor- rect predictions for the profiles of and the turbulent length scale, l. Also, the pre- dicted velocity profiles in the wave-affected layer, important e.g. for the interpretation of surface drifter experiments, are reproduced correctly only by the generic model. Implementation and computational costs of the generic model are comparable with traditonal two-equation models.
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…
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…
A Generic Model for Guiding the Integration of ICT into Teaching and Learning
ERIC Educational Resources Information Center
Wang, Qiyun
2008-01-01
Effective integration of Information and Communication Technology (ICT) into teaching and learning is becoming an essential competency for teachers. However, teachers do not usually follow linear instructional design models when they are planning for ICT integration. This paper proposes a generic model, which consists of three fundamental…
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.
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 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.
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
Mathematical modeling of the coating process.
Toschkoff, Gregor; Khinast, Johannes G
2013-12-01
Coating of tablets is a common unit operation in the pharmaceutical industry. In most cases, the final product must meet strict quality requirements; to meet them, a detailed understanding of the coating process is required. To this end, numerous experiment studies have been performed. However, to acquire a mechanistic understanding, experimental data must be interpreted in the light of mathematical models. In recent years, a combination of analytical modeling and computational simulations enabled deeper insights into the nature of the coating process. This paper presents an overview of modeling and simulation approaches of the coating process, covering various relevant aspects from scale-up considerations to coating mass uniformity investigations and models for drop atomization. The most important analytical and computational concepts are presented and the findings are compared.
Mathematical modelling of hepatic lipid metabolism.
Pratt, Adrian C; Wattis, Jonathan A D; Salter, Andrew M
2015-04-01
The aim of this paper is to develop a mathematical model capable of simulating the metabolic response to a variety of mixed meals in fed and fasted conditions with particular emphasis placed on the hepatic triglyceride element of the model. Model validation is carried out using experimental data for the ingestion of three mixed composition meals over a 24-h period. Comparison with experimental data suggests the model predicts key plasma lipids accurately given a prescribed insulin profile. One counter-intuitive observation to arise from simulations is that liver triglyceride initially decreases when a high fat meal is ingested, a phenomenon potentially explained by the carbohydrate portion of the meal raising plasma insulin.
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.
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
ERIC Educational Resources Information Center
Nardi, Elena; Jaworski, Barbara J.
This paper reports from a research project at Oxford in the UK that focused (a) on university mathematics teachers' conceptualizations of first-year undergraduate teaching related to observation of their teaching; and (b) on issues relating the conceptualizations to mathematics as a discipline. This research builds on a qualitative study of…
Some mathematical models of intermolecular autophosphorylation.
Doherty, Kevin; Meere, Martin; Piiroinen, Petri T
2015-04-01
Intermolecular autophosphorylation refers to the process whereby a molecule of an enzyme phosphorylates another molecule of the same enzyme. The enzyme thereby catalyses its own phosphorylation. In the present paper, we develop two generic models of intermolecular autophosphorylation that also include dephosphorylation by a phosphatase of constant concentration. The first of these, a solely time-dependent model, is written as one ordinary differential equation that relies upon mass-action and Michaelis-Menten kinetics. Beginning with the enzyme in its dephosphorylated state, it predicts a lag before the enzyme becomes significantly phosphorylated, for suitable parameter values. It also predicts that there exists a threshold concentration for the phosphorylation of enzyme and that for suitable parameter values, a continuous or discontinuous switch in the phosphorylation of enzyme are possible. The model developed here has the advantage that it is relatively easy to analyse compared with most existing models for autophosphorylation and can qualitatively describe many different systems. We also extend our time-dependent model of autophosphorylation to include a spatial dependence, as well as localised binding reactions. This spatio-temporal model consists of a system of partial differential equations that describe a soluble autophosphorylating enzyme in a spherical geometry. We use the spatio-temporal model to describe the phosphorylation of an enzyme throughout the cell due to an increase in local concentration by binding. Using physically realistic values for model parameters, our results provide a proof-of-concept of the process of activation by local concentration and suggest that, in the presence of a phosphatase, this activation can be irreversible.
Mathematical modeling of human brain physiological data
NASA Astrophysics Data System (ADS)
Böhm, Matthias; Faltermeier, Rupert; Brawanski, Alexander; Lang, Elmar W.
2013-12-01
Recently, a mathematical model of the basic physiological processes regulating the cerebral perfusion and oxygen supply was introduced [Jung , J. Math. Biol.JMBLAJ0303-681210.1007/s00285-005-0343-5 51, 491 (2005)]. Although this model correctly describes the interdependence of arterial blood pressure (ABP) and intracranial pressure (ICP), it fails badly when it comes to explaining certain abnormal correlations seen in about 80% of the recordings of ABP together with ICP and the partial oxygen pressure (TiPO2) of the neuronal tissue, taken at an intensive care unit during neuromonitoring of patients with a severe brain trauma. Such recordings occasionally show segments, where the mean arterial blood pressure is correlated with the partial oxygen pressure in tissue but anticorrelated with the intracranial pressure. The origin of such abnormal correlations has not been fully understood yet. Here, two extensions to the previous approach are proposed which can reproduce such abnormal correlations in simulations quantitatively. Furthermore, as the simulations are based on a mathematical model, additional insight into the physiological mechanisms from which such abnormal correlations originate can be gained.
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
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 mathematical model of leptin resistance.
Jacquier, Marine; Soula, Hédi A; Crauste, Fabien
2015-09-01
Obesity is often associated with leptin resistance, which leads to a physiological system with high leptin concentration but unable to respond to leptin signals and to regulate food intake. We propose a mathematical model of the leptin-leptin receptors system, based on the assumption that leptin is a regulator of its own receptor activity, and investigate its qualitative behavior. Based on current knowledge and previous models developed for body weight dynamics in rodents, the model includes the dynamics of leptin, leptin receptors and the regulation of food intake and body weight. It displays two stable equilibria, one representing a healthy state and the other one an obese and leptin resistant state. We show that a constant leptin injection can lead to leptin resistance and that a temporal variation in some parameter values influencing food intake can induce a change of equilibrium and a pathway to leptin resistance and obesity.
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.
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
GENERIC THERMO-MECHANICAL MODEL FOR JOINTED ROCK MASSES
Vorobiev, O
2007-03-08
A new nonlinear thermo-mechanical model for heavily jointed rock masses is presented. The model uses correlation functions between the porosity and the basic rock properties such as elastic moduli, tensile and compressive strength. The model assumes that the media is isotropic and is characterized by two variable parameters: insipient porosity and in-situ-to-intact modulus ratio.
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…
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.…
Computer-Assisted Mathematics--A Model Approach.
ERIC Educational Resources Information Center
Bitter, Gary G.
1987-01-01
Discussion of need for improved mathematics education of preservice teachers focuses on a model program, the Mathematics Fitness Project, that includes a computer-generated testing system, management system, and remediation system. Use of the system to improve mathematics skills and attitudes of college students and post high school adults is…
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.
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.
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.
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.
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…
Middle School Mathematics Clinic: A Theoretical Model.
ERIC Educational Resources Information Center
Gore, Ethel V.
This paper describes a middle school mathematics clinic in the District of Columbia Public Schools, which was designed to aid students in the transition from mathematics in the primary grades to high school mathematics courses. It is intended to provide the low achiever with effective diagnostic and corrective instruction by the best trained…
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.
Mathematical model of renal interstitial fibrosis
Hao, Wenrui; Rovin, Brad H.; Friedman, Avner
2014-01-01
Lupus nephritis (LN) is an autoimmune disease that occurs when autoantibodies complex with self-antigen and form immune complexes that accumulate in the glomeruli. These immune complexes initiate an inflammatory response resulting in glomerular injury. LN often concomitantly affects the tubulointerstitial compartment of the kidney, leading first to interstitial inflammation and subsequently to interstitial fibrosis and atrophy of the renal tubules if not appropriately treated. Presently the only way to assess interstitial inflammation and fibrosis is through kidney biopsy, which is invasive and cannot be repeated frequently. Hence, monitoring of disease progression and response to therapy is suboptimal. In this paper we describe a mathematical model of the progress from tubulointerstitial inflammation to fibrosis. We demonstrate how the model can be used to monitor treatments for interstitial fibrosis in LN with drugs currently being developed or used for nonrenal fibrosis. PMID:25225370
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.
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 Modeling of the Auditory Periphery.
NASA Astrophysics Data System (ADS)
Koshigoe, Shozo
The auditory periphery is conventionally divided into three parts, namely, the outer, middle, and inner ear (or cochlea). Mathematical modeling of the auditory periphery has been used for increasing our understanding of its mechanics via the simulation of experimental results, and for estimating unknown parameters. The various techniques used in this study for modeling the auditory periphery are: (1) Green function methods for investigation of the external ear directional filter functions; (2) finite difference methods in cochlear mechanical model calculations; (3) dispersion relation tests of the consistency of model calculations; (4) dispersion relation checks of experimental cochlear response data for approximate consistency with the implications of causality, linearity, time translation invariance, and minimum phase behavior; (5) dispersion relation tests of the stability of the linear cochlear models with active elements; (6) the introduction of viscosity effects in cochlear mechanics in order to account for data on the low frequency cochlear input impedance; and (7) the incorporation of a non-linear feedback outer-hair-cell model into a cochlear model in order to account for the physiological and psychological data (such as spontaneous and induced acoustic emissions from human ears and their active non-linear interactions with external stimuli).
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
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(-), [Formula: see text] ) 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 cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-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.
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.
Incorporating neurophysiological concepts in mathematical thermoregulation models.
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.
Generic model for district heating: a geothermal appliance
Reisman, A.
1980-11-01
Brookhaven National Laboratory (BNL) is developing a model desgined to assess the engineering and economic requirements which must be addressed when the implementation of district heating is seriously considered. A brief overview of the structure of the BNL District Heating Model is presented, including a discussion of the function of each of its major program components. The model is composed of four submodels, each of which serves a distinct function in the analysis of district heating. These are the Heat Demand, Heat Source, District Heating, and Market analysis Submodels. (MHR)
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.
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 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.
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
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.
Generic Raman-based calibration models enabling real-time monitoring of cell culture bioreactors.
Mehdizadeh, Hamidreza; Lauri, David; Karry, Krizia M; Moshgbar, Mojgan; Procopio-Melino, Renee; Drapeau, Denis
2015-01-01
Raman-based multivariate calibration models have been developed for real-time in situ monitoring of multiple process parameters within cell culture bioreactors. Developed models are generic, in the sense that they are applicable to various products, media, and cell lines based on Chinese Hamster Ovarian (CHO) host cells, and are scalable to large pilot and manufacturing scales. Several batches using different CHO-based cell lines and corresponding proprietary media and process conditions have been used to generate calibration datasets, and models have been validated using independent datasets from separate batch runs. All models have been validated to be generic and capable of predicting process parameters with acceptable accuracy. The developed models allow monitoring multiple key bioprocess metabolic variables, and hence can be utilized as an important enabling tool for Quality by Design approaches which are strongly supported by the U.S. Food and Drug Administration.
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
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.
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…
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…
Mathematical model for contemplative amoeboid locomotion.
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.
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.
Mathematical modelling of autothermal thermophilic aerobic digesters.
Gomez, J; de Gracia, M; Ayesa, E; Garcia-Heras, J L
2007-03-01
This paper presents a new mathematical model for Autothermal Thermophilic Aerobic Digesters. The reactor has been modelled as two completely mixed volumes to separately predict the behaviour of the liquid and gaseous phases as well as the interrelation between them. The model includes biochemical transformations based on the standard Activated Sludge Models of IWA, as well as physico-chemical transformations associated with the chemical equilibria and the mass transfer between the liquid and the gaseous phases similar to those proposed in the ADM1 of IWA. An energy balance has also been included in the model in order to predict the temperature of the system. This thermal balance takes into account all those biochemical and physico-chemical transformations that entail the most relevant heat interchanges. Reactor performance has been explored by simulation in two different scenarios: in the first where it acts as the initial stage in a Dual system, and in the second where it acts as a single-stage treatment. Each scenario enabled the identification of the relevance of the different parameters. PMID:17258787
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.
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 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.
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.
Genetic demographic networks: Mathematical model and applications.
Kimmel, Marek; Wojdyła, Tomasz
2016-10-01
Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise
Konur, Dinçer; Golias, Mihalis M; Darks, Brandon
2013-03-01
State Departments of Transportation (S-DOT's) periodically allocate budget for safety upgrades at railroad-highway crossings. Efficient resource allocation is crucial for reducing accidents at railroad-highway crossings and increasing railroad as well as highway transportation safety. While a specific method is not restricted to S-DOT's, sorting type of procedures are recommended by the Federal Railroad Administration (FRA), United States Department of Transportation for the resource allocation problem. In this study, a generic mathematical model is proposed for the resource allocation problem for railroad-highway crossing safety upgrades. The proposed approach is compared to sorting based methods for safety upgrades of public at-grade railroad-highway crossings in Tennessee. The comparison shows that the proposed mathematical modeling approach is more efficient than sorting methods in reducing accidents and severity.
Noise in restaurants: levels and mathematical model.
To, Wai Ming; Chung, Andy
2014-01-01
Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Noise in restaurants: levels and mathematical model.
To, Wai Ming; Chung, Andy
2014-01-01
Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA. PMID:25387532
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.
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%.
NASA Astrophysics Data System (ADS)
Butenschön, Momme; Clark, James; Aldridge, John N.; Icarus Allen, Julian; Artioli, Yuri; Blackford, Jeremy; Bruggeman, Jorn; Cazenave, Pierre; Ciavatta, Stefano; Kay, Susan; Lessin, Gennadi; van Leeuwen, Sonja; van der Molen, Johan; de Mora, Lee; Polimene, Luca; Sailley, Sevrine; Stephens, Nicholas; Torres, Ricardo
2016-04-01
The European Regional Seas Ecosystem Model (ERSEM) is one of the most established ecosystem models for the lower trophic levels of the marine food web in the scientific literature. Since its original development in the early nineties it has evolved significantly from a coastal ecosystem model for the North Sea to a generic tool for ecosystem simulations from shelf seas to the global ocean. The current model release contains all essential elements for the pelagic and benthic parts of the marine ecosystem, including the microbial food web, the carbonate system, and calcification. Its distribution is accompanied by a testing framework enabling the analysis of individual parts of the model. Here we provide a detailed mathematical description of all ERSEM components along with case studies of mesocosm-type simulations, water column implementations, and a brief example of a full-scale application for the north-western European shelf. Validation against in situ data demonstrates the capability of the model to represent the marine ecosystem in contrasting environments.
NASA Astrophysics Data System (ADS)
Butenschön, M.; Clark, J.; Aldridge, J. N.; Allen, J. I.; Artioli, Y.; Blackford, J.; Bruggeman, J.; Cazenave, P.; Ciavatta, S.; Kay, S.; Lessin, G.; van Leeuwen, S.; van der Molen, J.; de Mora, L.; Polimene, L.; Sailley, S.; Stephens, N.; Torres, R.
2015-08-01
The ERSEM model is one of the most established ecosystem models for the lower trophic levels of the marine food-web in the scientific literature. Since its original development in the early nineties it has evolved significantly from a coastal ecosystem model for the North-Sea to a generic tool for ecosystem simulations from shelf seas to the global ocean. The current model release contains all essential elements for the pelagic and benthic part of the marine ecosystem, including the microbial food-web, the carbonate system and calcification. Its distribution is accompanied by a testing framework enabling the analysis of individual parts of the model. Here we provide a detailed mathematical description of all ERSEM components along with case-studies of mesocosm type simulations, water column implementations and a brief example of a full-scale application for the North-West European shelf. Validation against in situ data demonstrates the capability of the model to represent the marine ecosystem in contrasting environments.
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.
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
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.
Generic inference of inflation models by local non-Gaussianity
NASA Astrophysics Data System (ADS)
Dorn, Sebastian; Ramirez, Erandy; Kunze, Kerstin E.; Hofmann, Stefan; Enßlin, Torsten A.
2014-05-01
The presence of multiple fields during inflation might seed a detectable amount of non-Gaussianity in the curvature perturbations, which in turn becomes observable in present data sets like the cosmic microwave background (CMB) or the large scale structure (LSS). Within this proceeding we present a fully analytic method to infer inflationary parameters from observations by exploiting higher-order statistics of the curvature perturbations. To keep this analyticity, and thereby to dispense with numerically expensive sampling techniques, a saddle-point approximation is introduced whose precision has been validated for a numerical toy example. Applied to real data, this approach might enable to discriminate among the still viable models of inflation.
A generic 3D kinetic model of gene expression
NASA Astrophysics Data System (ADS)
Zhdanov, Vladimir P.
2012-04-01
Recent experiments show that mRNAs and proteins can be localized both in prokaryotic and eukaryotic cells. To describe such situations, I present a 3D mean-field kinetic model aimed primarily at gene expression in prokaryotic cells, including the formation of mRNA, its translation into protein, and slow diffusion of these species. Under steady-state conditions, the mRNA and protein spatial distribution is described by simple exponential functions. The protein concentration near the gene transcribed into mRNA is shown to depend on the protein and mRNA diffusion coefficients and degradation rate constants.
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
Mathematical model insights into arsenic detoxification
2011-01-01
Background Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs), which then undergoes hepatic methylation to methylarsonic acid (MMAs) and a second methylation to dimethylarsinic acid (DMAs). Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation. Methods We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects. Results We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic methyltransferase has been
On Mathematical Modeling Of Quantum Systems
Achuthan, P.; Narayanankutty, Karuppath
2009-07-02
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Mathematical Models of Cardiac Pacemaking Function
NASA Astrophysics Data System (ADS)
Li, Pan; Lines, Glenn T.; Maleckar, Mary M.; Tveito, Aslak
2013-10-01
Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.
On Mathematical Modeling Of Quantum Systems
NASA Astrophysics Data System (ADS)
Achuthan, P.; Narayanankutty, Karuppath
2009-07-01
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
A generic hydrological model for a green roof drainage layer.
Vesuviano, Gianni; Stovin, Virginia
2013-01-01
A rainfall simulator of length 5 m and width 1 m was used to supply constant intensity and largely spatially uniform water inflow events to 100 different configurations of commercially available green roof drainage layer and protection mat. The runoff from each inflow event was collected and sampled at one-second intervals. Time-series runoff responses were subsequently produced for each of the tested configurations, using the average response of three repeat tests. Runoff models, based on storage routing (dS/dt = I-Q) and a power-law relationship between storage and runoff (Q = kS(n)), and incorporating a delay parameter, were created. The parameters k, n and delay were optimized to best fit each of the runoff responses individually. The range and pattern of optimized parameter values was analysed with respect to roof and event configuration. An analysis was performed to determine the sensitivity of the shape of the runoff profile to changes in parameter values. There appears to be potential to consolidate values of n by roof slope and drainage component material.
Mathematical Modeling of Electrochemical Flow Capacitors
Hoyt, NC; Wainright, JS; Savinell, RF
2015-01-13
Electrochemical flow capacitors (EFCs) for grid-scale energy storage are a new technology that is beginning to receive interest. Prediction of the expected performance of such systems is important as modeling can be a useful avenue in the search for design improvements. Models based off of circuit analogues exist to predict EFC performance, but these suffer from deficiencies (e.g. a multitude of fitting constants that are required and the ability to analyze only one spatial direction at a time). In this paper mathematical models based off of three-dimensional macroscopic balances (similar to models for porous electrodes) are reported. Unlike existing three-dimensional porous electrode-based approaches for modeling slurry electrodes, advection (i.e., transport associated with bulk fluid motion) of the overpotential is included in order to account for the surface charge at the interface between flowing particles and the electrolyte. Doing so leads to the presence of overpotential boundary layers that control the performance of EFCs. These models were used to predict the charging behavior of an EFC under both flowing and non-flowing conditions. Agreement with experimental data was good, including proper prediction of the steady-state current that is achieved during charging of a flowing EFC. (C) The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives 4.0 License (CC BY-NC-ND, http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is not changed in any way and is properly cited. For permission for commercial reuse, please email: oa@electrochem.org. All rights reserved.
Modelling Mathematical Argumentation: The Importance of Qualification
ERIC Educational Resources Information Center
Inglis, Matthew; Mejia-Ramos, Juan; Simpson, Adrian
2007-01-01
In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…
Mathematics Teacher TPACK Standards and Development Model
ERIC Educational Resources Information Center
Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis
2009-01-01
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…
Modelling Mathematical Reasoning in Physics Education
ERIC Educational Resources Information Center
Uhden, Olaf; Karam, Ricardo; Pietrocola, Mauricio; Pospiech, Gesche
2012-01-01
Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…
Some Models of Mathematics Teachers' Centres.
ERIC Educational Resources Information Center
Seiferth, Berniece B.
There are two types of teacher centres in Great Britain, multi-purpose centres designed for all subjects of the curriculum, and topical centres which deal specifically with one area of subject matter such as mathematics, English, etc. In this paper, the five mathematics centres in London are analyzed for purpose, materials available, and…
Improving the Generic Camera Calibration Technique by an Extended Model of Calibration Display
NASA Astrophysics Data System (ADS)
Reh, T.; Li, W.; Burke, J.; Bergmann, R. B.
2014-10-01
Generic camera calibration is a method to characterize vision sensors by describing a line of sight for every single pixel. This procedure frees the calibration process from the restriction to pinhole-like optics that arises in the common photogrammetric camera models. Generic camera calibration also enables the calibration of high-frequency distortions, which is beneficial for high-precision measurement systems. The calibration process is as follows: To collect sufficient data for calculating a line of sight for each pixel, active grids are used as calibration reference rather than static markers such as corners of chessboard patterns. A common implementation of active grids are sinusoidal fringes presented on a flat TFT display. So far, the displays have always been treated as ideally flat. In this work we propose new and more sophisticated models to account for additional properties of the active grid display: The refraction of light in the glass cover is taken into account as well as a possible deviation of the top surface from absolute flatness. To examine the effectiveness of the new models, an example fringe projection measurement system is characterized with the resulting calibration methods and with the original generic camera calibration. Evaluating measurements using the different calibration methods shows that the extended display model substantially improves the uncertainty of the measurement system.
Mathematical modeling of Chikungunya fever control
NASA Astrophysics Data System (ADS)
Hincapié-Palacio, Doracelly; Ospina, Juan
2015-05-01
Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.
iSTEM: Promoting Fifth Graders' Mathematical Modeling
ERIC Educational Resources Information Center
Yanik, H. Bahadir; Karabas, Celil
2014-01-01
Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…
Students' Approaches to Learning a New Mathematical Model
ERIC Educational Resources Information Center
Flegg, Jennifer A.; Mallet, Daniel G.; Lupton, Mandy
2013-01-01
In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quantitative data based around the students' approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to…
Mathematical Manipulative Models: In Defense of "Beanbag Biology"
ERIC Educational Resources Information Center
Jungck, John R.; Gaff, Holly; Weisstein, Anton E.
2010-01-01
Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process--1) use of physical manipulatives, 2) interactive exploration of computer…
Visual Modeling as a Motivation for Studying Mathematics and Art
ERIC Educational Resources Information Center
Sendova, Evgenia; Grkovska, Slavica
2005-01-01
The paper deals with the possibility of enriching the curriculum in mathematics, informatics and art by means of visual modeling of abstract paintings. The authors share their belief that in building a computer model of a construct, one gains deeper insight into the construct, and is motivated to elaborate one's knowledge in mathematics and…
Genetic demographic networks: Mathematical model and applications.
Kimmel, Marek; Wojdyła, Tomasz
2016-10-01
Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise
Boore, David
2016-01-01
This short note contains two contributions related to deriving depth‐dependent velocity and density models for use in computing generic crustal amplifications. The first contribution is a method for interpolating two velocity profiles to obtain a third profile with a time‐averaged velocity to depth Z that is equal to a specified value (e.g., for shear‐wave velocity VS, for Z=30 m, in which the subscript S has been added to indicate that the average is for shear‐wave velocities). The second contribution is a procedure for obtaining densities from VS. The first contribution is used to extend and revise the Boore and Joyner (1997) generic rock VS model, for which , to a model with the more common . This new model is then used with the densities from the second contribution to compute crustal amplifications for a generic site with .
Mathematical modeling of biomass fuels formation process.
Gaska, Krzysztof; Wandrasz, Andrzej J
2008-01-01
The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task.
A mathematical model of a computational problem solving system
NASA Astrophysics Data System (ADS)
Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan
2015-05-01
This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.
The development of an advanced generic solar dynamic heat receiver thermal model
NASA Technical Reports Server (NTRS)
Wu, Y. C.; Roschke, E. J.; Kohout, L.
1988-01-01
An advanced generic solar dynamic heat receiver thermal model under development which can analyze both orbital transient and orbital average conditions is discussed. This model can be used to study advanced receiver concepts, evaluate receiver concepts under development, analyze receiver thermal characteristics under various operational conditions, and evaluate solar dynamic system thermal performances in various orbit conditions. The model and the basic considerations that led to its creation are described, and results based on a set of baseline orbit, configuration, and operational conditions are presented to demonstrate the working of the receiver model.
NASA Astrophysics Data System (ADS)
Kon, Cynthia Mui Lian; Labadin, Jane
2016-06-01
Malaria is a critical infection caused by parasites which are spread to humans through mosquito bites. Approximately half of the world's population is in peril of getting infected by malaria. Mosquito-borne diseases have a standard behavior where they are transmitted in the same manner, only through vector mosquito. Taking this into account, a generic spatial-temporal model for transmission of multiple mosquito-borne diseases had been formulated. Our interest is to reproduce the actual cases of different mosquito-borne diseases using the generic model and then predict future cases so as to improve control and target measures competently. In this paper, we utilize notified weekly malaria cases in four districts in Sarawak, Malaysia, namely Kapit, Song, Belaga and Marudi. The actual cases for 36 weeks, which is from week 39 in 2012 to week 22 in 2013, are compared with simulations of the generic spatial-temporal transmission mosquito-borne diseases model. We observe that the simulation results display corresponding result to the actual malaria cases in the four districts.
Mathematical modeling and simulation of seated stability.
Tanaka, Martin L; Ross, Shane D; Nussbaum, Maury A
2010-03-22
Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the "wobble chair"). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight, and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications.
A Mathematical Model for Suppression Subtractive Hybridization
Gadgil, Chetan; Rink, Anette; Beattie, Craig
2002-01-01
Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assessing the effect of various parameters to facilitate its optimization. We derive an equation for the probability that a particular differentially expressed species is successfully isolated and use this to quantify the effect of the following parameters related to the cDNA sample: (a) mRNA abundance; (b) partial sequence complementarity to other species; and (3) degree of differential expression. We also evaluate the effect of parameters related to the process, including: (a) reaction times; and (b) extent of driver excess used in the two hybridization reactions. The optimum set of process parameters for successful isolation of differentially expressed species depends on transcript abundance. We show that the reaction conditions have a significant effect on the occurrence of false-positives and formulate strategies to isolate specific subsets of differentially expressed genes. We also quantify the effect of non-specific hybridization on the false-positive results and present strategies for spiking cDNA sequences to address this problem. PMID:18629052
Helping Students Become Better Mathematical Modelers: Pseudosteady-State Approximations.
ERIC Educational Resources Information Center
Bunge, Annette L.; Miller, Ronald L.
1997-01-01
Undergraduate and graduate students are often confused about several aspects of modeling physical systems. Describes an approach to address these issues using a single physical transport problem that can be analyzed with multiple mathematical models. (DKM)
NASA Technical Reports Server (NTRS)
Partridge, J. K.; Notardonato, W. U.; Johnson, W. L.; Tuttle, J. W.
2011-01-01
Among the many factors that determine overall rocket performance, propellant density is important because it affects the size of the rocket. Thus, in order to decrease the size of a rocket, it may be desirable to increase the density of propellants. This study analyzes the concept of increasing the propellant density by employing a cooling source submerged in the liquid propellant. A simple, mathematical model was developed to predict the rate of densification and the propellant temperature profile. The mathematical model is generic and applicable to multiple propellants. The densification rate was determined experimentally by submerging a cooling source in liquid oxygen at constant, positive pressure, and measuring the time rate of change in temperature with respect to vertical position. The results from the mathematical model provided a reasonable fit when compared to experimental results.
Szymańska, Zuzanna; Parisot, Martin; Lachowicz, Mirosław
2014-12-21
In this paper we propose a mathematical model of protein and mRNA transport inside a cell. The spatio-temporal model takes into account the active transport along microtubules in the cytoplasm as well as diffusion and is able to reproduce the oscillatory changes in protein concentration observed in many experimental data. In the model the protein and the mRNA interact with each other that allows us to classify the model as a simple gene regulatory network. The proposed model is generic and may be adapted to specific signaling pathways. On the basis of numerical simulations, we formulate a new hypothesis that the oscillatory dynamics is allowed by the mRNA active transport along microtubules from the nucleus to distant locations.
Typhoid transmission: a historical perspective on mathematical model development.
Bakach, Iurii; Just, Matthew R; Gambhir, Manoj; Fung, Isaac Chun-Hai
2015-11-01
Mathematical models of typhoid transmission were first developed nearly half a century ago. To facilitate a better understanding of the historical development of this field, we reviewed mathematical models of typhoid and summarized their structures and limitations. Eleven models, published in 1971 to 2014, were reviewed. While models of typhoid vaccination are well developed, we highlight the need to better incorporate water, sanitation and hygiene interventions into models of typhoid and other foodborne and waterborne diseases. Mathematical modeling is a powerful tool to test and compare different intervention strategies which is important in the world of limited resources. By working collaboratively, epidemiologists and mathematicians should build better mathematical models of typhoid transmission, including pharmaceutical and non-pharmaceutical interventions, which will be useful in epidemiological and public health practice.
Physical vs. Mathematical Models in Rock Mechanics
NASA Astrophysics Data System (ADS)
Morozov, I. B.; Deng, W.
2013-12-01
One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an
An Assessment Model for Proof Comprehension in Undergraduate Mathematics
ERIC Educational Resources Information Center
Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron
2012-01-01
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…
Mathematical Modeling, Sense Making, and the Common Core State Standards
ERIC Educational Resources Information Center
Schoenfeld, Alan H.
2013-01-01
On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…
Bridging the Gap Between Common Sense and Mathematical Models
ERIC Educational Resources Information Center
Press, Laurence
1975-01-01
Describes a four-phase method of helping students who are mathematically unsophisticated and have difficulty relating their common sense, English-language understanding of a system to an abstract, mathematical description. The approach uses interactive simulation models. (Author/IRT)
Using Spreadsheets to Teach Aspects of Biology Involving Mathematical Models
ERIC Educational Resources Information Center
Carlton, Kevin; Nicholls, Mike; Ponsonby, David
2004-01-01
Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…
Teaching Writing and Communication in a Mathematical Modeling Course
ERIC Educational Resources Information Center
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
Mathematics in the Biology Classroom: A Model of Interdisciplinary Education
ERIC Educational Resources Information Center
Hodgson, Ted; Keck, Robert; Patterson, Richard; Maki, Dan
2005-01-01
This article describes an interdisciplinary course that develops essential mathematical modeling skills within an introductory biology setting. The course embodies recent recommendations regarding the need for interdisciplinary, inquiry-based mathematical preparation of undergraduates in the biological sciences. Evaluation indicates that the…
Mathematical Modeling and Simulation of Seated Stability
Tanaka, Martin L.; Ross, Shane D.; Nussbaum, Maury A.
2009-01-01
Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications. PMID:20018288
Studying PMMA films on silica surfaces with generic microscopic and mesoscale models
NASA Astrophysics Data System (ADS)
Zhang, J.; Mukherji, D.; Daoulas, K. Ch.
2016-07-01
Polymer films on solid substrates present significant interest for fundamental polymer physics and industrial applications. For their mesoscale study, we develop a hybrid particle-based representation where polymers are modeled as worm-like chains and non-bonded interactions are introduced through a simple density functional. The mesoscale description is parameterized to match a generic microscopic model, which nevertheless can represent real materials. Choosing poly (methyl methacrylate) adsorbed on silica as a case study, the consistency of both models in describing conformational and structural properties in polymer films is investigated. We compare selected quantifiers of chain-shape, the structure of the adsorbed layer, as well as the statistics of loops, tails, and trains. Overall, the models are found to be consistent with each other. Some deviations in conformations and structure of adsorbed layer can be attributed to the simplified description of polymer/surface interactions and local liquid packing in the mesoscale model. These results are encouraging for a future development of pseudo-dynamical schemes, parameterizing the kinetics in the hybrid model via the dynamics of the generic microscopic model.
Explore or Exploit? A Generic Model and an Exactly Solvable Case
NASA Astrophysics Data System (ADS)
Gueudré, Thomas; Dobrinevski, Alexander; Bouchaud, Jean-Philippe
2014-02-01
Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.
Mathematical modeling of efficient protocols to control glioma growth.
Branco, J R; Ferreira, J A; de Oliveira, Paula
2014-09-01
In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included.
Mathematics of tsunami: modelling and identification
NASA Astrophysics Data System (ADS)
Krivorotko, Olga; Kabanikhin, Sergey
2015-04-01
Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of
Adequate mathematical modelling of environmental processes
NASA Astrophysics Data System (ADS)
Chashechkin, Yu. D.
2012-04-01
In environmental observations and laboratory visualization both large scale flow components like currents, jets, vortices, waves and a fine structure are registered (different examples are given). The conventional mathematical modeling both analytical and numerical is directed mostly on description of energetically important flow components. The role of a fine structures is still remains obscured. A variety of existing models makes it difficult to choose the most adequate and to estimate mutual assessment of their degree of correspondence. The goal of the talk is to give scrutiny analysis of kinematics and dynamics of flows. A difference between the concept of "motion" as transformation of vector space into itself with a distance conservation and the concept of "flow" as displacement and rotation of deformable "fluid particles" is underlined. Basic physical quantities of the flow that are density, momentum, energy (entropy) and admixture concentration are selected as physical parameters defined by the fundamental set which includes differential D'Alembert, Navier-Stokes, Fourier's and/or Fick's equations and closing equation of state. All of them are observable and independent. Calculations of continuous Lie groups shown that only the fundamental set is characterized by the ten-parametric Galilelian groups reflecting based principles of mechanics. Presented analysis demonstrates that conventionally used approximations dramatically change the symmetries of the governing equations sets which leads to their incompatibility or even degeneration. The fundamental set is analyzed taking into account condition of compatibility. A high order of the set indicated on complex structure of complete solutions corresponding to physical structure of real flows. Analytical solutions of a number problems including flows induced by diffusion on topography, generation of the periodic internal waves a compact sources in week-dissipative media as well as numerical solutions of the same
Mathematical modeling of urea transport in the kidney.
Layton, Anita T
2014-01-01
Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.
a Discrete Mathematical Model to Simulate Malware Spreading
NASA Astrophysics Data System (ADS)
Del Rey, A. Martin; Sánchez, G. Rodriguez
2012-10-01
With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.
[Mathematical model of value of population].
Sha, J; Wang, S
1983-09-29
The authors define the value of population as an economic concept and present mathematical formulas for calculating this value. Included in this theoretical discussion are different kinds of surplus value of population and the social significance of population value. PMID:12279805
Making Insulation Decisions through Mathematical Modeling
ERIC Educational Resources Information Center
Yanik, H. Bahadir; Memis, Yasin
2014-01-01
Engaging students in studies about conservation and sustainability can support their understanding of making environmental conscious decisions to conserve Earth. This article aims to contribute these efforts and direct students' attention to how they can use mathematics to make environmental decisions. Contributors to iSTEM: Integrating…
Modeling Students' Interest in Mathematics Homework
ERIC Educational Resources Information Center
Xu, Jianzhong; Yuan, Ruiping; Xu, Brian; Xu, Melinda
2016-01-01
The authors examine the factors influencing mathematics homework interest for Chinese students and compare the findings with a recent study involving U.S. students. The findings from multilevel analyses revealed that some predictors for homework interest functioned similarly (e.g., affective attitude toward homework, learning-oriented reasons,…
Mechanical-mathematical modeling for landslide process
NASA Astrophysics Data System (ADS)
Svalova, V.
2009-04-01
500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.
A mathematical model of a fishery with variable market price: sustainable fishery/over-exploitation.
Mansal, Fulgence; Nguyen-Huu, Tri; Auger, Pierre; Balde, Moussa
2014-09-01
We present a mathematical bioeconomic model of a fishery with a variable price. The model describes the time evolution of the resource, the fishing effort and the price which is assumed to vary with respect to supply and demand. The supply is the instantaneous catch while the demand function is assumed to be a monotone decreasing function of price. We show that a generic market price equation (MPE) can be derived and has to be solved to calculate non trivial equilibria of the model. This MPE can have 1, 2 or 3 equilibria. We perform the analysis of local and global stability of equilibria. The MPE is extended to two cases: an age-structured fish population and a fishery with storage of the resource.
Salcedo-Sora, J Enrique; Mc Auley, Mark T
2016-03-01
The metabolic biochemistry of folate biosynthesis and utilisation has evolved into a complex network of reactions. Although this complexity represents challenges to the field of folate research it has also provided a renewed source for antimetabolite targets. A range of improved folate chemotherapy continues to be developed and applied particularly to cancer and chronic inflammatory diseases. However, new or better antifolates against infectious diseases remain much more elusive. In this paper we describe the assembly of a generic deterministic mathematical model of microbial folate metabolism. Our aim is to explore how a mathematical model could be used to explore the dynamics of this inherently complex set of biochemical reactions. Using the model it was found that: (1) a particular small set of folate intermediates are overrepresented, (2) inhibitory profiles can be quantified by the level of key folate products, (3) using the model to scan for the most effective combinatorial inhibitions of folate enzymes we identified specific targets which could complement current antifolates, and (4) the model substantiates the case for a substrate cycle in the folinic acid biosynthesis reaction. Our model is coded in the systems biology markup language and has been deposited in the BioModels Database (MODEL1511020000), this makes it accessible to the community as a whole. PMID:26794619
Quantitative model for the generic 3D shape of ICMEs at 1 AU
NASA Astrophysics Data System (ADS)
Démoulin, P.; Janvier, M.; Masías-Meza, J. J.; Dasso, S.
2016-10-01
Context. Interplanetary imagers provide 2D projected views of the densest plasma parts of interplanetary coronal mass ejections (ICMEs), while in situ measurements provide magnetic field and plasma parameter measurements along the spacecraft trajectory, that is, along a 1D cut. The data therefore only give a partial view of the 3D structures of ICMEs. Aims: By studying a large number of ICMEs, crossed at different distances from their apex, we develop statistical methods to obtain a quantitative generic 3D shape of ICMEs. Methods: In a first approach we theoretically obtained the expected statistical distribution of the shock-normal orientation from assuming simple models of 3D shock shapes, including distorted profiles, and compared their compatibility with observed distributions. In a second approach we used the shock normal and the flux rope axis orientations together with the impact parameter to provide statistical information across the spacecraft trajectory. Results: The study of different 3D shock models shows that the observations are compatible with a shock that is symmetric around the Sun-apex line as well as with an asymmetry up to an aspect ratio of around 3. Moreover, flat or dipped shock surfaces near their apex can only be rare cases. Next, the sheath thickness and the ICME velocity have no global trend along the ICME front. Finally, regrouping all these new results and those of our previous articles, we provide a quantitative ICME generic 3D shape, including the global shape of the shock, the sheath, and the flux rope. Conclusions: The obtained quantitative generic ICME shape will have implications for several aims. For example, it constrains the output of typical ICME numerical simulations. It is also a base for studying the transport of high-energy solar and cosmic particles during an ICME propagation as well as for modeling and forecasting space weather conditions near Earth.
A generic emission model to predict release of organic substances from materials in consumer goods.
Holmgren, Tomas; Persson, Leif; Andersson, Patrik L; Haglund, Peter
2012-10-15
Organic chemicals may be released when consumer goods are used, contributing to environmental and human levels of potentially hazardous chemicals. A generic model was developed to predict emissions of organic chemicals from various materials in consumer products. The model involved three modules, which each predict a key parameter needed to calculate the mass of individual chemicals emitted. Partition coefficients between a material and the surrounding air were predicted using Abraham solvation parameters, diffusion coefficients in materials were calculated using the Piringer equation, and convective mass transfer coefficients were evaluated by applying the Chilton-Colburn analogy. The calculated emission rates from predicted parameters were evaluated and agreed well with literature data. The release of plasticizers from vinyl flooring used in Sweden was calculated to demonstrate the utility of the generic model. The estimated emitted masses of di(2-ethylhexyl)phthalate (DEHP), di-iso-nonylphthalate (DINP), and 1,2-cyclohexanedicarboxylic acid di-iso-nonyl ester (DINCH) in 2012 were 210 kg, 40 kg, and 3.6 kg respectively. Emissions from vinyl flooring were estimated for the period 1990 to 2035 and it was shown that the recent substitution of DEHP with DINP will help to reduce plasticizer emissions. Model calculations for alternative plasticizers revealed that DINCH would yield similar emissions to DINP, whereas use of diethyl hexyl-iso-sorbide or diethyl hexyl adipate would result in higher emissions. PMID:22947618
A generic emission model to predict release of organic substances from materials in consumer goods.
Holmgren, Tomas; Persson, Leif; Andersson, Patrik L; Haglund, Peter
2012-10-15
Organic chemicals may be released when consumer goods are used, contributing to environmental and human levels of potentially hazardous chemicals. A generic model was developed to predict emissions of organic chemicals from various materials in consumer products. The model involved three modules, which each predict a key parameter needed to calculate the mass of individual chemicals emitted. Partition coefficients between a material and the surrounding air were predicted using Abraham solvation parameters, diffusion coefficients in materials were calculated using the Piringer equation, and convective mass transfer coefficients were evaluated by applying the Chilton-Colburn analogy. The calculated emission rates from predicted parameters were evaluated and agreed well with literature data. The release of plasticizers from vinyl flooring used in Sweden was calculated to demonstrate the utility of the generic model. The estimated emitted masses of di(2-ethylhexyl)phthalate (DEHP), di-iso-nonylphthalate (DINP), and 1,2-cyclohexanedicarboxylic acid di-iso-nonyl ester (DINCH) in 2012 were 210 kg, 40 kg, and 3.6 kg respectively. Emissions from vinyl flooring were estimated for the period 1990 to 2035 and it was shown that the recent substitution of DEHP with DINP will help to reduce plasticizer emissions. Model calculations for alternative plasticizers revealed that DINCH would yield similar emissions to DINP, whereas use of diethyl hexyl-iso-sorbide or diethyl hexyl adipate would result in higher emissions.
Classical and Weak Solutions for Two Models in Mathematical Finance
NASA Astrophysics Data System (ADS)
Gyulov, Tihomir B.; Valkov, Radoslav L.
2011-12-01
We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.
Efficient tunable generic model for self-assembling fluid bilayer membranes
NASA Astrophysics Data System (ADS)
Deserno, Markus
2005-03-01
We present a new model for the simulation of generic lipid bilayers in the mesoscopic regime (between a few nanometers and many tens of nanometers), which is very robust, versatile, and extremely efficient, since it avoids the need for an embedding solvent. Based entirely on simple pair potentials, it features a wide region of unassisted self assembly into fluid bilayers without the need for careful parameter tuning. The resulting membranes display the correct continuum elastic behavior with bending constants in the experimentally relevant range. It can be readily used to study events like bilayer fusion, bilayer melting, lipid mixtures, rafts, and protein-bilayer interactions.
Generic incommensurate transition in the two-dimensional boson Hubbard model
NASA Astrophysics Data System (ADS)
Alet, Fabien; Sørensen, Erik S.
2004-07-01
The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multipeak structure in the energy distribution for finite lattices, usually indicative of a first-order phase transition. However, this multipeak structure is shown to disappear in the thermodynamic limit, revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.
The Generic Genome Browser: A Building Block for a Model Organism System Database
Stein, Lincoln D.; Mungall, Christopher; Shu, ShengQiang; Caudy, Michael; Mangone, Marco; Day, Allen; Nickerson, Elizabeth; Stajich, Jason E.; Harris, Todd W.; Arva, Adrian; Lewis, Suzanna
2002-01-01
The Generic Model Organism System Database Project (GMOD) seeks to develop reusable software components for model organism system databases. In this paper we describe the Generic Genome Browser (GBrowse), a Web-based application for displaying genomic annotations and other features. For the end user, features of the browser include the ability to scroll and zoom through arbitrary regions of a genome, to enter a region of the genome by searching for a landmark or performing a full text search of all features, and the ability to enable and disable tracks and change their relative order and appearance. The user can upload private annotations to view them in the context of the public ones, and publish those annotations to the community. For the data provider, features of the browser software include reliance on readily available open source components, simple installation, flexible configuration, and easy integration with other components of a model organism system Web site. GBrowse is freely available under an open source license. The software, its documentation, and support are available at http://www.gmod.org. PMID:12368253
NASA Astrophysics Data System (ADS)
Honkonen, I.
2014-07-01
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 any modification of existing code. This is an advantage for the development and testing of computational modeling software as each submodel can be developed and tested independently and subsequently used without modification in a more complex coupled program. Support for parallel programming is also provided by allowing users to select which simulation variables to transfer between processes via a Message Passing Interface 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 presented here requires a C++ compiler that supports variadic templates which were standardized in 2011 (C++11). The code is available at: https://github.com/nasailja/gensimcell for everyone to use, study, modify and redistribute; those that do are kindly requested to cite this work.
Some Aspects of Mathematical Model of Collaborative Learning
ERIC Educational Resources Information Center
Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu
2012-01-01
There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…
Academic Libraries as a Context for Teaching Mathematical Modeling
ERIC Educational Resources Information Center
Warwick, Jon
2008-01-01
The teaching of mathematical modeling to undergraduate students requires that students are given ample opportunity to develop their own models and experience first-hand the process of model building. Finding an appropriate context within which modeling can be undertaken is not a simple task as it needs to be readily understandable and seen as…
Generic framework for mining cellular automata models on protein-folding simulations.
Diaz, N; Tischer, I
2016-01-01
Cellular automata model identification is an important way of building simplified simulation models. In this study, we describe a generic architectural framework to ease the development process of new metaheuristic-based algorithms for cellular automata model identification in protein-folding trajectories. Our framework was developed by a methodology based on design patterns that allow an improved experience for new algorithms development. The usefulness of the proposed framework is demonstrated by the implementation of four algorithms, able to obtain extremely precise cellular automata models of the protein-folding process with a protein contact map representation. Dynamic rules obtained by the proposed approach are discussed, and future use for the new tool is outlined. PMID:27323045
OpenDA Open Source Generic Data Assimilation Environment and its Application in Process Models
NASA Astrophysics Data System (ADS)
El Serafy, Ghada; Verlaan, Martin; Hummel, Stef; Weerts, Albrecht; Dhondia, Juzer
2010-05-01
Data Assimilation techniques are essential elements in state-of-the-art development of models and their optimization with data in the field of groundwater, surface water and soil systems. They are essential tools in calibration of complex modelling systems and improvement of model forecasts. The OpenDA is a new and generic open source data assimilation environment for application to a choice of physical process models, applied to case dependent domains. OpenDA was introduced recently when the developers of Costa, an open-source TU Delft project [http://www.costapse.org; Van Velzen and Verlaan; 2007] and those of the DATools from the former WL|Delft Hydraulics [El Serafy et al 2007; Weerts et al. 2009] decided to join forces. OpenDA makes use of a set of interfaces that describe the interaction between models, observations and data assimilation algorithms. It focuses on flexible applications in portable systems for modelling geophysical processes. It provides a generic interfacing protocol that allows combination of the implemented data assimilation techniques with, in principle, any time-stepping model duscribing a process(atmospheric processes, 3D circulation, 2D water level, sea surface temperature, soil systems, groundwater etc.). Presently, OpenDA features filtering techniques and calibration techniques. The presentation will give an overview of the OpenDA and the results of some of its practical applications. Application of data assimilation in portable operational forecasting systems—the DATools assimilation environment, El Serafy G.Y., H. Gerritsen, S. Hummel, A. H. Weerts, A.E. Mynett and M. Tanaka (2007), Journal of Ocean Dynamics, DOI 10.1007/s10236-007-0124-3, pp.485-499. COSTA a problem solving environment for data assimilation applied for hydrodynamical modelling, Van Velzen and Verlaan (2007), Meteorologische Zeitschrift, Volume 16, Number 6, December 2007 , pp. 777-793(17). Application of generic data assimilation tools (DATools) for flood
NASA Technical Reports Server (NTRS)
Rabitz, Herschel
1987-01-01
The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.
ERIC Educational Resources Information Center
Michelsen, Claus
2015-01-01
Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…
Evaluation of Limb Load Asymmetry Using Two New Mathematical Models
Kumar, Senthil NS; Omar, Baharudin; Joseph, Leonard H.; Htwe, Ohnmar; Jagannathan, K.; Hamdan, Nor M Y; Rajalakshmi, D.
2015-01-01
Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns. PMID:25716372
NASA Astrophysics Data System (ADS)
Ji, S.; Yuan, X.
2016-06-01
A generic probabilistic model, under fundamental Bayes' rule and Markov assumption, is introduced to integrate the process of mobile platform localization with optical sensors. And based on it, three relative independent solutions, bundle adjustment, Kalman filtering and particle filtering are deduced under different and additional restrictions. We want to prove that first, Kalman filtering, may be a better initial-value supplier for bundle adjustment than traditional relative orientation in irregular strips and networks or failed tie-point extraction. Second, in high noisy conditions, particle filtering can act as a bridge for gap binding when a large number of gross errors fail a Kalman filtering or a bundle adjustment. Third, both filtering methods, which help reduce the error propagation and eliminate gross errors, guarantee a global and static bundle adjustment, who requires the strictest initial values and control conditions. The main innovation is about the integrated processing of stochastic errors and gross errors in sensor observations, and the integration of the three most used solutions, bundle adjustment, Kalman filtering and particle filtering into a generic probabilistic localization model. The tests in noisy and restricted situations are designed and examined to prove them.
A Generic Model to Simulate Air-Borne Diseases as a Function of Crop Architecture
Casadebaig, Pierre; Quesnel, Gauthier; Langlais, Michel; Faivre, Robert
2012-01-01
In a context of pesticide use reduction, alternatives to chemical-based crop protection strategies are needed to control diseases. Crop and plant architectures can be viewed as levers to control disease outbreaks by affecting microclimate within the canopy or pathogen transmission between plants. Modeling and simulation is a key approach to help analyze the behaviour of such systems where direct observations are difficult and tedious. Modeling permits the joining of concepts from ecophysiology and epidemiology to define structures and functions generic enough to describe a wide range of epidemiological dynamics. Additionally, this conception should minimize computing time by both limiting the complexity and setting an efficient software implementation. In this paper, our aim was to present a model that suited these constraints so it could first be used as a research and teaching tool to promote discussions about epidemic management in cropping systems. The system was modelled as a combination of individual hosts (population of plants or organs) and infectious agents (pathogens) whose contacts are restricted through a network of connections. The system dynamics were described at an individual scale. Additional attention was given to the identification of generic properties of host-pathogen systems to widen the model's applicability domain. Two specific pathosystems with contrasted crop architectures were considered: ascochyta blight on pea (homogeneously layered canopy) and potato late blight (lattice of individualized plants). The model behavior was assessed by simulation and sensitivity analysis and these results were discussed against the model ability to discriminate between the defined types of epidemics. Crop traits related to disease avoidance resulting in a low exposure, a slow dispersal or a de-synchronization of plant and pathogen cycles were shown to strongly impact the disease severity at the crop scale. PMID:23226209
A generic model to simulate air-borne diseases as a function of crop architecture.
Casadebaig, Pierre; Quesnel, Gauthier; Langlais, Michel; Faivre, Robert
2012-01-01
In a context of pesticide use reduction, alternatives to chemical-based crop protection strategies are needed to control diseases. Crop and plant architectures can be viewed as levers to control disease outbreaks by affecting microclimate within the canopy or pathogen transmission between plants. Modeling and simulation is a key approach to help analyze the behaviour of such systems where direct observations are difficult and tedious. Modeling permits the joining of concepts from ecophysiology and epidemiology to define structures and functions generic enough to describe a wide range of epidemiological dynamics. Additionally, this conception should minimize computing time by both limiting the complexity and setting an efficient software implementation. In this paper, our aim was to present a model that suited these constraints so it could first be used as a research and teaching tool to promote discussions about epidemic management in cropping systems. The system was modelled as a combination of individual hosts (population of plants or organs) and infectious agents (pathogens) whose contacts are restricted through a network of connections. The system dynamics were described at an individual scale. Additional attention was given to the identification of generic properties of host-pathogen systems to widen the model's applicability domain. Two specific pathosystems with contrasted crop architectures were considered: ascochyta blight on pea (homogeneously layered canopy) and potato late blight (lattice of individualized plants). The model behavior was assessed by simulation and sensitivity analysis and these results were discussed against the model ability to discriminate between the defined types of epidemics. Crop traits related to disease avoidance resulting in a low exposure, a slow dispersal or a de-synchronization of plant and pathogen cycles were shown to strongly impact the disease severity at the crop scale. PMID:23226209
A generic model for evaluating payor net cost savings from a disease management program.
McKay, Niccie L
2006-01-01
Private and public payors increasingly are turning to disease management programs as a means of improving the quality of care provided and controlling expenditures for individuals with specific medical conditions. This article presents a generic model that can be adapted to evaluate payor net cost savings from a variety of types of disease management programs, with net cost savings taking into account both changes in expenditures resulting from the program and the costs of setting up and operating the program. The model specifies the required data, describes the data collection process, and shows how to calculate the net cost savings in a spreadsheet format. An accompanying hypothetical example illustrates how to use the model.
NASA Astrophysics Data System (ADS)
Moeini, Ali; Faez, Karim; Moeini, Hossein
2014-09-01
An efficient method for expression-invariant three-dimensional (3-D) face reconstruction from a frontal face image with a variety of facial expressions (FE) using the FE generic elastic model (GEM) is proposed. Three generic models are employed for FE modeling in the generic elastic model (GEM) framework, which are combined based on the similarity distance around the lips. Exclusively, FE-GEM demonstrated that it is more precisely able to estimate a 3-D model of a frontal face, attaining a more robust and better quality 3-D face reconstruction under a variety of FEs compared to the original GEM approach. It is tested on an available 3-D face database and its accuracy and robustness are demonstrated compared to the GEM approach under a variety of FEs. Also, the FE-GEM method is tested on available two-dimensional face databases and a new synthesized pose is generated from gallery images for handling pose variations in face recognition.
Mathematical Modeling of the Induced Mutation Process in Bacterial Cells
NASA Astrophysics Data System (ADS)
Belov, Oleg V.; Krasavin, Evgeny A.; Parkhomenko, Alexander Yu.
2010-01-01
A mathematical model of the ultraviolet (UV) irradiation-induced mutation process in bacterial cells Escherichia coli is developed. Using mathematical approaches, the whole chain of events is tracked from a cell exposure to the damaging factor to mutation formation in the DNA chain. An account of the key special features of the regulation of this genetic network allows predicting the effects induced by the cell exposure to certain UV energy fluence.
Mathematical modeling and physical reality in noncovalent interactions.
Politzer, Peter; Murray, Jane S; Clark, Timothy
2015-03-01
The Hellmann-Feynman theorem provides a straightforward interpretation of noncovalent bonding in terms of Coulombic interactions, which encompass polarization (and accordingly include dispersion). Exchange, Pauli repulsion, orbitals, etc., are part of the mathematics of obtaining the system's wave function and subsequently its electronic density. They do not correspond to physical forces. Charge transfer, in the context of noncovalent interactions, is equivalent to polarization. The key point is that mathematical models must not be confused with physical reality. PMID:25697332
A generic bio-economic farm model for environmental and economic assessment of agricultural systems.
Janssen, Sander; Louhichi, Kamel; Kanellopoulos, Argyris; Zander, Peter; Flichman, Guillermo; Hengsdijk, Huib; Meuter, Eelco; Andersen, Erling; Belhouchette, Hatem; Blanco, Maria; Borkowski, Nina; Heckelei, Thomas; Hecker, Martin; Li, Hongtao; Oude Lansink, Alfons; Stokstad, Grete; Thorne, Peter; van Keulen, Herman; van Ittersum, Martin K
2010-12-01
Bio-economic farm models are tools to evaluate ex-post or to assess ex-ante the impact of policy and technology change on agriculture, economics and environment. Recently, various BEFMs have been developed, often for one purpose or location, but hardly any of these models are re-used later for other purposes or locations. The Farm System Simulator (FSSIM) provides a generic framework enabling the application of BEFMs under various situations and for different purposes (generating supply response functions and detailed regional or farm type assessments). FSSIM is set up as a component-based framework with components representing farmer objectives, risk, calibration, policies, current activities, alternative activities and different types of activities (e.g., annual and perennial cropping and livestock). The generic nature of FSSIM is evaluated using five criteria by examining its applications. FSSIM has been applied for different climate zones and soil types (criterion 1) and to a range of different farm types (criterion 2) with different specializations, intensities and sizes. In most applications FSSIM has been used to assess the effects of policy changes and in two applications to assess the impact of technological innovations (criterion 3). In the various applications, different data sources, level of detail (e.g., criterion 4) and model configurations have been used. FSSIM has been linked to an economic and several biophysical models (criterion 5). The model is available for applications to other conditions and research issues, and it is open to be further tested and to be extended with new components, indicators or linkages to other models. PMID:21113782
A generic bio-economic farm model for environmental and economic assessment of agricultural systems.
Janssen, Sander; Louhichi, Kamel; Kanellopoulos, Argyris; Zander, Peter; Flichman, Guillermo; Hengsdijk, Huib; Meuter, Eelco; Andersen, Erling; Belhouchette, Hatem; Blanco, Maria; Borkowski, Nina; Heckelei, Thomas; Hecker, Martin; Li, Hongtao; Oude Lansink, Alfons; Stokstad, Grete; Thorne, Peter; van Keulen, Herman; van Ittersum, Martin K
2010-12-01
Bio-economic farm models are tools to evaluate ex-post or to assess ex-ante the impact of policy and technology change on agriculture, economics and environment. Recently, various BEFMs have been developed, often for one purpose or location, but hardly any of these models are re-used later for other purposes or locations. The Farm System Simulator (FSSIM) provides a generic framework enabling the application of BEFMs under various situations and for different purposes (generating supply response functions and detailed regional or farm type assessments). FSSIM is set up as a component-based framework with components representing farmer objectives, risk, calibration, policies, current activities, alternative activities and different types of activities (e.g., annual and perennial cropping and livestock). The generic nature of FSSIM is evaluated using five criteria by examining its applications. FSSIM has been applied for different climate zones and soil types (criterion 1) and to a range of different farm types (criterion 2) with different specializations, intensities and sizes. In most applications FSSIM has been used to assess the effects of policy changes and in two applications to assess the impact of technological innovations (criterion 3). In the various applications, different data sources, level of detail (e.g., criterion 4) and model configurations have been used. FSSIM has been linked to an economic and several biophysical models (criterion 5). The model is available for applications to other conditions and research issues, and it is open to be further tested and to be extended with new components, indicators or linkages to other models.
A Generic Bio-Economic Farm Model for Environmental and Economic Assessment of Agricultural Systems
Louhichi, Kamel; Kanellopoulos, Argyris; Zander, Peter; Flichman, Guillermo; Hengsdijk, Huib; Meuter, Eelco; Andersen, Erling; Belhouchette, Hatem; Blanco, Maria; Borkowski, Nina; Heckelei, Thomas; Hecker, Martin; Li, Hongtao; Oude Lansink, Alfons; Stokstad, Grete; Thorne, Peter; van Keulen, Herman; van Ittersum, Martin K.
2010-01-01
Bio-economic farm models are tools to evaluate ex-post or to assess ex-ante the impact of policy and technology change on agriculture, economics and environment. Recently, various BEFMs have been developed, often for one purpose or location, but hardly any of these models are re-used later for other purposes or locations. The Farm System Simulator (FSSIM) provides a generic framework enabling the application of BEFMs under various situations and for different purposes (generating supply response functions and detailed regional or farm type assessments). FSSIM is set up as a component-based framework with components representing farmer objectives, risk, calibration, policies, current activities, alternative activities and different types of activities (e.g., annual and perennial cropping and livestock). The generic nature of FSSIM is evaluated using five criteria by examining its applications. FSSIM has been applied for different climate zones and soil types (criterion 1) and to a range of different farm types (criterion 2) with different specializations, intensities and sizes. In most applications FSSIM has been used to assess the effects of policy changes and in two applications to assess the impact of technological innovations (criterion 3). In the various applications, different data sources, level of detail (e.g., criterion 4) and model configurations have been used. FSSIM has been linked to an economic and several biophysical models (criterion 5). The model is available for applications to other conditions and research issues, and it is open to be further tested and to be extended with new components, indicators or linkages to other models. PMID:21113782
Mathematical Modeling and the Redesign of a Teaching Ambulatory Clinic
ERIC Educational Resources Information Center
Baker, Duke H.; Mamlin, Joseph
1976-01-01
Mathematical modeling was utilized in the planning and decision-making process involved in reorganizing a teaching clinic to effect continuity of care. The model interrelated physicians, time, and space, facilitating value judgments and decisions. The reorganization was successful and the outcomes remarkably similar to model predictions.…
Mathematical Modelling in Physics and Engineering--Part 2.
ERIC Educational Resources Information Center
Oke, K. H.; Jones, A. L.
1982-01-01
Mathematical modelling and an example used with undergraduates were presented in part 1 (v17, n5, p212-18, 1982). A second example, Power from Windmills, is provided which has considerable potential for development both as a model and as a series of modelling experiences of increasing difficulty for students with different backgrounds. (Author/JN)
An Introduction to Mathematical Modelling for Ecologists and Environmental Scientists.
ERIC Educational Resources Information Center
Smith, I. R.; Henderson-Sellers, B.
1981-01-01
Describes the basic philosophy, nomenclature, and techniques used in mathematical modelling to enable biologists, engineers, land managers, and others to understand the concepts and usefulness of models. Contrasts conceptual and empirical approaches, using ecosystem models as an example of the former. (DC)
Validation and upgrading of physically based mathematical models
NASA Technical Reports Server (NTRS)
Duval, Ronald
1992-01-01
The validation of the results of physically-based mathematical models against experimental results was discussed. Systematic techniques are used for: (1) isolating subsets of the simulator mathematical model and comparing the response of each subset to its experimental response for the same input conditions; (2) evaluating the response error to determine whether it is the result of incorrect parameter values, incorrect structure of the model subset, or unmodeled external effects of cross coupling; and (3) modifying and upgrading the model and its parameter values to determine the most physically appropriate combination of changes.
A Review on Mathematical Modeling for Textile Processes
NASA Astrophysics Data System (ADS)
Chattopadhyay, R.
2015-10-01
Mathematical model is a powerful tool in engineering for studying variety of problems related to design and development of products and processes, optimization of manufacturing process, understanding a phenomenon and predicting product's behaviour in actual use. An insight of the process and use of appropriate mathematical tools are necessary for developing models. In the present paper, a review of types of model, procedure followed in developing them and their limitations have been discussed. Modeling techniques being used in few textile processes available in the literature have been cited as examples.
A mathematical model for evolution and SETI.
Maccone, Claudio
2011-12-01
Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.
A Mathematical Model for Evolution and SETI
NASA Astrophysics Data System (ADS)
Maccone, Claudio
2011-12-01
Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.
A mathematical model for evolution and SETI.
Maccone, Claudio
2011-12-01
Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation. PMID:22139521
An Integrated Used Fuel Disposition and Generic Repository Model for Fuel Cycle Analysis
NASA Astrophysics Data System (ADS)
Huff, Kathryn D.
As the United States and other nuclear nations consider alternative fuel cycles and waste disposal options simultaneously, an integrated fuel cycle and generic disposal system analysis tool grows increasingly necessary for informing spent nuclear fuel management policy. The long term performance characteristics of deep geologic disposal concepts are affected by heat and radionuclide release characteristics sensitive to disposal system choices as well as variable spent fuel compositions associated with alternative fuel cycles. Computational tools capable of simulating the dynamic, heterogeneous spent fuel isotopics resulting from alternative nuclear fuel cycles and fuel cycle transition scenarios are, however, lacking in disposal system modeling options. This work has resulted in Cyder, a generic repository software library appropriate for system analysis of potential future fuel cycle deployment scenarios. By emphasizing modularity and speed, Cyder is capable of representing the dominant physics of candidate geologic host media, repository designs, and engineering components. Robust and flexible integration with the Cyclus fuel cycle simulator enables this analysis in the context of fuel cycle options.
Far field pacing supersedes anti-tachycardia pacing in a generic model of excitable media
NASA Astrophysics Data System (ADS)
Bittihn, Philip; Luther, Gisela; Bodenschatz, Eberhard; Krinsky, Valentin; Parlitz, Ulrich; Luther, Stefan
2008-10-01
Removing anchored spirals from obstacles is an important step in terminating cardiac arrhythmia. Conventional anti-tachycardia pacing (ATP) has this ability, but only under very restrictive conditions. In a generic model of excitable media, we demonstrate that for unpinning spiral waves from obstacles this profound limitation of ATP can be overcome by far field pacing (FFP). More specifically, an argument is presented for why FFP includes and thus can only extend the capabilities of ATP in the configurations considered. By numerical simulations, we show that in the model there exists a parameter region in which unpinning is possible by FFP but not by ATP. The relevance of this result regarding clinical applications is discussed.
The Concept of Model. What is Remarkable in Mathematical Models
NASA Astrophysics Data System (ADS)
Bezruchko, Boris P.; Smirnov, Dmitry A.
Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.
Mathematical model of layered metallurgical furnaces and units
NASA Astrophysics Data System (ADS)
Shvydkiy, V. S.; Spirin, N. A.; Lavrov, V. V.
2016-09-01
The basic approaches to mathematical modeling of the layered steel furnaces and units are considered. It is noted that the particular importance have the knowledge about the mechanisms and physical nature of processes of the charge column movement and the gas flow in the moving layer, as well as regularities of development of heat- and mass-transfer in them. The statement and mathematical description of the problem solution targeting the potential gas flow in the layered unit of an arbitrary profile are presented. On the basis of the proposed mathematical model the software implementation of information-modeling system of BF gas dynamics is carried out. The results of the computer modeling of BF non-isothermal gas dynamics with regard to the cohesion zone, gas dynamics of the combustion zone and calculation of hot-blast stoves are provided
An agent-based mathematical model about carp aggregation
NASA Astrophysics Data System (ADS)
Liang, Yu; Wu, Chao
2005-05-01
This work presents an agent-based mathematical model to simulate the aggregation of carp, a harmful fish in North America. The referred mathematical model is derived from the following assumptions: (1) instead of the consensus among every carps involved in the aggregation, the aggregation of carp is completely a random and spontaneous physical behavior of numerous of independent carp; (2) carp aggregation is a collective effect of inter-carp and carp-environment interaction; (3) the inter-carp interaction can be derived from the statistical analytics about large-scale observed data. The proposed mathematical model is mainly based on empirical inter-carp force field, whose effect is featured with repulsion, parallel orientation, attraction, out-of-perception zone, and blind. Based on above mathematical model, the aggregation behavior of carp is formulated and preliminary simulation results about the aggregation of small number of carps within simple environment are provided. Further experiment-based validation about the mathematical model will be made in our future work.
Meille, Christophe; Barbolosi, Dominique; Ciccolini, Joseph; Freyer, Gilles; Iliadis, Athanassios
2016-08-01
Controlling effects of drugs administered in combination is particularly challenging with a densified regimen because of life-threatening hematological toxicities. We have developed a mathematical model to optimize drug dosing regimens and to redesign the dose intensification-dose escalation process, using densified cycles of combined anticancer drugs. A generic mathematical model was developed to describe the main components of the real process, including pharmacokinetics, safety and efficacy pharmacodynamics, and non-hematological toxicity risk. This model allowed for computing the distribution of the total drug amount of each drug in combination, for each escalation dose level, in order to minimize the average tumor mass for each cycle. This was achieved while complying with absolute neutrophil count clinical constraints and without exceeding a fixed risk of non-hematological dose-limiting toxicity. The innovative part of this work was the development of densifying and intensifying designs in a unified procedure. This model enabled us to determine the appropriate regimen in a pilot phase I/II study in metastatic breast patients for a 2-week-cycle treatment of docetaxel plus epirubicin doublet, and to propose a new dose-ranging process. In addition to the present application, this method can be further used to achieve optimization of any combination therapy, thus improving the efficacy versus toxicity balance of such a regimen.
Redundancy management of electrohydraulic servoactuators by mathematical model referencing
NASA Technical Reports Server (NTRS)
Campbell, R. A.
1971-01-01
A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.
Dependability breakeven point mathematical model for production - quality strategy support
NASA Astrophysics Data System (ADS)
Vilcu, Adrian; Verzea, Ion; Chaib, Rachid
2016-08-01
This paper connects the field of dependability system with the production-quality strategies through a new mathematical model based on breakeven points. The novelties consist in the identification of the parameters of dependability system which, in safety control, represents the degree to which an item is capable of performing its required function at any randomly chosen time during its specified operating period disregarding non-operation related influences, as well as the analysis of the production-quality strategies, defining a mathematical model based on a new concept - dependability breakeven points, model validation on datasets and shows the practical applicability of this new approach.
Applicability of mathematical modeling to problems of environmental physiology
NASA Technical Reports Server (NTRS)
White, Ronald J.; Lujan, Barbara F.; Leonard, Joel I.; Srinivasan, R. Srini
1988-01-01
The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.
The Singing Wineglass: An Exercise in Mathematical Modelling
ERIC Educational Resources Information Center
Voges, E. L.; Joubert, S. V.
2008-01-01
Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…
Mathematical models of ABE fermentation: review and analysis.
Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S
2013-12-01
Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities. PMID:23072615
Mathematical models of ABE fermentation: review and analysis.
Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S
2013-12-01
Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.
Metaphors and Models in Translation between College and Workplace Mathematics
ERIC Educational Resources Information Center
Williams, Julian; Wake, Geoff
2007-01-01
We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…
Mitochondrial DNA damage and efficiency of ATP biosynthesis: mathematical model.
Beregovskaya, N; Maiboroda, R
1995-01-21
The role of mitochondrial DNA (mtDNA) damage in ageing processes and in malignant transformation of a cell is discussed. A mathematical model of the mtDNA population in a cell and in tissue is constructed. The model describes the effects of mtDNA damages accumulated during ageing and some features of malignant transformation and regeneration.
PARCC Model Content Frameworks: Mathematics--Grades 3-11
ERIC Educational Resources Information Center
Partnership for Assessment of Readiness for College and Careers (NJ1), 2011
2011-01-01
As part of its proposal to the U.S. Department of Education, the Partnership for Assessment of Readiness for College and Careers (PARCC) committed to developing model content frameworks for mathematics to serve as a bridge between the Common Core State Standards and the PARCC assessments. The PARCC Model Content Frameworks were developed through a…
Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration
ERIC Educational Resources Information Center
Warwick, Jon
2015-01-01
This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…
Mathematical model of an air-filled alpha stirling refrigerator
NASA Astrophysics Data System (ADS)
McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir
2013-10-01
This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.
A generic, process-based model of microbial pollution in aquatic systems
NASA Astrophysics Data System (ADS)
Hipsey, Matthew R.; Antenucci, Jason P.; Brookes, Justin D.
2008-07-01
Based on a comprehensive synthesis of data available within the literature, a new process-based model of microbial pollution is presented, which is applicable for surface and coastal waters. The model is based on a generic set of parameterisations that describe the dynamics of most protozoan, bacterial and viral organisms of interest, including pathogens and microbial indicator organisms. The parameterisations dynamically account for the effects of temperature, salinity, pH, dissolved oxygen, sunlight, nutrients and turbidity on the growth and mortality of enteric organisms. Parameters for a range of organisms are also presented which are based on collation of literature data. The model has been implemented within an aquatic ecology model, Computational Aquatic Ecosystem Dynamics Model (CAEDYM), which can couple to multidimensional hydrodynamic models. Without adjustment of the literature derived parameter values, a 3-D implementation is validated against observed data from three freshwater systems that differ in their climatic zone, trophic status and operation. The simulations highlight the spatial and temporal variability that may be encountered by operators. Additionally, large differences in the fate and distribution of different species originate from variable rates of growth, mortality and sedimentation and it is emphasized that the use of surrogates for quantifying risk is problematic. The model can be used to help design targeted monitoring programs, explore differences between species, and to support real-time decision-making. Areas where insufficient understanding and data exist are discussed.
The analysis of a generic air-to-air missile simulation model
NASA Technical Reports Server (NTRS)
Kaplan, Joseph A.; Chappell, Alan R.; Mcmanus, John W.
1994-01-01
A generic missile model was developed to evaluate the benefits of using a dynamic missile fly-out simulation system versus a static missile launch envelope system for air-to-air combat simulation. This paper examines the performance of a launch envelope model and a missile fly-out model. The launch envelope model bases its probability of killing the target aircraft on the target aircraft's position at the launch time of the weapon. The benefits gained from a launch envelope model are the simplicity of implementation and the minimal computational overhead required. A missile fly-out model takes into account the physical characteristics of the missile as it simulates the guidance, propulsion, and movement of the missile. The missile's probability of kill is based on the missile miss distance (or the minimum distance between the missile and the target aircraft). The problems associated with this method of modeling are a larger computational overhead, the additional complexity required to determine the missile miss distance, and the additional complexity of determining the reason(s) the missile missed the target. This paper evaluates the two methods and compares the results of running each method on a comprehensive set of test conditions.
Mathematical models of regulatory mechanisms of sleep-wake rhythms.
Nakao, M; Karashima, A; Katayama, N
2007-05-01
Studies of regulatory mechanisms of sleep-wake rhythms have benefited greatly from mathematical modeling. There are two major frameworks of modeling: one integrates homeostatic and circadian regulations and the other consists of multiple interacting oscillators. In this article, model constructions based on these respective frameworks and their characteristics are reviewed. The two-process model and the multioscillator model are explained in detail. An appropriate mathematical abstraction is also shown to provide a viewpoint unifying the model structures, which might seem to be distinct. Recently acquired knowledge of neural regulatory mechanisms of sleep-wake rhythm has prompted modeling at the neural network level. Such a detailed model is also reviewed, and could be used to explore a possible neural mechanism underlying a pathological state of sleep-wake rhythm. PMID:17364138
A minimal generic model of bacteria-induced intracellular Ca2+ oscillations in epithelial cells.
Oxhamre, Camilla; Richter-Dahlfors, Agneta; Zhdanov, Vladimir P; Kasemo, Bengt
2005-04-01
The toxin alpha-hemolysin expressed by uropathogenic Escherichia coli bacteria was recently shown as the first pathophysiologically relevant protein to induce oscillations of the intracellular Ca(2+) concentration in target cells. Here, we propose a generic three-variable kinetic model describing the Ca(2+) oscillations induced in single rat renal epithelial cells by this toxin. Specifically, we take into account the interplay between 1), the cytosolic Ca(2+) concentration; 2), IP(3)-sensitive Ca(2+) channels located in the membrane separating the cytosol and endoplasmic reticulum; and 3), toxin-related activation of production of IP(3) by phospholipase C. With these ingredients, the predicted response of cells exposed to the toxin is in good agreement with the results of experiments.
Membrane-Protein Interactions in a Generic Coarse-Grained Model for Lipid Bilayers
West, Beate; Brown, Frank L.H.; Schmid, Friederike
2009-01-01
Abstract We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deformation profiles of membranes around single proteins. However, its prediction for the potential of mean force between proteins is not compatible with the simulation data for large distances. The simulations show that the lipid-mediated interactions are governed by five competing factors: direct interactions; lipid-induced depletion interactions; lipid bridging; lipid packing; and a smooth long-range contribution. The mechanisms leading to hydrophobic mismatch interactions are critically analyzed. PMID:18835907
Loads and Performance Data from a Wind-Tunnel Test of Generic Model Helicopter Rotor Blades
NASA Technical Reports Server (NTRS)
Yeager, William T., Jr.; Wilbur, Matthew L.
2005-01-01
An investigation was conducted in the NASA Langley Transonic Dynamics Tunnel to acquire data for use in assessing the ability of current and future comprehensive analyses to predict helicopter rotating-system and fixed-system vibratory loads. The investigation was conducted with a generic model helicopter rotor system using blades with rectangular planform, no built-in twist, uniform radial distribution of mass and stiffnesses, and a NACA 0012 airfoil section. Rotor performance data, as well as mean and vibratory components of blade bending and torsion moments, fixed-system forces and moments, and pitch link loads were obtained at advance ratios up to 0.35 for various combinations of rotor shaft angle-of-attack and collective pitch. The data are presented without analysis.
Higher order direct model reference adaptive control with generic uniform ultimate boundedness
NASA Astrophysics Data System (ADS)
Maity, Arnab; Höcht, Leonhard; Holzapfel, Florian
2015-10-01
This paper proposes a new higher order model reference adaptive control (HO-MRAC) approach following direct adaptive control philosophy, which estimates unknown time-varying parameters. This approach leads to a Lyapunov based conventional MRAC update law, augmented by an observer type parameter predictor dynamics. The predictor dynamics are composed of a stable known part, a feedback of the parameter error and unknown higher order parameters, which are updated using a Lyapunov based adaptive design. So, this HO-MRAC can cope with rapidly changing parameters, due to estimation of their time derivatives. Moreover, for stability analysis, a Lyapunov based generic ultimate boundedness theorem is presented, which allows for a computation of separate bounds for each state vector partition. Furthermore, this theorem formulates the explicit specification of transient and ultimate bounds, reaching time on the ultimate bounds and a set of admissible initial conditions. Two challenging illustrative examples demonstrate the effectiveness of the proposed approach.
Modeling eBook acceptance: A study on mathematics teachers
NASA Astrophysics Data System (ADS)
Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad
2014-12-01
The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.
A full body mathematical model of an oil palm harvester
NASA Astrophysics Data System (ADS)
Tumit, NP; Rambely, A. S.; BMT, Shamsul; Shahriman A., B.; Ng Y., G.; Deros, B. M.; Zailina, H.; Goh Y., M.; Arumugam, Manohar; Ismail I., A.; Abdul Hafiz A., R.
2015-09-01
The main purpose of this article is to develop a mathematical model of human body during harvesting via Kane's method. This paper is an extension model of previous biomechanical model representing a harvester movement during harvesting a Fresh Fruit Bunch (FFB) from a palm oil tree. The ten segment model consists of foot, leg, trunk, the head and the arms segment. Finally, the inverse dynamic equations are represented in a matrix form.
Mathematically modelling proportions of Japanese populations by industry
NASA Astrophysics Data System (ADS)
Hirata, Yoshito
2016-10-01
I propose a mathematical model for temporal changes of proportions for industrial sectors. I prove that the model keeps the proportions for the primary, the secondary, and the tertiary sectors between 0 and 100% and preserves their total as 100%. The model fits the Japanese historical data between 1950 and 2005 for the population proportions by industry very well. The model also predicts that the proportion for the secondary industry becomes negligible and becomes less than 1% at least around 2080.
Mathematical model of the SH-3G helicopter
NASA Technical Reports Server (NTRS)
Phillips, J. D.
1982-01-01
A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.
Mathematical modelling of undrained clay behavior
NASA Technical Reports Server (NTRS)
Prevost, J. H.; Noeg, K.
1976-01-01
The proposed general analytical model describes the anisotropic, elastoplastic, path-dependent, stress-strain properties of inviscid saturated clays under undrained conditions. Model parameters are determined by using results from strain-controlled simple shear tests on a saturated clay. The model's accuracy is evaluated by applying it to predict the results of other tests on the same clay, including monotonic and cyclic loading. The model explains the very anisotropic shear strength behavior observed for weak marine clays.
Mathematical models of magnetite desliming for automated quality control systems
NASA Astrophysics Data System (ADS)
Olevska, Yu.; Mishchenko, V.; Olevskyi, V.
2016-10-01
The aim of the study is to provide multifactor mathematical models suitable for use in automatic control systems of desliming process. For this purpose we described the motion of a two-phase environment regard to the shape the desliming machine and technological parameters of the enrichment process. We created the method for preparation of dependences of the enrichment process quality from the technological and design parameters. To automate the process we constructed mathematical models to justify intensive technological modes and optimal parameters for design of desliming machine.
Asymmetrical passive intermodulation distortions of memristors with mathematical behavior models
NASA Astrophysics Data System (ADS)
Wu, Yongle; Jin, Qiuyan; Wang, Weimin; Liu, Yuanan
2016-10-01
A rigorous mathematical explanation and accurate numerical prediction for asymmetrical passive intermodulation (PIM) distortions of memristors are investigated in this article. This theoretical explanation is based on behavior models of memristors representing the interrelation between terminated voltages and currents. The simulated single-tone and two-tone signal spectrums for extremely low-frequency (Hz) and microwave (GHz) applications verify our proposed mathematical approach and the new discovery of asymmetrical PIM distortions. This presented method provides an innovative choice to model and simulate the external performance of circuits and systems with asymmetrical PIM distortions in the future.
Mathematical modelling in the computer-aided process planning
NASA Astrophysics Data System (ADS)
Mitin, S.; Bochkarev, P.
2016-04-01
This paper presents new approaches to organization of manufacturing preparation and mathematical models related to development of the computer-aided multi product process planning (CAMPP) system. CAMPP system has some peculiarities compared to the existing computer-aided process planning (CAPP) systems: fully formalized developing of the machining operations; a capacity to create and to formalize the interrelationships among design, process planning and process implementation; procedures for consideration of the real manufacturing conditions. The paper describes the structure of the CAMPP system and shows the mathematical models and methods to formalize the design procedures.
A mathematical look at a physical power prediction model
Landberg, L.
1997-12-31
This paper takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations, and to give guidelines as to where the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.
Mathematical model in controlling dengue transmission with sterile mosquito strategies
NASA Astrophysics Data System (ADS)
Aldila, D.; Nuraini, N.; Soewono, E.
2015-09-01
In this article, we propose a mathematical model for controlling dengue disease transmission with sterile mosquito techniques (SIT). Sterile male introduced from lab in to habitat to compete with wild male mosquito for mating with female mosquito. Our aim is to displace gradually the natural mosquito from the habitat. Mathematical model analysis for steady states and the basic reproductive ratio are performed analytically. Numerical simulation are shown in some different scenarios. We find that SIT intervention is potential to controlling dengue spread among humans population
NASA Astrophysics Data System (ADS)
Weerts, A.; van Velzen, N.; Verlaan, M.; Sumihar, J.; Hummel, S.; El Serafy, G.; Dhondia, J.; Gerritsen, H.; Vermeer-Ooms, S.; Loots, E.; Markus, A.; Kockx, A.
2011-12-01
Data Assimilation techniques are essential elements in state-of-the-art development of models and their use in operational forecasting and real-time control in the fields of groundwater, surface water and soil systems. In meteorological and atmospheric sciences, steady improvements in numerical weather forecasting and climate prediction over the last couple of decades have been enabled to a large degree by the development of community-based models and data assimilation systems. The hydrologic community should learn from the experiences of the meteorological and atmospheric communities by accelerating the transition of hydrologic DA research into operations and developing community-supported, open-source modeling and forecasting systems and data assimilation tools. In 2010, a community based open source initiative named OpenDA was started. The openDA initiative bears similarities with the well-known openMI initiative. OpenDA makes use of a set of interfaces that describe the interaction between models, observations and data assimilation algorithms. It focuses on flexible applications in portable systems for modeling geophysical processes. It provides a generic interfacing protocol that allows combination of the implemented data assimilation techniques with, in principle, any time-stepping model describing a process (atmospheric processes, 3D circulation, 2D water flow, rainfall-runoff, unsaturated flow, groundwater flow, etc.). Presently, openDA features filtering techniques and calibration techniques. The presentation will give an overview of openDA and the results of some of its practical applications.
Enhancement of Generic Building Models by Recognition and Enforcement of Geometric Constraints
NASA Astrophysics Data System (ADS)
Meidow, J.; Hammer, H.; Pohl, M.; Bulatov, D.
2016-06-01
Many buildings in 3D city models can be represented by generic models, e.g. boundary representations or polyhedrons, without expressing building-specific knowledge explicitly. Without additional constraints, the bounding faces of these building reconstructions do not feature expected structures such as orthogonality or parallelism. The recognition and enforcement of man-made structures within model instances is one way to enhance 3D city models. Since the reconstructions are derived from uncertain and imprecise data, crisp relations such as orthogonality or parallelism are rarely satisfied exactly. Furthermore, the uncertainty of geometric entities is usually not specified in 3D city models. Therefore, we propose a point sampling which simulates the initial point cloud acquisition by airborne laser scanning and provides estimates for the uncertainties. We present a complete workflow for recognition and enforcement of man-made structures in a given boundary representation. The recognition is performed by hypothesis testing and the enforcement of the detected constraints by a global adjustment of all bounding faces. Since the adjustment changes not only the geometry but also the topology of faces, we obtain improved building models which feature regular structures and a potentially reduced complexity. The feasibility and the usability of the approach are demonstrated with a real data set.
A generic biokinetic model for noble gases with application to radon.
Leggett, Rich; Marsh, James; Gregoratto, Demetrio; Blanchardon, Eric
2013-06-01
To facilitate the estimation of radiation doses from intake of radionuclides, the International Commission on Radiological Protection (ICRP) publishes dose coefficients (dose per unit intake) based on reference biokinetic and dosimetric models. The ICRP generally has not provided biokinetic models or dose coefficients for intake of noble gases, but plans to provide such information for (222)Rn and other important radioisotopes of noble gases in a forthcoming series of reports on occupational intake of radionuclides (OIR). This paper proposes a generic biokinetic model framework for noble gases and develops parameter values for radon. The framework is tailored to applications in radiation protection and is consistent with a physiologically based biokinetic modelling scheme adopted for the OIR series. Parameter values for a noble gas are based largely on a blood flow model and physical laws governing transfer of a non-reactive and soluble gas between materials. Model predictions for radon are shown to be consistent with results of controlled studies of its biokinetics in human subjects. PMID:23612507
Dark matter direct detection rate in a generic model with micrOMEGAs_2.2
NASA Astrophysics Data System (ADS)
Bélanger, G.; Boudjema, F.; Pukhov, A.; Semenov, A.
2009-05-01
We present a new module of the micrOMEGAs package for the calculation of WIMP-nuclei elastic scattering cross sections relevant for the direct detection of dark matter through its interaction with nuclei in a large detector. With this new module, the computation of the direct detection rate is performed automatically for a generic model of new physics which contains a WIMP candidate. This model needs to be implemented within micrOMEGAs 2.2. Program summaryProgram title: micrOMEGAs2.2 Catalogue identifier: ADQR_v2_2 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADQR_v2_2.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 206 949 No. of bytes in distributed program, including test data, etc.: 2 245 230 Distribution format: tar.gz Programming language: C and Fortran Computer: PC, Alpha, Mac Operating system: UNIX (Linux, OSF1, Darwin, Cygwin) RAM: 17 MB depending on the number of processes required Classification: 1.9, 11.6 Catalogue identifier of previous version: ADQR_v2_1 Journal reference of previous version: Comput. Phys. Comm. 177 (2007) 894 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the relic density and of direct and indirect detection rates of the lightest stable particle in a generic new model of particle physics. Solution method: In numerically solving the evolution equation for the density of darkmatter, relativistic formulae for the thermal average are used. All tree-level processes for annihilation and coannihilation of new particles in the model are included. The cross-sections for all processes are calculated exactly with CalcHEP after definition of a model file. Higher-order QCD corrections to Higgs couplings to quark pairs are included. The coefficients of the effective Lagrangian which describes the
Mathematical modeling and the neuroscience of metaphor
NASA Astrophysics Data System (ADS)
Rising, Hawley K., III
2008-02-01
We look at a characterization of metaphor from cognitive linguistics, extracting the salient features of metaphorical processing. We examine the neurobiology of dendrites, specifically spike timing-dependent plasticity (STDP), and the modulation of backpropagating action potentials (bAPs), to generate a neuropil-centric model of cortical processing based on signal timing and reverberation between regions. We show how this model supports the basic features of metaphorical processing previously extracted. Finally, we model this system using a combination of euclidean, projective, and hyperbolic geometries, and show how the resulting model accounts for this processing, and relates to other neural network models
An applied mathematics perspective on stochastic modelling for climate.
Majda, Andrew J; Franzke, Christian; Khouider, Boualem
2008-07-28
Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new low-dimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here. PMID:18445572
On correct mathematical models of ecological LSS of high closure
NASA Astrophysics Data System (ADS)
Bartsev, S. I.
Usually mathematical models of natural ecological systems are implicitly based on the assumption of stoichiometrically rigid metabolism In most cases such assumption is applicable but in the case of ecological systems of high closure it can cause errors of forecast For completely closed ecological system the assumption of rigid metabolism results in completely incorrect forecast Since CELSS for long-duration missions have to be of high closure then using adequate mathematical description is of great importance for successfulness of a space mission Possible variants of non-rigid metabolism applicable to different type of biological components of CELSS are considered in the paper It is shown non-rigid models of metabolism not only eliminate incorrectness of mathematical description but as well allow to obtain more adequate estimation of stability of closed ecological systems
NASA Astrophysics Data System (ADS)
Schmidt, Patricia; Ohme, Frank; Hannam, Mark
2015-01-01
Gravitational waves (GWs) emitted by generic black-hole binaries show a rich structure that directly reflects the complex dynamics introduced by the precession of the orbital plane, which poses a real challenge to the development of generic waveform models. Recent progress in modelling these signals relies on an approximate decoupling between the nonprecessing secular inspiral and a precession-induced rotation. However, the latter depends in general on all physical parameters of the binary which makes modelling efforts as well as understanding parameter-estimation prospects prohibitively complex. Here we show that the dominant precession effects can be captured by a reduced set of spin parameters. Specifically, we introduce a single effective precession spin parameter, χp, which is defined from the spin components that lie in the orbital plane at some (arbitrary) instant during the inspiral. We test the efficacy of this parameter by considering binary inspiral configurations specified by the physical parameters of a corresponding nonprecessing-binary configuration (total mass, mass ratio, and spin components (anti)parallel to the orbital angular momentum), plus the effective precession spin applied to the larger black hole. We show that for an overwhelming majority of random precessing configurations, the precession dynamics during the inspiral are well approximated by our equivalent configurations. Our results suggest that in the comparable-mass regime waveform models with only three spin parameters faithfully represent generic waveforms, which has practical implications for the prospects of GW searches, parameter estimation and the numerical exploration of the precessing-binary parameter space.
Mathematical modeling of the human knee joint
Ricafort, Juliet
1996-05-01
A model was developed to determine the forces exerted by several flexor and extensor muscles of the human knee under static conditions. The following muscles were studied: the gastrocnemius, biceps femoris, semitendinosus, semimembranosus, and the set of quadricep muscles. The tibia and fibula were each modeled as rigid bodies; muscles were modeled by their functional lines of action in space. Assumptions based on previous data were used to resolve the indeterminacy.
Mathematical modeling of lithium iodine discharge data
Kim, J.S.; Brennen, K.R.
1980-01-01
An improved numerical model has been developed to project the capacities of Li/I/sub 2/ cardiac pacemaker batteries. The model uses accelerated rate discharge data, collected over a two year period, to project the capacities of batteries that will not be depleted in the field for approximately 8 years. Inclusion of new terms to account for self-discharge results in increased accuracy in this new model. Self-discharge is shown to be a small loss in the batteries modeled. 3 refs.
NASA Technical Reports Server (NTRS)
Hueschen, Richard M.
2011-01-01
A six degree-of-freedom, flat-earth dynamics, non-linear, and non-proprietary aircraft simulation was developed that is representative of a generic mid-sized twin-jet transport aircraft. The simulation was developed from a non-proprietary, publicly available, subscale twin-jet transport aircraft simulation using scaling relationships and a modified aerodynamic database. The simulation has an extended aerodynamics database with aero data outside the normal transport-operating envelope (large angle-of-attack and sideslip values). The simulation has representative transport aircraft surface actuator models with variable rate-limits and generally fixed position limits. The simulation contains a generic 40,000 lb sea level thrust engine model. The engine model is a first order dynamic model with a variable time constant that changes according to simulation conditions. The simulation provides a means for interfacing a flight control system to use the simulation sensor variables and to command the surface actuators and throttle position of the engine model.
Undergraduate Research: Mathematical Modeling of Mortgages
ERIC Educational Resources Information Center
Choi, Youngna; Spero, Steven
2010-01-01
In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current…
A Mathematical Model for Segmenting ECG Signals
NASA Astrophysics Data System (ADS)
Feier, Horea; Roşu, Doina; Falniţǎ, Lucian; Roşu, Şerban; Pater, Liana
2010-09-01
This paper deals with the behavior of the modulus of the continuous wavelet transform (CWT) for some known mother wavelets like the Morlet wavelet and the Mexican Hat. By exploiting these properties, the models presented can behave as a segmentation/ recognition signal processing tool by modeling the temporal structure of the observed surface ECG.
A mathematical model of intestinal oedema formation.
Young, Jennifer; Rivière, Béatrice; Cox, Charles S; Uray, Karen
2014-03-01
Intestinal oedema is a medical condition referring to the build-up of excess fluid in the interstitial spaces of the intestinal wall tissue. Intestinal oedema is known to produce a decrease in intestinal transit caused by a decrease in smooth muscle contractility, which can lead to numerous medical problems for the patient. Interstitial volume regulation has thus far been modelled with ordinary differential equations, or with a partial differential equation system where volume changes depend only on the current pressure and not on updated tissue stress. In this work, we present a computational, partial differential equation model of intestinal oedema formation that overcomes the limitations of past work to present a comprehensive model of the phenomenon. This model includes mass and momentum balance equations which give a time evolution of the interstitial pressure, intestinal volume changes and stress. The model also accounts for the spatially varying mechanical properties of the intestinal tissue and the inhomogeneous distribution of fluid-leaking capillaries that create oedema. The intestinal wall is modelled as a multi-layered, deforming, poroelastic medium, and the system of equations is solved using a discontinuous Galerkin method. To validate the model, simulation results are compared with results from four experimental scenarios. A sensitivity analysis is also provided. The model is able to capture the final submucosal interstitial pressure and total fluid volume change for all four experimental cases, and provide further insight into the distribution of these quantities across the intestinal wall.
Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.
Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław
2015-07-22
A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform. PMID:26120897
Molecular modeling: An open invitation for applied mathematics
NASA Astrophysics Data System (ADS)
Mezey, Paul G.
2013-10-01
Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.
Cancer evolution: mathematical models and computational inference.
Beerenwinkel, Niko; Schwarz, Roland F; Gerstung, Moritz; Markowetz, Florian
2015-01-01
Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy.
Cancer Evolution: Mathematical Models and Computational Inference
Beerenwinkel, Niko; Schwarz, Roland F.; Gerstung, Moritz; Markowetz, Florian
2015-01-01
Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy. PMID:25293804
Mathematical analysis and numerical simulation of a model of morphogenesis.
Muñoz, Ana I; Tello, José Ignacio
2011-10-01
We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters.
Automatic mathematical modeling for real time simulation system
NASA Technical Reports Server (NTRS)
Wang, Caroline; Purinton, Steve
1988-01-01
A methodology for automatic mathematical modeling and generating simulation models is described. The models will be verified by running in a test environment using standard profiles with the results compared against known results. The major objective is to create a user friendly environment for engineers to design, maintain, and verify their model and also automatically convert the mathematical model into conventional code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine Simulation. It is written in LISP and MACSYMA and runs on a Symbolic 3670 Lisp Machine. The program provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. It 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. The system is then able to automatically generate the model and FORTRAN code. The future goal which is under construction is to download the FORTRAN code to VAX/VMS system for conventional computation. The SSME mathematical model will be verified in a test environment and the solution compared with the real data profile. The use of artificial intelligence techniques has shown that the process of the simulation modeling can be simplified.
Physical and Mathematical Modeling in Experimental Papers.
Möbius, Wolfram; Laan, Liedewij
2015-12-17
An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations.
A Mathematical Model for Railway Control Systems
NASA Technical Reports Server (NTRS)
Hoover, D. N.
1996-01-01
We present a general method for modeling safety aspects of railway control systems. Using our modeling method, one can progressively refine an abstract railway safety model, sucessively adding layers of detail about how a real system actually operates, while maintaining a safety property that refines the original abstract safety property. This method supports a top-down approach to specification of railway control systems and to proof of a variety of safety-related properties. We demonstrate our method by proving safety of the classical block control system.
Physical and Mathematical Modeling in Experimental Papers.
Möbius, Wolfram; Laan, Liedewij
2015-12-17
An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations. PMID:26687351
A predator-prey model with generic birth and death rates for the predator.
Terry, Alan J
2014-02-01
We propose and study a predator-prey model in which the predator has a Holling type II functional response and generic per capita birth and death rates. Given that prey consumption provides the energy for predator activity, and that the predator functional response represents the prey consumption rate per predator, we assume that the per capita birth and death rates for the predator are, respectively, increasing and decreasing functions of the predator functional response. These functions are monotonic, but not necessarily strictly monotonic, for all values of the argument. In particular, we allow the possibility that the predator birth rate is zero for all sufficiently small values of the predator functional response, reflecting the idea that a certain level of energy intake is needed before a predator can reproduce. Our analysis reveals that the model exhibits the behaviours typically found in predator-prey models - extinction of the predator population, convergence to a periodic orbit, or convergence to a co-existence fixed point. For a specific example, in which the predator birth and death rates are constant for all sufficiently small or large values of the predator functional response, we corroborate our analysis with numerical simulations. In the unlikely case where these birth and death rates equal the same constant for all sufficiently large values of the predator functional response, the model is capable of structurally unstable behaviour, with a small change in the initial conditions leading to a more pronounced change in the long-term dynamics.
A generic statistical model of hydride formation in a random alloy
NASA Astrophysics Data System (ADS)
Zhdanov, Vladimir P.
2016-09-01
Hydride formation in metals (e.g. in Pd), accompanied by a hysteresis loop in the absorption isotherms, is one of the generic examples of first-order phase transitions (FOPTs). During the last decade, the corresponding experimental studies, driven by applications related to hydrogen storage, have shifted towards metal particles sized from a few nanometers to micrometers in general and to alloyed particles of these sizes in particular. The understanding of hydride formation in alloys is, however, still far from complete. Herein, a statistical model of hydride formation in a random alloy is presented. The model is focused on the situation when this process is favorable in metal 1 (e.g. Pd) and shows what may happen when atoms of metal 2 make it less favorable due to decrease of the hydrogen binding energy and/or attractive hydrogen-hydrogen (H-H) interaction. Random distribution of metal atoms is taken explicitly into account. The attractive H-H interaction, including its dependence on fraction of metal 2 in the alloy, is described at the mean-field level. With increasing fraction of the latter metal, the critical temperature is found to decrease linearly or nonlinearly depending on the values of the model parameters. If the decrease of the hydrogen binding energy with increasing number of nearest-neighbor (nn) atoms of metal 2 is appreciable, the model predicts up to three hysteresis loops.
A Mathematical Model of the Thermo-Anemometric Flowmeter.
Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman
2015-01-01
A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.
A mathematical model of the CH-53 helicopter
NASA Technical Reports Server (NTRS)
Sturgeon, W. R.; Phillips, J. D.
1980-01-01
A mathematical model suitable for real time simulation of the CH-53 helicopter is presented. This model, which is based on modified nonlinear classical rotor theory and nonlinear fuselage aerodynamics, will be used to support terminal-area guidance and navigation studies on a fixed-base simulator. Validation is achieved by comparing the model response with that of a similar aircraft and by a qualitative comparison of the handling characteristics made by experienced pilots.
Search for predictive generic model of aqueous solubility using Bayesian neural nets.
Bruneau, P
2001-01-01
Several predictive models of aqueous solubility have been published. They have good performances on the data sets which have been used for training the models, but usually these data sets do not contain many structures similar to the structures of interest to the drug research and their applicability in drug hunting is questionable. A very diverse data set has been gathered with compounds issued from literature reports and proprietary compounds. These compounds have been grouped in a so-called literature data set I, a proprietary data set II, and a mixed data set III formed by I and II. About 100 descriptors emphasizing surface properties were calculated for every compound. Bayesian learning of neural nets which cumulates the advantages of neural nets without having their weaknesses was used to select the most parsimonious models and train them, from I, II, and III. The models were established by either selecting the most efficient descriptors one by one using a modified Gram-Schmidt procedure (GS) or by simplifying a most complete model using automatic relevance procedure (ARD). The predictive ability of the models was accessed using validation data sets as much unrelated to the training sets as possible, using two new parameters: NDD(x,ref) the normalized smallest descriptor distance of a compound x to a reference data set and CD(x,mod) the combination of NDD(x,ref) with the dispersion of the Bayesian neural nets calculations. The results show that it is possible to obtain a generic predictive model from database I but that the diversity of database II is too restricted to give a model with good generalization ability and that the ARD method applied to the mixed database III gives the best predictive model.
System and mathematical modeling of quadrotor dynamics
NASA Astrophysics Data System (ADS)
Goodman, Jacob M.; Kim, Jinho; Gadsden, S. Andrew; Wilkerson, Stephen A.
2015-05-01
Unmanned aerial systems (UAS) are becoming increasingly visible in our daily lives; and range in operation from search and rescue, monitoring hazardous environments, and to the delivery of goods. One of the most popular UAS are based on a quad-rotor design. These are typically small devices that rely on four propellers for lift and movement. Quad-rotors are inherently unstable, and rely on advanced control methodologies to keep them operating safely and behaving in a predictable and desirable manner. The control of these devices can be enhanced and improved by making use of an accurate dynamic model. In this paper, we examine a simple quadrotor model, and note some of the additional dynamic considerations that were left out. We then compare simulation results of the simple model with that of another comprehensive model.
Discrete mathematical physics and particle modeling
NASA Astrophysics Data System (ADS)
Greenspan, D.
The theory and application of the arithmetic approach to the foundations of both Newtonian and special relativistic mechanics are explored. Using only arithmetic, a reformulation of the Newtonian approach is given for: gravity; particle modeling of solids, liquids, and gases; conservative modeling of laminar and turbulent fluid flow, heat conduction, and elastic vibration; and nonconservative modeling of heat convection, shock-wave generation, the liquid drop problem, porous flow, the interface motion of a melting solid, soap films, string vibrations, and solitons. An arithmetic reformulation of special relativistic mechanics is given for theory in one space dimension, relativistic harmonic oscillation, and theory in three space dimensions. A speculative quantum mechanical model of vibrations in the water molecule is also discussed.
Mathematical Model For Engineering Analysis And Optimization
NASA Technical Reports Server (NTRS)
Sobieski, Jaroslaw
1992-01-01
Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.
The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study
ERIC Educational Resources Information Center
Mischo, Christoph; Maaß, Katja
2013-01-01
This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…
Mathematical modeling of clearing liquid drop diffusion after intradermal injection
NASA Astrophysics Data System (ADS)
Stolnitz, Mikhail M.; Bashkatov, Alexey N.; Genina, Elina A.; Tuchin, Valery V.
2007-05-01
The mathematical model of clearing agent diffusion after intradermal injection has been developed. Skin was presented as multilayer medium, but one layer with proper boundary conditions is considered. Analytical solution of the boundary problem for small and large time intervals is obtained.
Mathematical model of single-photon emission computed tomography
Clough, A.V.
1986-01-01
Single-photon emission computed tomography (SPECT) is a nuclear-medicine imaging technique that has been shown to provide clinically useful images of radionuclide distributions within the body. The problem of quantitative determination of tomographic activity images from a projection data set leads to a mathematical inverse problem which is formulated as an integral equation. The solution of this problem then depends on an accurate mathematical model as well as a reliable and efficient inversion algorithm. The effects of attenuation and Compton scatter within the body have been incorporated into the model in the hopes of providing a more physically realistic mathematical model. The attenuated Radon transform is the mathematical basis of SPECT. In this work, the case of constant attenuation is reviewed and a new proof of the Tretiak-Metz algorithm is presented. A space-domain version of the inverse attenuated Radon transform is derived. A special case of this transform that is applicable when the object is rotationally symmetric, and attenuated Abel transform is derived, and its inverse is found. A numerical algorithm for the implementation of the inverse attenuated Radon transform with constant attenuation is described and computer simulations are performed to demonstrate the results of the inversion procedure. With the use of the single-scatter approximation and an energy-windowed detector, the effects of Compton scatter are incorporated into the model. The data are then taken to be the sum of primary photons and single-scattered photons.
Fibrin polymerization as a phase transition wave: A mathematical model
NASA Astrophysics Data System (ADS)
Lobanov, A. I.
2016-06-01
A mathematical model of fibrin polymerization is described. The problem of the propagation of phase transition wave is reduced to a nonlinear Stefan problem. A one-dimensional discontinuity fitting difference scheme is described, and the results of one-dimensional computations are presented.
Optimization of a new mathematical model for bacterial growth
Technology Transfer Automated Retrieval System (TEKTRAN)
The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...
Mathematical Modelling of Bacterial Quorum Sensing: A Review.
Pérez-Velázquez, Judith; Gölgeli, Meltem; García-Contreras, Rodolfo
2016-08-01
Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges. PMID:27561265
A mathematical model concerning reflectance from a row crop
NASA Technical Reports Server (NTRS)
Jaggi, R. K.
1972-01-01
The recent work of Allen, Gayle, and Richardson (1970) and Suits (1972) has been extended to compute directional reflectance from a crop row. A model is constructed which takes into account edge effects and aids in discriminating crops with leaf orientation in preferred directions. This report only contains the development of the mathematical equations. Numerical results will be published in a forthcoming report.
Lesson Study: A Professional Development Model for Mathematics Reform
ERIC Educational Resources Information Center
Taylor, Ann R.; Anderson, Shari; Meyer, Karen; Wagner, Mary Kay; West, Christine
2005-01-01
In this action research report 4 teachers and 1 teacher educator use the Japanese lesson study model of professional development for 15 months in rural Carlinville, Illinois. In March 2001, 4 teachers identified a goal to improve their students' understanding of two step word problems in 2nd grade elementary mathematics. Teachers completed three…
Mathematical Model Of Variable-Polarity Plasma Arc Welding
NASA Technical Reports Server (NTRS)
Hung, R. J.
1996-01-01
Mathematical model of variable-polarity plasma arc (VPPA) welding process developed for use in predicting characteristics of welds and thus serves as guide for selection of process parameters. Parameters include welding electric currents in, and durations of, straight and reverse polarities; rates of flow of plasma and shielding gases; and sizes and relative positions of welding electrode, welding orifice, and workpiece.
Mathematical modeling of the instability of viscous fluid films
NASA Astrophysics Data System (ADS)
Prokudina, L. A.
2016-08-01
Nonlinear mathematical model of free surface fluid film is presents. Increment, frequency, phase velocity for thin layers of viscous liquids at low Reynolds numbers are calculated. The instability region is found. Optimal flow regimes of films of water and alcohol, corresponding to the maximum values of increment, are calculated.
A Mathematical Model for HIV Drug-Resistance
NASA Astrophysics Data System (ADS)
Faedo, Ivan; Raimundo, Silvia Martorano; Venturino, Ezio
2010-09-01
In this paper we present a mathematical model of the transmission of HIV infection here the individuals receive antiretroviral drugs but may not respond to treatment. In such case the latter can be changed to a different therapy, and individuals may or may not respond also to this second set of drugs.
Mathematical modeling of the aerodynamic characteristics in flight dynamics
NASA Technical Reports Server (NTRS)
Tobak, M.; Chapman, G. T.; Schiff, L. B.
1984-01-01
Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.
Engaging Students in Mathematical Modeling through Service-Learning
ERIC Educational Resources Information Center
Carducci, Olivia M.
2014-01-01
I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…
Models of Intervention in Mathematics: Reweaving the Tapestry
ERIC Educational Resources Information Center
Fosnot, Catherine
2010-01-01
Explore successful models of intervention. No Child Left Behind has set the high expectation that every child meet grade level expectations. This publication synthesizes the research on intervention programs and best practices related to mathematical instructional pedagogy and differentiation to assist teachers, schools, and school districts in…
Mathematical Models in Educational Planning. Education and Development, Technical Reports.
ERIC Educational Resources Information Center
Organisation for Economic Cooperation and Development, Paris (France).
This volume contains papers, presented at a 1966 OECD meeting, on the possibilities of applying a number of related techniques such as mathematical model building, simulation, and systematic control theory to the problems of educational planning. The authors and their papers are (1) Richard Stone, "A View of the Conference," (2) Hector Correa, "A…
Innovative mathematical modeling in environmental remediation.
Yeh, Gour-Tsyh; Gwo, Jin-Ping; Siegel, Malcolm D; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steve B
2013-05-01
There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g., Ni, Cr, Co). The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport
Mathematical models for biodegradation of chlorinated solvents. 1: Model framework
Zhang, X.; Banerji, S.; Bajpai, R.
1996-12-31
Complete mineralization of chlorinated solvents by microbial action has been demonstrated under aerobic as well as anaerobic conditions. In most of the cases, it is believed that the biodegradation is initiated by broad-specificity enzymes involved in metabolism of a primary substrate. Under aerobic conditions, some of the primary carbon and energy substrates are methane, propane, toluene, phenol, and ammonia; under anaerobic conditions, glucose, sucrose, acetate, propionate, isopropanol, methanol, and even natural organics act as the carbon source. Published biochemical studies suggest that the limiting step is often the initial part of the biodegradation pathway within the microbial system. For aerobic systems, the limiting step is thought to be the reaction catalyzed by mono- and dioxygenases which are induced by most primary substrates, although some constitutive strains have been reported. Other critical features of the biodegradative pathway include: (1) activity losses of critical enzyme(s) through the action of metabolic byproducts, (2) energetic needs of contaminant biodegradation which must be met by catabolism of the primary substrates, (3) changes in metabolic patterns in mixed cultures found in nature depending on the availability of electron acceptors, and (4) the associated accumulation and disappearance of metabolic intermediates. Often, the contaminant pool itself consists of several chlorinated solvents with separate and interactive biochemical needs. The existing models address some of the issues mentioned above. However, their ability to successfully predict biological fate of chlorinated solvents in nature is severely limited due to the existing mathematical models. Limiting step(s), inactivation of critical enzymes, recovery action, energetics, and a framework for multiple degradative pathways will be presented as a comprehensive model. 91 refs.
Mathematical Existence Results for the Doi-Edwards Polymer Model
NASA Astrophysics Data System (ADS)
Chupin, Laurent
2016-07-01
In this paper, we present some mathematical results on the Doi-Edwards model describing the dynamics of flexible polymers in melts and concentrated solutions. This model, developed in the late 1970s, has been used and extensively tested in modeling and simulation of polymer flows. From a mathematical point of view, the Doi-Edwards model consists in a strong coupling between the Navier-Stokes equations and a highly nonlinear constitutive law. The aim of this article is to provide a rigorous proof of the well-posedness of the Doi-Edwards model, namely that it has a unique regular solution. We also prove, which is generally much more difficult for flows of viscoelastic type, that the solution is global in time in the two dimensional case, without any restriction on the smallness of the data.
A mathematical model for predicting the viability of airborne viruses.
Posada, J A; Redrow, J; Celik, I
2010-03-01
A mathematical model was developed to predict the viability of airborne viruses. The model uses water activity as the primary independent variable and an exponential decay function for the viability of the virus. This model was tested using published experimental data obtained by different investigators for influenza, Langat and polio viruses. The aerosolized media were modelled as a binary solution of water and sodium chloride. The water activity is related directly to the solute concentration in the binary solution. The minimum viability usually occurred just above the efflorescence point, which is the relative humidity at which the solution crystallizes. The relationship between water activity and relative humidity is based on the Köhler theory, whereby the Kelvin term was taken into account. Physical explanations are provided on the variation of viral viability at different relative humidity levels. The predictions obtained by the proposed mathematical model compare well with most of the published experimental data.
A mathematical model of the dynamics of antitumor laser immunotherapy
NASA Astrophysics Data System (ADS)
Dawkins, Bryan A.; Laverty, Sean M.
2014-02-01
We use a mathematical model to describe and predict the population dynamics of tumor cells, immune cells, and other immune components in a host undergoing laser immunotherapy treatment against metastatic cancer. We incorporate key elements of the treatment into the model: a function describing the laser-induced primary tumor cell death and parameters capturing the role and strength of the primary immunoadjuvant, glycated chitosan. We focus on identifying conditions that ensure a successful treatment. In particular, we study the patient response (i.e., anti-tumor immune dynamics and treatment outcome) in two different but related mathematical models as we vary quantitative features of the immune system (supply, proliferation, death, and interaction rates). We compare immune dynamics of a `baseline' immune model against an `augmented' model (with additional cell types and antibodies) and in both, we find that using strong immunoadjuvants, like glycated chitosan, that enhance dendritic cell activity yields more promising patient outcomes.
NASA Astrophysics Data System (ADS)
Buchert, Thomas; Nayet, Charly; Wiegand, Alexander
2013-06-01
Kinematical and dynamical properties of a generic inhomogeneous cosmological model, spatially averaged with respect to free-falling (generalized fundamental) observers, are investigated for the matter model “irrotational dust.” Paraphrasing a previous Newtonian investigation, we present a relativistic generalization of a backreaction model based on volume-averaging the “relativistic Zel’dovich approximation.” In this model we investigate the effect of “kinematical backreaction” on the evolution of cosmological parameters as they are defined in an averaged inhomogeneous cosmology, and we show that the backreaction model interpolates between orthogonal symmetry properties by covering subcases of the plane-symmetric solution, the Lemaître-Tolman-Bondi solution and the Szekeres solution. We so obtain a powerful model that lays the foundations for quantitatively addressing curvature inhomogeneities as they would be interpreted as “dark energy” or “dark matter” in a quasi-Newtonian cosmology. The present model, having a limited architecture due to an assumed Friedmann-Lemaître-Robertson-Walker background, is nevertheless capable of replacing 1/4 of the needed amount for dark energy on domains of 200 Mpc in diameter for typical (one-sigma) fluctuations in a cold dark matter initial power spectrum. However, the model is far from explaining dark energy on larger scales (spatially), where a 6% effect on 400 Mpc domains is identified that can be traced back to an on average negative intrinsic curvature today. One drawback of the quantitative results presented is the fact that the epoch when backreaction is effective on large scales and leads to volume acceleration lies in the future. We discuss this issue in relation to the initial spectrum, the dark matter problem, the coincidence problem, and the fact that large-scale dark energy is an effect on the past light cone (not spatial), and we pinpoint key elements of future research.
NASA Astrophysics Data System (ADS)
Volta, Chiara; Gildas Laruelle, Goulven; Arndt, Sandra; Regnier, Pierre
2016-03-01
This study applies the Carbon-Generic Estuary Model (C-GEM) modeling platform to simulate the estuarine biogeochemical dynamics - in particular the air-water CO2 exchange - in three idealized tidal estuaries characterized by increasing riverine influence, from a so-called "marine estuary" to a "riverine estuary". An intermediate case called "mixed estuary" is also considered. C-GEM uses a generic biogeochemical reaction network and a unique set of model parameters extracted from a comprehensive literature survey to perform steady-state simulations representing average conditions for temperate estuaries worldwide. Climate and boundary conditions are extracted from published global databases (e.g., World Ocean Atlas, GLORICH) and catchment model outputs (GlobalNEWS2). The whole-system biogeochemical indicators net ecosystem metabolism (NEM), C and N filtering capacities (FCTC and FCTN, respectively) and CO2 gas exchanges (FCO2) are calculated across the three idealized systems and are related to their main hydrodynamic and transport characteristics. A sensitivity analysis, which propagates the parameter uncertainties, is also carried out, followed by projections of changes in the biogeochemical indicators for the year 2050. Results show that the average C filtering capacities for baseline conditions are 40, 30 and 22 % for the marine, mixed and riverine estuary, respectively, while N filtering capacities, calculated in a similar fashion, range from 22 % for the marine estuary to 18 and 15 % for the mixed and the riverine estuaries. Sensitivity analysis performed by varying the rate constants for aerobic degradation, denitrification and nitrification over the range of values reported in the literature significantly widens these ranges for both C and N. Simulations for the year 2050 suggest that all estuaries will remain largely heterotrophic, although a slight improvement of the estuarine trophic status is predicted. In addition, our results suggest that, while the
Wang, Chi-Jen; Liu, Da-Jiang; Evans, J W
2012-04-01
Schloegl's second model on a (d ≥ 2)-dimensional hypercubic lattice involves: (i) spontaneous annihilation of particles with rate p and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of suitable pairs of neighboring particles. This model provides a prototype for nonequilibrium discontinuous phase transitions. However, it also exhibits nontrivial generic two-phase coexistence: Stable populated and vacuum states coexist for a finite range, pf(d)
model due to fluctuations. This feature is amplified for increasing d, thus complicating our analysis.
NASA Astrophysics Data System (ADS)
Ergin, Selma; Dobrucalı, Erinç
2014-06-01
The exhaust smoke dispersion for a generic frigate is investigated numerically through the numerical solution of the governing fluid flow, energy, species and turbulence equations. The main objective of this work is to obtain the effects of the yaw angle, velocity ratio and buoyancy on the dispersion of the exhaust smoke. The numerical method is based on the fully conserved control-volume representation of the fully elliptic Navier-Stokes equations. Turbulence is modeled using a two-equation ( k- ɛ) model. The flow visualization tests using a 1/100 scale model of the frigate in the wind tunnel were also carried out to determine the exhaust plume path and to validate the computational results. The results show that down wash phenomena occurs for the yaw angles between ψ =10° and 20°. The results with different exhaust gas temperatures show that the buoyancy effect increases with the increasing of the exhaust gas temperature. However, its effect on the plume rise is less significant in comparison with its momentum. A good agreement between the predictions and experiment results is obtained.
A generic model for creep rupture lifetime estimation on fibrous ceramic composites
NASA Technical Reports Server (NTRS)
Chuang, Tze-Jer
1992-01-01
Because of their high strength and toughness at elevated temperatures, fiber reinforced ceramic composites such as SiC(f)/SiC and SiC(f)/Si3N4 have become candidates for next-generation turbine engine materials. A generic model is proposed for assessing the lifetime of this class of materials when subjected to long-term creep rupture conditions. This 2D model consists of interfacial cracks growing between square grains and rectangular fibers in the direction normal to the principal tensile stress axis. Neglecting transient effects, the total lifetime is derived based on the criterion that rupture is due to coalescence of adjacent cracks. Lifetime is inversely proportional to crack growth rate, volume fraction, and aspect ratio of the fibers; but extremely sensitive to the applied stress, due to the high power of the V-K(I) law. This lifetime estimation seems to be in fair agreement with the creep rupture data of SiC(w)/Si3N4 composite with 0 and 30 vol percent reinforcement tested at 1250 C in air. TEM performed on the postcrept specimens revealed that creep damage is predominantly in the form of microcracks at matrix/matrix as well as fiber/matrix interfaces, approximately in accord with the model simulation.
A generic system for integrated modelling of multi-dimensional spatial data
NASA Astrophysics Data System (ADS)
Brown, I. M.
A generic approach to computer modelling of earth science data is presented, utilising a state-of-the-art scientific visualisation environment (AVS/Express). The greater flexibility of such an approach allows us to handle a wide variety of different data types, including geophysical data as well as other earth science data (eg. stratigraphy, geomorphology, palaeontology) which often contrast by being generally discrete bodies rather than continuous fields. Application of volume visualisation techniques generally demonstrates that the sparse nature of sampling favours using surface-extraction techniques, such as isosurfaces and slicing, rather than direct volume rendering techniques. These techniques have also been applied to temporal 4D data-sets by incorporating time-slices into animation. However, all these procedures require a high performance workstation to be effective. Therefore, to allow greater desktop analysis of complex models, we are using the Virtual Reality Modelling Language (VRML) which provides considerable scope for increased access to 3D/4D data for education and collaboration.
Mathematical modeling to predict residential solid waste generation
Ojeda Benitez, Sara; Vega, Carolina Armijo de
2008-07-01
One of the challenges faced by waste management authorities is determining the amount of waste generated by households in order to establish waste management systems, as well as trying to charge rates compatible with the principle applied worldwide, and design a fair payment system for households according to the amount of residential solid waste (RSW) they generate. The goal of this research work was to establish mathematical models that correlate the generation of RSW per capita to the following variables: education, income per household, and number of residents. This work was based on data from a study on generation, quantification and composition of residential waste in a Mexican city in three stages. In order to define prediction models, five variables were identified and included in the model. For each waste sampling stage a different mathematical model was developed, in order to find the model that showed the best linear relation to predict residential solid waste generation. Later on, models to explore the combination of included variables and select those which showed a higher R{sup 2} were established. The tests applied were normality, multicolinearity and heteroskedasticity. Another model, formulated with four variables, was generated and the Durban-Watson test was applied to it. Finally, a general mathematical model is proposed to predict residential waste generation, which accounts for 51% of the total.
Mathematical Modelling of the Infusion Test
NASA Astrophysics Data System (ADS)
Cieslicki, Krzysztof
2007-01-01
The objective of this paper was to improve the well established in clinical practice Marmarou model for intracranial volume-pressure compensation by adding the pulsatile components. It was demonstrated that complicated pulsation and growth in intracranial pressure during infusion test could be successfully modeled by the relatively simple analytical expression derived in this paper. The CSF dynamics were tested in 25 patients with clinical symptoms of hydrocephalus. Basing on the frequency spectrum of the patient's baseline pressure and identified parameters of CSF dynamic, for each patient an "ideal" infusion test curve free from artefacts and slow waves was simulated. The degree of correlation between simulated and real curves obtained from clinical observations gave insight into the adequacy of assumptions of Marmarou model. The proposed method of infusion tests analysis designates more exactly the value of the reference pressure, which is usually treated as a secondary and of uncertain significance. The properly identified value of the reference pressure decides on the degree of pulsation amplitude growth during IT, as well as on the value of elastance coefficient. The artificially generated tests with various pulsation components were also applied to examine the correctness of the used algorithm of identification of the original Marmarou model parameters.
Modeling Students' Mathematics Using Steffe's Fraction Schemes
ERIC Educational Resources Information Center
Norton, Anderson H.; McCloskey, Andrea V.
2008-01-01
Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…
Using Archeological Data to Model Mathematics
ERIC Educational Resources Information Center
Yanik, H. Bahadir; Kurz, Terri L.; Memis, Yasin
2014-01-01
The purpose of this investigation is to describe an implementation of a modeling task using mock data from an ancient archeological find. Students discover the relationship between the height of a person and his or her stride length. Qualitative data from student discussions document thinking and reasoning.
Mathematical Modelling of Continuous Biotechnological Processes
ERIC Educational Resources Information Center
Pencheva, T.; Hristozov, I.; Shannon, A. G.
2003-01-01
Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…
Mathematical models for space shuttle ground systems
NASA Technical Reports Server (NTRS)
Tory, E. G.
1985-01-01
Math models are a series of algorithms, comprised of algebraic equations and Boolean Logic. At Kennedy Space Center, math models for the Space Shuttle Systems are performed utilizing the Honeywell 66/80 digital computers, Modcomp II/45 Minicomputers and special purpose hardware simulators (MicroComputers). The Shuttle Ground Operations Simulator operating system provides the language formats, subroutines, queueing schemes, execution modes and support software to write, maintain and execute the models. The ground systems presented consist primarily of the Liquid Oxygen and Liquid Hydrogen Cryogenic Propellant Systems, as well as liquid oxygen External Tank Gaseous Oxygen Vent Hood/Arm and the Vehicle Assembly Building (VAB) High Bay Cells. The purpose of math modeling is to simulate the ground hardware systems and to provide an environment for testing in a benign mode. This capability allows the engineers to check out application software for loading and launching the vehicle, and to verify the Checkout, Control, & Monitor Subsystem within the Launch Processing System. It is also used to train operators and to predict system response and status in various configurations (normal operations, emergency and contingent operations), including untried configurations or those too dangerous to try under real conditions, i.e., failure modes.
Innovative mathematical modeling in environmental remediation
Yeh, Gour T.; Gwo, Jin Ping; Siegel, Malcolm D.; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steven B.
2013-05-01
There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g.,Ni, Cr, Co).The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport models
Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research
NASA Technical Reports Server (NTRS)
Shitzer, A.
1972-01-01
An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.
Mathematical modelling of triple arterial stenoses.
Ang, K C; Mazumdar, J
1995-06-01
This paper examines the effects of triple stenoses (ie. three stenoses in series) in a reasonably large artery. The model developed is axi-symmetric and blood is assumed to be a Newtonian fluid. The governing equations are the Navier-Stokes equations and the continuity equation. These equations are solved using the Finite Element Method and the FIDAP computational fluid dynamics (C.F.D.) package. Various combinations of differing degrees of stenosis in the triplet are considered. Pressure drop profiles and streamline plots of the solutions to these models show that the effects of milder stenoses are diminished in the presence of more severe ones. Also, a pressure recovery is observed whenever a mild stenosis follows a more severe stenosis in multiply stenosed arteries.
Generalized mathematical models in design optimization
NASA Technical Reports Server (NTRS)
Papalambros, Panos Y.; Rao, J. R. Jagannatha
1989-01-01
The theory of optimality conditions of extremal problems can be extended to problems continuously deformed by an input vector. The connection between the sensitivity, well-posedness, stability and approximation of optimization problems is steadily emerging. The authors believe that the important realization here is that the underlying basis of all such work is still the study of point-to-set maps and of small perturbations, yet what has been identified previously as being just related to solution procedures is now being extended to study modeling itself in its own right. Many important studies related to the theoretical issues of parametric programming and large deformation in nonlinear programming have been reported in the last few years, and the challenge now seems to be in devising effective computational tools for solving these generalized design optimization models.
Mathematical modeling of pathogenicity of Cryptococcus neoformans
Garcia, Jacqueline; Shea, John; Alvarez-Vasquez, Fernando; Qureshi, Asfia; Luberto, Chiara; Voit, Eberhard O; Del Poeta, Maurizio
2008-01-01
Cryptococcus neoformans (Cn) is the most common cause of fungal meningitis worldwide. In infected patients, growth of the fungus can occur within the phagolysosome of phagocytic cells, especially in non-activated macrophages of immunocompromised subjects. Since this environment is characteristically acidic, Cn must adapt to low pH to survive and efficiently cause disease. In the present work, we designed, tested, and experimentally validated a theoretical model of the sphingolipid biochemical pathway in Cn under acidic conditions. Simulations of metabolic fluxes and enzyme deletions or downregulation led to predictions that show good agreement with experimental results generated post hoc and reconcile intuitively puzzling results. This study demonstrates how biochemical modeling can yield testable predictions and aid our understanding of fungal pathogenesis through the design and computational simulation of hypothetical experiments. PMID:18414484
Physical and mathematical modeling of antimicrobial photodynamic therapy
NASA Astrophysics Data System (ADS)
Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang
2014-07-01
Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.
On the Treatment of Airline Travelers in Mathematical Models
Johansson, Michael A.; Arana-Vizcarrondo, Neysarí; Biggerstaff, Brad J.; Staples, J. Erin; Gallagher, Nancy; Marano, Nina
2011-01-01
The global spread of infectious diseases is facilitated by the ability of infected humans to travel thousands of miles in short time spans, rapidly transporting pathogens to distant locations. Mathematical models of the actual and potential spread of specific pathogens can assist public health planning in the case of such an event. Models should generally be parsimonious, but must consider all potentially important components of the system to the greatest extent possible. We demonstrate and discuss important assumptions relative to the parameterization and structural treatment of airline travel in mathematical models. Among other findings, we show that the most common structural treatment of travelers leads to underestimation of the speed of spread and that connecting travel is critical to a realistic spread pattern. Models involving travelers can be improved significantly by relatively simple structural changes but also may require further attention to details of parameterization. PMID:21799782
A software package for the configuration of hardware devices following a generic model
NASA Astrophysics Data System (ADS)
Almeida, N.; Alemany, R.; Glege, F.; da Silva, J. C.; Varela, J.
2004-10-01
This paper describes a software package developed in C++ under the Linux environment that is intended for automatic hardware configuration in VME or PCI buses. Based on a generic model, users specify the configuration procedures and data in configuration files. Actual hardware configuration is performed by the software package, accessed through a simple C++ interface. The model is well suited for storage of configuration data in XML files or databases. The package is now being used in the local data acquisition system of the Electromagnetic Calorimeter of the CMS experiment at CERN. Program summaryTitle of program: Generic Configurator Catalogue identifier: ADUK Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUK Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Intel Pentium IV PC Installations: ECAL Data Acquisition of the CMS experiment at CERN Operating systems or monitors under which the program has been tested: Linux 2.4.2 Programming language used: C++ Memory required to execute with typical data: depends on the complexity of the module configuration. Test runs requires less then 500 KB Number of bits in a word: 32 Number of processors used: 1 Distribution format: tar gzip file Number of bytes in distributed program, including test data, etc.: 234 542 Number of lines in distributed program, including test data etc.: 17 365 Nature of physical problem: Generalization of hardware device configuration procedure in VME or PCI buses. Method of solution: The developed package uses a generic configuration model that allows users to configure VME and PCI devices. The hardware configuration parameters and the data structures associated to each hardware register are specified in XML files. The package performs the desired configuration using these files along with a description of the hardware access proprieties of each register. Typical
Mathematical modeling of solid oxide fuel cells
NASA Technical Reports Server (NTRS)
Lu, Cheng-Yi; Maloney, Thomas M.
1988-01-01
Development of predictive techniques, with regard to cell behavior, under various operating conditions is needed to improve cell performance, increase energy density, reduce manufacturing cost, and to broaden utilization of various fuels. Such technology would be especially beneficial for the solid oxide fuel cells (SOFC) at it early demonstration stage. The development of computer models to calculate the temperature, CD, reactant distributions in the tubular and monolithic SOFCs. Results indicate that problems of nonuniform heat generation and fuel gas depletion in the tubular cell module, and of size limitions in the monolithic (MOD 0) design may be encountered during FC operation.
Mathematical models for the EPIC code
Buchanan, H.L.
1981-06-03
EPIC is a fluid/envelope type computer code designed to study the energetics and dynamics of a high energy, high current electron beam passing through a gas. The code is essentially two dimensional (x, r, t) and assumes an axisymmetric beam whose r.m.s. radius is governed by an envelope model. Electromagnetic fields, background gas chemistry, and gas hydrodynamics (density channel evolution) are all calculated self-consistently as functions of r, x, and t. The code is a collection of five major subroutines, each of which is described in some detail in this report.
A mathematical model of lung parenchyma.
Karakaplan, A D; Bieniek, M P; Skalak, R
1980-05-01
The geometry of the proposed model of the parenchyma of a mammalian lung reproduces a cluster of alveoli arranged around a lowest-level air duct. The alveolar walls are assumed to be nonlinear elastic membranes, whose properties are described in terms of a strain energy function which reflects the hardening character of the stress-strain curve. The effect of the surfactant is included in terms of a variable (area-dependent) surface tension. Analyses of various mechanical processes in the parenchyma are performed with the aid of the finite element method, with the geometric and physical nonlinearities of the problem taken into account. PMID:6893348
Mathematical model of induced flow on the airplane vertical tail
NASA Astrophysics Data System (ADS)
Rotaru, Constantin; Cîrciu, Ionicǎ; Edu, Raluca Ioana
2016-06-01
In this paper is presented a mathematical model of the flow around the vertical tail of an airplane, based on the general elements of the aerodynamic design, with details leading to the separate formulation of the Fourier coefficients in the series solution of the Prandtl's lifting-line equation. Numerical results are obtained in Maple soft environment, for a standard configuration of an airplane geometry. The results include the discussion of the vortex model for the sidewash gradient on the vertical stabilizer.
Mathematical Reliability Model of Building Components by Rayleigh
NASA Astrophysics Data System (ADS)
Nowogońska, Beata
2015-03-01
The patterns of process situations play an important role in the monitoring of diagnostic processes. The adaptation of mathematical models describing the degradation processes in mechanical and electronic devices creates opportunities to develop diagnostic standards for buildings erected in traditional technology. This article presents a proposal for the prediction of building operational reliability, which is a prognostic process model within the full period of its use.
On a Mathematical Model of Brain Activities
Fichtner, K.-H.; Fichtner, L.; Freudenberg, W.; Ohya, M.
2007-12-03
The procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an 'expexted view of the world'. Then the brain compares a signal arising from our senses with the signal chosen from the memory leading to a change of the state of both signals. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from 'excited' to 'nonexcited'. For that reason a statistical model of the recognition process should reflect both--the change of the signals and the loss of excited neurons. A first attempt to explain the process of recognition in terms of quantum statistics was given. In the present note it is not possible to present this approach in detail. In lieu we will sketch roughly a few of the basic ideas and structures of the proposed model of the recognition process (Section). Further, we introduce the basic spaces and justify the choice of spaces used in this approach. A more elaborate presentation including all proofs will be given in a series of some forthcoming papers. In this series also the procedures of creation of signals from the memory, amplification, accumulation and transformation of input signals, and measurements like EEG and MEG will be treated in detail.
On a Mathematical Model of Brain Activities
NASA Astrophysics Data System (ADS)
Fichtner, K.-H.; Fichtner, L.; Freudenberg, W.; Ohya, M.
2007-12-01
The procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an "expexted view of the world". Then the brain compares a signal arising from our senses with the signal chosen from the memory leading to a change of the state of both signals. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from "excited" to "nonexcited". For that reason a statistical model of the recognition process should reflect both—the change of the signals and the loss of excited neurons. A first attempt to explain the process of recognition in terms of quantum statistics was given in [1]. In the present note it is not possible to present this approach in detail. In lieu we will sketch roughly a few of the basic ideas and structures of the proposed model of the recognition process (Section). Further, we introduce the basic spaces and justify the choice of spaces used in this approach. A more elaborate presentation including all proofs will be given in a series of some forthcoming papers [2, 3]. In this series also the procedures of creation of signals from the memory, amplification, accumulation and transformation of input signals, and measurements like EEG and MEG will be treated in detail.
Eckert, Andreas
2013-05-31
In this project generic anticline structures have been used for numerical modeling analyses to study the influence of geometrical parameters, fluid flow boundary conditions, in situ stress regime and inter-bedding friction coefficient on geomechanical risks such as fracture reactivation and fracture generation. The resulting stress states for these structures are also used to determine safe drilling directions and a methodology for wellbore trajection optimization is developed that is applicable for non-Andersonian stress states. The results of the fluid flow simulation show that the type of fluid flow boundary condition is of utmost importance and has significant impact on all injection related parameters. It is recommended that further research is conducted to establish a method to quantify the fluid flow boundary conditions for injection applications. The results of the geomechanical simulation show that in situ stress regime is a crucial, if not the most important, factor determining geomechanical risks. For extension and strike slip stress regimes anticline structures should be favored over horizontally layered basin as they feature higher ΔP{sub c} magnitudes. If sedimentary basins are tectonically relaxed and their state of stress is characterized by the uni-axial strain model the basin is in exact frictional equilibrium and fluids should not be injected. The results also show that low inter bedding friction coefficients effectively decouple layers resulting in lower ΔP{sub c} magnitudes, especially for the compressional stress regime.
Development of a Dynamically Scaled Generic Transport Model Testbed for Flight Research Experiments
NASA Technical Reports Server (NTRS)
Jordan, Thomas; Langford, William; Belcastro, Christine; Foster, John; Shah, Gautam; Howland, Gregory; Kidd, Reggie
2004-01-01
This paper details the design and development of the Airborne Subscale Transport Aircraft Research (AirSTAR) test-bed at NASA Langley Research Center (LaRC). The aircraft is a 5.5% dynamically scaled, remotely piloted, twin-turbine, swept wing, Generic Transport Model (GTM) which will be used to provide an experimental flight test capability for research experiments pertaining to dynamics modeling and control beyond the normal flight envelope. The unique design challenges arising from the dimensional, weight, dynamic (inertial), and actuator scaling requirements necessitated by the research community are described along with the specific telemetry and control issues associated with a remotely piloted subscale research aircraft. Development of the necessary operational infrastructure, including operational and safety procedures, test site identification, and research pilots is also discussed. The GTM is a unique vehicle that provides significant research capacity due to its scaling, data gathering, and control characteristics. By combining data from this testbed with full-scale flight and accident data, wind tunnel data, and simulation results, NASA will advance and validate control upset prevention and recovery technologies for transport aircraft, thereby reducing vehicle loss-of-control accidents resulting from adverse and upset conditions.
From LCAs to simplified models: a generic methodology applied to wind power electricity.
Padey, Pierryves; Girard, Robin; le Boulch, Denis; Blanc, Isabelle
2013-02-01
This study presents a generic methodology to produce simplified models able to provide a comprehensive life cycle impact assessment of energy pathways. The methodology relies on the application of global sensitivity analysis to identify key parameters explaining the impact variability of systems over their life cycle. Simplified models are built upon the identification of such key parameters. The methodology is applied to one energy pathway: onshore wind turbines of medium size considering a large sample of possible configurations representative of European conditions. Among several technological, geographical, and methodological parameters, we identified the turbine load factor and the wind turbine lifetime as the most influent parameters. Greenhouse Gas (GHG) performances have been plotted as a function of these key parameters identified. Using these curves, GHG performances of a specific wind turbine can be estimated, thus avoiding the undertaking of an extensive Life Cycle Assessment (LCA). This methodology should be useful for decisions makers, providing them a robust but simple support tool for assessing the environmental performance of energy systems. PMID:23259663
Wilderjans, T F; Ceulemans, E; Kuppens, P
2012-06-01
In many areas of the behavioral sciences, different groups of objects are measured on the same set of binary variables, resulting in coupled binary object × variable data blocks. Take, as an example, success/failure scores for different samples of testees, with each sample belonging to a different country, regarding a set of test items. When dealing with such data, a key challenge consists of uncovering the differences and similarities between the structural mechanisms that underlie the different blocks. To tackle this challenge for the case of a single data block, one may rely on HICLAS, in which the variables are reduced to a limited set of binary bundles that represent the underlying structural mechanisms, and the objects are given scores for these bundles. In the case of multiple binary data blocks, one may perform HICLAS on each data block separately. However, such an analysis strategy obscures the similarities and, in the case of many data blocks, also the differences between the blocks. To resolve this problem, we proposed the new Clusterwise HICLAS generic modeling strategy. In this strategy, the different data blocks are assumed to form a set of mutually exclusive clusters. For each cluster, different bundles are derived. As such, blocks belonging to the same cluster have the same bundles, whereas blocks of different clusters are modeled with different bundles. Furthermore, we evaluated the performance of Clusterwise HICLAS by means of an extensive simulation study and by applying the strategy to coupled binary data regarding emotion differentiation and regulation.
From LCAs to simplified models: a generic methodology applied to wind power electricity.
Padey, Pierryves; Girard, Robin; le Boulch, Denis; Blanc, Isabelle
2013-02-01
This study presents a generic methodology to produce simplified models able to provide a comprehensive life cycle impact assessment of energy pathways. The methodology relies on the application of global sensitivity analysis to identify key parameters explaining the impact variability of systems over their life cycle. Simplified models are built upon the identification of such key parameters. The methodology is applied to one energy pathway: onshore wind turbines of medium size considering a large sample of possible configurations representative of European conditions. Among several technological, geographical, and methodological parameters, we identified the turbine load factor and the wind turbine lifetime as the most influent parameters. Greenhouse Gas (GHG) performances have been plotted as a function of these key parameters identified. Using these curves, GHG performances of a specific wind turbine can be estimated, thus avoiding the undertaking of an extensive Life Cycle Assessment (LCA). This methodology should be useful for decisions makers, providing them a robust but simple support tool for assessing the environmental performance of energy systems.
Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling
Du, Qiang
2014-11-12
The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of which is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next
The Kiel data management infrastructure - arising from a generic data model
NASA Astrophysics Data System (ADS)
Fleischer, D.; Mehrtens, H.; Schirnick, C.; Springer, P.
2010-12-01
The Kiel Data Management Infrastructure (KDMI) started from a cooperation of three large-scale projects (SFB574, SFB754 and Cluster of Excellence The Future Ocean) and the Leibniz Institute of Marine Sciences (IFM-GEOMAR). The common strategy for project data management is a single person collecting and transforming data according to the requirements of the targeted data center(s). The intention of the KDMI cooperation is to avoid redundant and potentially incompatible data management efforts for scientists and data managers and to create a single sustainable infrastructure. An increased level of complexity in the conceptual planing arose from the diversity of marine disciplines and approximately 1000 scientists involved. KDMI key features focus on the data provenance which we consider to comprise the entire workflow from field sampling thru labwork to data calculation and evaluation. Managing the data of each individual project participant in this way yields the data management for the entire project and warrants the reusability of (meta)data. Accordingly scientists provide a workflow definition of their data creation procedures resulting in their target variables. The central idea in the development of the KDMI presented here is based on the object oriented programming concept which allows to have one object definition (workflow) and infinite numbers of object instances (data). Each definition is created by a graphical user interface and produces XML output stored in a database using a generic data model. On creation of a data instance the KDMI translates the definition into web forms for the scientist, the generic data model then accepts all information input following the given data provenance definition. An important aspect of the implementation phase is the possibility of a successive transition from daily measurement routines resulting in single spreadsheet files with well known points of failure and limited reuseability to a central infrastructure as a
Tibia Fracture Healing Prediction Using First-Order Mathematical Model.
Sridevi, M; Prakasam, P; Kumaravel, S; Sarma, P Madhava
2015-01-01
The prediction of healing period of a tibia fracture in humans across limb using first-order mathematical model is demonstrated. At present, fracture healing is diagnosed using X-rays. Recent studies have demonstrated electric stimulation as a diagnostic tool in fracture healing. A DC electric voltage of 0.7 V was applied across the fracture and stabilized with Teflon coated carbon rings and the data was recorded at different time intervals until the fracture heals. The experimental data fitted a first-order plus dead time zero model (FOPDTZ) that coincided with the mathematical model of electrical simulated tibia fracture limb. Fracture healing diagnosis was proposed using model parameter process gain. Current stabilization in terms of process gain parameter becoming constant indicates that the healing of fracture is a new finding in the work. An error analysis was performed and it was observed that the measured data correlated to the FOPDTZ model with an error of less than 2 percent. Prediction of fracture healing period was done by one of the identified model parameters, namely, process gain. Moreover, mathematically, it is justified that once the fracture is completely united there is no capacitance present across the fracture site, which is a novelty of the work. PMID:26495032
A novel mathematical model for controllable near-field electrospinning
Ru, Changhai E-mail: luojun@shu.edu.cn; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun E-mail: luojun@shu.edu.cn
2014-01-15
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
Mathematical analysis of intermittent gas injection model in oil production
NASA Astrophysics Data System (ADS)
Tasmi, Silvya, D. R.; Pudjo, S.; Leksono, M.; Edy, S.
2016-02-01
Intermittent gas injection is a method to help oil production process. Gas is injected through choke in surface and then gas into tubing. Gas forms three areas in tubing: gas column area, film area and slug area. Gas column is used to propel slug area until surface. A mathematical model of intermittent gas injection is developed in gas column area, film area and slug area. Model is expanding based on mass and momentum conservation. Using assume film thickness constant in tubing, model has been developed by Tasmi et. al. [14]. Model consists of 10 ordinary differential equations. In this paper, assumption of pressure in gas column is uniform. Model consist of 9 ordinary differential equations. Connection of several variables can be obtained from this model. Therefore, dynamics of all variables that affect to intermittent gas lift process can be seen from four equations. To study the behavior of variables can be analyzed numerically and mathematically. In this paper, simple mathematically analysis approach is used to study behavior of the variables. Variables that affect to intermittent gas injection are pressure in upstream valve and in gas column. Pressure in upstream valve will decrease when gas mass in valve greater than gas mass in choke. Dynamic of the pressure in the gas column will decrease and increase depending on pressure in upstream valve.
Mathematical modeling of near-critical convection
Cox, B.L.; Pruess, K.; McKibbin, R.
1988-01-01
Fluid and heat flow at temperatures approaching or exceeding that at the critical point (374ºC for pure water, higher for saline fluids) may be encountered in deep zones of geothermal systems and above cooling intrusives. Laboratory experiments have demonstrated strong enhancements in heat transfer at near-critical conditions (Dunn and Hardee, 1981). We have developed special numerical techniques for modeling porous flow at near-critical conditions, which can handle the extreme non-linearities in water properties near the critical point. Our numerical experiments show strong enhancements of convective heat transfer at near-critical conditions; however, the heat transfer rates obtained in the numerical simulations are considerably smaller than those seen in the laboratory experiments by Dunn and Hardee. We discuss possible reasons for this discrepancy and develop suggestions for additional laboratory experiments.
ERIC Educational Resources Information Center
Carrejo, David J.; Marshall, Jill
2007-01-01
This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…
Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis
Yan, Ruqiang; Chen, Xuefeng; Li, Weihua; Sheng, Shuangwen
2014-12-18
Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issue is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.
Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis
Yan, Ruqiang; Chen, Xuefeng; Li, Weihua; Sheng, Shuangwen
2014-12-18
Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less
Mathematical model for wound healing following autologous keratinocyte transplantation.
Renner, Regina; Teuwen, Isabell; Gebhardt, Carl; Simon, Jan C
2008-06-01
In times of increasing economical pressure on the health care systems, it is important to optimise the outpatient treatment of chronic wounds. Another aim of wound healing research is to discover agents to accelerate healing. Wound healing trajectories or healing velocities can provide information to demonstrate the endpoints for wound healing. A great problem in clinical trials is to specify these parameters. Therefore, we developed a mathematical model for more transparency. In this initial project, we observed 19 wounds to construct the wound healing trajectories after transplantation of autologous keratinocytes, and the results are so encouraging that investigation in this area will continue. The developed mathematical model describes the clinical observed healing process. It was possible to find parameters to distinguish between old and young patients, retrospectively or prospectively calculate the healing rates and to determine exactly the endpoint of healing. Therefore, our model might be very useful in practices or for studies.
Aspects of Mathematical Modelling of Pressure Retarded Osmosis
Anissimov, Yuri G.
2016-01-01
In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696
Aspects of Mathematical Modelling of Pressure Retarded Osmosis.
Anissimov, Yuri G
2016-02-03
In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed.
Mathematical Modeling of Microbial Community Dynamics: A Methodological Review
Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.; Konopka, Allan
2014-10-17
Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can be potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.
A mathematical model of the sleep/wake cycle.
Rempe, Michael J; Best, Janet; Terman, David
2010-05-01
We present a biologically-based mathematical model that accounts for several features of the human sleep/wake cycle. These features include the timing of sleep and wakefulness under normal and sleep-deprived conditions, ultradian rhythms, more frequent switching between sleep and wakefulness due to the loss of orexin and the circadian dependence of several sleep measures. The model demonstrates how these features depend on interactions between a circadian pacemaker and a sleep homeostat and provides a biological basis for the two-process model for sleep regulation. The model is based on previous "flip-flop" conceptual models for sleep/wake and REM/NREM and we explore whether the neuronal components in these flip-flop models, with the inclusion of a sleep-homeostatic process and the circadian pacemaker, are sufficient to account for the features of the sleep/wake cycle listed above. The model is minimal in the sense that, besides the sleep homeostat and constant cortical drives, the model includes only those nuclei described in the flip-flop models. Each of the cell groups is modeled by at most two differential equations for the evolution of the total population activity, and the synaptic connections are consistent with those described in the flip-flop models. A detailed analysis of the model leads to an understanding of the mathematical mechanisms, as well as insights into the biological mechanisms, underlying sleep/wake dynamics.
Modeling HIV/AIDS Drug Price Determinants in Brazil: Is Generic Competition a Myth?
Meiners, Constance; Sagaon-Teyssier, Luis; Hasenclever, Lia; Moatti, Jean-Paul
2011-01-01
Background Brazil became the first developing country to guarantee free and universal access to HIV/AIDS treatment, with antiretroviral drugs (ARVs) being delivered to nearly 190,000 patients. The analysis of ARV price evolution and market dynamics in Brazil can help anticipate issues soon to afflict other developing countries, as the 2010 revision of the World Health Organization guidelines shifts demand towards more expensive treatments, and, at the same time, current evolution of international legislation and trade agreements on intellectual property rights may reduce availability of generic drugs for HIV care. Methods and Findings Our analyses are based on effective prices paid for ARV procurement in Brazil between 1996 and 2009. Data panel structure was exploited to gather ex-ante and ex-post information and address various sources of statistical bias. In-difference estimation offered in-depth information on ARV market characteristics which significantly influence prices. Although overall ARV prices follow a declining trend, changing characteristics in the generic segment help explain recent increase in generic ARV prices. Our results show that generic suppliers are more likely to respond to factors influencing demand size and market competition, while originator suppliers tend to set prices strategically to offset compulsory licensing threats and generic competition. Significance In order to guarantee the long term sustainability of access to antiretroviral treatment, our findings highlight the importance of preserving and stimulating generic market dynamics to sustain developing countries' bargaining power in price negotiations undertaken with originator companies. PMID:21858138
Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience
ERIC Educational Resources Information Center
Charpin, J. P. F.; O'Hara, S.; Mackey, D.
2013-01-01
In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…
The Academic Merits of Modelling in Higher Mathematics Education: A Case Study
ERIC Educational Resources Information Center
Perrenet, Jacob; Adan, Ivo
2010-01-01
Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge…
ERIC Educational Resources Information Center
Chitera, Nancy
2011-01-01
In this article, the author presents a discussion of how mathematics teacher educators model school mathematics teaching in initial teacher training colleges, as they prepare the student teachers to teach mathematics in multilingual classrooms in Malawi. In particular, the article examines the instructional practices that mathematics teacher…
Helicopter mathematical models and control law development for handling qualities research
NASA Technical Reports Server (NTRS)
Chen, Robert T. N.; Lebacqz, J. Victor; Aiken, Edwin W.; Tischler, Mark B.
1988-01-01
Progress made in joint NASA/Army research concerning rotorcraft flight-dynamics modeling, design methodologies for rotorcraft flight-control laws, and rotorcraft parameter identification is reviewed. Research into these interactive disciplines is needed to develop the analytical tools necessary to conduct flying qualities investigations using both the ground-based and in-flight simulators, and to permit an efficient means of performing flight test evaluation of rotorcraft flying qualities for specification compliance. The need for the research is particularly acute for rotorcraft because of their mathematical complexity, high order dynamic characteristics, and demanding mission requirements. The research in rotorcraft flight-dynamics modeling is pursued along two general directions: generic nonlinear models and nonlinear models for specific rotorcraft. In addition, linear models are generated that extend their utilization from 1-g flight to high-g maneuvers and expand their frequency range of validity for the design analysis of high-gain flight control systems. A variety of methods ranging from classical frequency-domain approaches to modern time-domain control methodology that are used in the design of rotorcraft flight control laws is reviewed. Also reviewed is a study conducted to investigate the design details associated with high-gain, digital flight control systems for combat rotorcraft. Parameter identification techniques developed for rotorcraft applications are reviewed.
Raffo-Caiado, Ana Claudia; Begovich, John M; Ferrada, Juan J
2009-11-01
This is the final report that closed a joint collaboration effort between DOE and the National Nuclear Energy Commission of Brazil (CNEN). In 2005, DOE and CNEN started a collaborative effort to evaluate measures that can strengthen the effectiveness of international safeguards at a natural uranium conversion plant (NUCP). The work was performed by DOE s Oak Ridge National Laboratory and CNEN. A generic model of a NUCP was developed and typical processing steps were defined. Advanced instrumentation and techniques for verification purposes were identified and investigated. The scope of the work was triggered by the International Atomic Energy Agency s 2003 revised policy concerning the starting point of safeguards at uranium conversion facilities. Prior to this policy only the final products of the uranium conversion plant were considered to be of composition and purity suitable for use in the nuclear fuel cycle and therefore, subject to the IAEA safeguards control. DOE and CNEN have explored options for implementing the IAEA policy, although Brazil understands that the new policy established by the IAEA is beyond the framework of the Quadripartite Agreement of which it is one of the parties, together with Argentina, the Brazilian-Argentine Agency for Accounting and Control of Nuclear Materials (ABACC) and the IAEA. Two technical papers on this subject were published at the 2005 and 2008 INMM Annual Meetings.
Thermal effect of microwave antenna radiation on a generic model of thyroid gland
NASA Astrophysics Data System (ADS)
Gavriloaia, Gheorghe; Gavriloaia, Mariuca-Roxana; Ghemigean, Adina-Mariana
2010-11-01
The rapid diffusion of wireless communication systems has caused an increased concern for the potential detrimental effects on human health deriving from exposure to electromagnetic field. It penetrates the body and acts on all the organs, altering the cell membrane potential and the distribution of ions and dipoles. The thyroid gland is one of the most exposed vital organs and may be a target for electromagnetic radiation. This paper presents the computed temperature and specific absorption rate inside to a generic model of a human thyroid using signals radiated by an antenna operating in the 2450 MHz band and the power density levels up to 100 W/cm2. Calculations were carried out using the Finite Difference Time Domain method for the solving of two coupled differential equations, Maxwell and Pennes. The results show that the temperature can rise up to very dangerous levels, i.e., 46 °C, in a very short time. The estimated temperature distribution in the human thyroid due to exposure from microwave signals can be used to design the dangerous aria for personal working around high power emitted antenna and for medical applications.
NASA Astrophysics Data System (ADS)
Michelsen, Claus
2015-07-01
Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students’ achievement and attitude in both physics and mathematics. But although there are overwhelming amounts of literature on modeling in science and mathematics education, the interdisciplinary position is seldom addressed explicitly. Furthermore, there has been a striking lack of exposure of the question of how future teachers, who are largely educated in a mono-disciplinary fashion, can best become equipped to introduce genuinely interdisciplinary teaching activities to their future pupils. This paper presents some preliminary reflections upon a graduate course, which aims to prepare future physics and mathematics teachers for interdisciplinary teaching, and which has been designed on the basis of influential theoretical expositions of the concept of interdisciplinarity.
Performance of four turbulence closure models implemented using a generic length scale method
Warner, J.C.; Sherwood, C.R.; Arango, H.G.; Signell, R.P.
2005-01-01
A two-equation turbulence model (one equation for turbulence kinetic energy and a second for a generic turbulence length-scale quantity) proposed by Umlauf and Burchard [J. Marine Research 61 (2003) 235] is implemented in a three-dimensional oceanographic model (Regional Oceanographic Modeling System; ROMS v2.0). These two equations, along with several stability functions, can represent many popular turbulence closures, including the k-kl (Mellor-Yamada Level 2.5), k-??, and k-?? schemes. The implementation adds flexibility to the model by providing an unprecedented range of turbulence closure selections in a single 3D oceanographic model and allows comparison and evaluation of turbulence models in an otherwise identical numerical environment. This also allows evaluation of the effect of turbulence models on other processes such as suspended-sediment distribution or ecological processes. Performance of the turbulence models and sediment-transport schemes is investigated with three test cases for (1) steady barotropic flow in a rectangular channel, (2) wind-induced surface mixed-layer deepening in a stratified fluid, and (3) oscillatory stratified pressure-gradient driven flow (estuarine circulation) in a rectangular channel. Results from k-??, k-??, and gen (a new closure proposed by Umlauf and Burchard [J. Marine Research 61 (2003) 235]) are very similar for these cases, but the k-kl closure results depend on a wall-proximity function that must be chosen to suit the flow. Greater variations appear in simulations of suspended-sediment concentrations than in salinity simulations because the transport of suspended-sediment amplifies minor variations in the methods. The amplification is caused by the added physics of a vertical settling rate, bottom stress dependent resuspension, and diffusive transport of sediment in regions of well mixed salt and temperature. Despite the amplified sensitivity of sediment to turbulence models in the estuary test case, the four
Preventing clonal evolutionary processes in cancer: Insights from mathematical models.
Rodriguez-Brenes, Ignacio A; Wodarz, Dominik
2015-07-21
Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.
Mathematical models of continuous flow electrophoresis: Electrophoresis technology
NASA Technical Reports Server (NTRS)
Saville, Dudley A.
1986-01-01
Two aspects of continuous flow electrophoresis were studied: (1) the structure of the flow field in continuous flow devices; and (2) the electrokinetic properties of suspended particles relevant to electrophoretic separations. Mathematical models were developed to describe flow structure and stability, with particular emphasis on effects due to buoyancy. To describe the fractionation of an arbitrary particulate sample by continuous flow electrophoresis, a general mathematical model was constructed. In this model, chamber dimensions, field strength, buffer composition, and other design variables can be altered at will to study their effects on resolution and throughput. All these mathematical models were implemented on a digital computer and the codes are available for general use. Experimental and theoretical work with particulate samples probed how particle mobility is related to buffer composition. It was found that ions on the surface of small particles are mobile, contrary to the widely accepted view. This influences particle mobility and suspension conductivity. A novel technique was used to measure the mobility of particles in concentrated suspensions.
Mathematical and computer modeling of component surface shaping
NASA Astrophysics Data System (ADS)
Lyashkov, A.
2016-04-01
The process of shaping technical surfaces is an interaction of a tool (a shape element) and a component (a formable element or a workpiece) in their relative movements. It was established that the main objects of formation are: 1) a discriminant of a surfaces family, formed by the movement of the shape element relatively the workpiece; 2) an enveloping model of the real component surface obtained after machining, including transition curves and undercut lines; 3) The model of cut-off layers obtained in the process of shaping. When modeling shaping objects there are a lot of insufficiently solved or unsolved issues that make up a single scientific problem - a problem of qualitative shaping of the surface of the tool and then the component surface produced by this tool. The improvement of known metal-cutting tools, intensive development of systems of their computer-aided design requires further improvement of the methods of shaping the mating surfaces. In this regard, an important role is played by the study of the processes of shaping of technical surfaces with the use of the positive aspects of analytical and numerical mathematical methods and techniques associated with the use of mathematical and computer modeling. The author of the paper has posed and has solved the problem of development of mathematical, geometric and algorithmic support of computer-aided design of cutting tools based on computer simulation of the shaping process of surfaces.
Aerodynamic Effects of Simulated Ice Accretion on a Generic Transport Model
NASA Technical Reports Server (NTRS)
Broeren, Andy P.; Lee, Sam; Shah, Gautam H.; Murphy, Patrick C.
2012-01-01
An experimental research effort was begun to develop a database of airplane aerodynamic characteristics with simulated ice accretion over a large range of incidence and sideslip angles. Wind-tunnel testing was performed at the NASA Langley 12-ft Low-Speed Wind Tunnel using a 3.5 percent scale model of the NASA Langley Generic Transport Model. Aerodynamic data were acquired from a six-component force and moment balance in static-model sweeps from alpha = -5deg to 85deg and beta = -45 deg to 45 deg at a Reynolds number of 0.24 x10(exp 6) and Mach number of 0.06. The 3.5 percent scale GTM was tested in both the clean configuration and with full-span artificial ice shapes attached to the leading edges of the wing, horizontal and vertical tail. Aerodynamic results for the clean airplane configuration compared favorably with similar experiments carried out on a 5.5 percent scale GTM. The addition of the large, glaze-horn type ice shapes did result in an increase in airplane drag coefficient but had little effect on the lift and pitching moment. The lateral-directional characteristics showed mixed results with a small effect of the ice shapes observed in some cases. The flow visualization images revealed the presence and evolution of a spanwise-running vortex on the wing that was the dominant feature of the flowfield for both clean and iced configurations. The lack of ice-induced performance and flowfield effects observed in this effort was likely due to Reynolds number effects for the clean configuration. Estimates of full-scale baseline performance were included in this analysis to illustrate the potential icing effects.
Mathematical Modelling of Bacterial Populations in Bio-remediation Processes
NASA Astrophysics Data System (ADS)
Vasiliadou, Ioanna A.; Vayenas, Dimitris V.; Chrysikopoulos, Constantinos V.
2011-09-01
An understanding of bacterial behaviour concerns many field applications, such as the enhancement of water, wastewater and subsurface bio-remediation, the prevention of environmental pollution and the protection of human health. Numerous microorganisms have been identified to be able to degrade chemical pollutants, thus, a variety of bacteria are known that can be used in bio-remediation processes. In this study the development of mathematical models capable of describing bacterial behaviour considered in bio-augmentation plans, such as bacterial growth, consumption of nutrients, removal of pollutants, bacterial transport and attachment in porous media, is presented. The mathematical models may be used as a guide in designing and assessing the conditions under which areas contaminated with pollutants can be better remediated.
Mathematical modeling for a thermionic-AMTEC cascade system
Lodhi, M.A.; Schuller, M.; Hausgen, P.
1996-03-01
A mathematical modeling of a system consisting of a cascade of a thermionic energy conversion (TIEC) device and an alkali metal thermal to electrical conversion (AMTEC) device has been performed. The TIEC is heated by electron bombardment which converts heat partially into electricity and rejects the remaining. The AMTEC utilizes this reject heat of the TIEC. A mathematical thermal model of the cascade converter has been developed to analyze effects of key parameters such as power level, heat fluxes, temperatures, cascade geometry, etc. In this effort, a 9-node system of nonlinear simultaneous equations has been constructed which is solved by MATHCAD predicting the temperatures of the principal components and the heat flow. Through this study, a better understanding of the thermal coupling of the two converters was gained which helps to produce a more efficient cascade. {copyright} {ital 1996 American Institute of Physics.}
[Dolphin's flukes: A mathematical model of rigid wing].
Romanenko, E V; Pushkov, S G; Lopatin, V N
2015-01-01
New analytical method is used to estimate hydrodynamic forces produced by dolphin's flukes. A mathematical model is proposed that describes dolphin's flukes as a flat rigid rectangular wing whose pitch axis location varies, heaving and pitching amplitudes are sufficiently large, and the phase angle shift for the combined oscillations can change arbitrarily. The dolphin's flukes kinematic parameters are obtained and used to estimate hydrodynamic forces.
Mathematical modeling of a nickel-cadmium battery
NASA Technical Reports Server (NTRS)
Fan, Deyuan; White, Ralph E.
1991-01-01
Extensions are presented for a mathematical model of an Ni-CD cell (Fan and White, 1991). These extensions consist of intercalation thermodynamics for the nickel electrode and oxygen generation and reduction reactions during charge and overcharge. The simulated results indicate that intercalation may be important in the nickel electrode and that including the oxygen reactions provides a means of predicting the efficiency of the cell on charge and discharge.
Mathematical Model of the Jet Engine Fuel System
NASA Astrophysics Data System (ADS)
Klimko, Marek
2015-05-01
The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor) engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator) will be described, with respect to advanced predetermined simplifications.
Mathematical modeling of DNA's transcription process for the cancer study
NASA Astrophysics Data System (ADS)
Morales-Peñaloza, A.; Meza-López, C. D.; Godina-Nava, J. J.
2012-10-01
The cancer is a phenomenon caused by an anomaly in the DNA's transcription process, therefore it is necessary to known how such anomaly is generated in order to implement alternative therapies to combat it. We propose to use mathematical modeling to treat the problem. Is implemented a simulation of the process of transcription and are studied the transport properties in the heterogeneous case using nonlinear dynamics.
Mathematical analysis techniques for modeling the space network activities
NASA Technical Reports Server (NTRS)
Foster, Lisa M.
1992-01-01
The objective of the present work was to explore and identify mathematical analysis techniques, and in particular, the use of linear programming. This topic was then applied to the Tracking and Data Relay Satellite System (TDRSS) in order to understand the space network better. Finally, a small scale version of the system was modeled, variables were identified, data was gathered, and comparisons were made between actual and theoretical data.
[Dolphin's flukes: A mathematical model of rigid wing].
Romanenko, E V; Pushkov, S G; Lopatin, V N
2015-01-01
New analytical method is used to estimate hydrodynamic forces produced by dolphin's flukes. A mathematical model is proposed that describes dolphin's flukes as a flat rigid rectangular wing whose pitch axis location varies, heaving and pitching amplitudes are sufficiently large, and the phase angle shift for the combined oscillations can change arbitrarily. The dolphin's flukes kinematic parameters are obtained and used to estimate hydrodynamic forces. PMID:26852573
A Mathematical Model of Cancer Treatment by Radiotherapy
Yang, Chenxue
2014-01-01
A periodic mathematical model of cancer treatment by radiotherapy is presented and studied in this paper. Conditions on the coexistence of the healthy and cancer cells are obtained. Furthermore, sufficient conditions on the existence and globally asymptotic stability of the positive periodic solution, the cancer eradication periodic solution, and the cancer win periodic solution are established. Some numerical examples are shown to verify the validity of the results. A discussion is presented for further study. PMID:25478002
Mathematical modeling of stormwater pollution in a tidal embayment
Najjar, K.F.
1989-01-01
It has been recognized for many years that stormwater runoff provides a transport mechanism for non-point pollutants into the nation's waterways. As more watershed areas continue to urbanize, greater increases in pollutant loadings will continue to impact the water quality of the receiving water bodies. In many instances, the pollutant impact exceeds the assimilative capacity of the receiving water. To estimate the potential impacts of stormwater pollution, mathematical models are constructed. In this dissertation, mathematical models have been constructed to estimate the non-point pollutant loadings from an urbanizing area as well as to model the assimilative capacity of the receiving tidal embayment system. The models are capable of simulating the hydrologic aspects as well as the water quality cycles of the system as a function of urbanization. In determining the response of the receiving water system to stormwater loadings, the change in receiving water quality is modeled spatially as well as temporally. The overall model is composed of three subsystem models: a stormwater model, a hydrodynamic tidal model, and a receiving water quality model. Construction of the stormwater model is based on STORM (Storage, Treatment, Overflow, Runoff Model) by the US Army Corps of Engineers. A ground water component to the model has been added to adjust the model for application to the study area, Lakes Bay, New Jersey. The tidal model is developed from a pseudo two-dimensional approach. The methodology utilizes the link-node concept to simulate the embayment system. Solutions to equations of motion and continuity are solved using a finite difference method. The receiving water quality model is a two-dimensional time variable water quality model which is based in a finite segment approach.
A Mathematical Model of the Thermo-Anemometric Flowmeter
Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman
2015-01-01
A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed. PMID:26378535
The limitations of mathematical modeling in high school physics education
NASA Astrophysics Data System (ADS)
Forjan, Matej
The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems
A Mathematical Model Coupling Tumor Growth and Angiogenesis
Gomez, Hector
2016-01-01
We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments. PMID:26891163
Mathematical Model of a Thermostating Coating with a Thermoelectric Module
NASA Astrophysics Data System (ADS)
Zarubin, V. S.; Kuvyrkin, G. N.; Savel‧eva, I. Yu.
2015-11-01
On the basis of a variational formulation of the problem of stationary heat conduction in a heterogeneous solid, a mathematical model of a fragment of a flat heat-insulating layer containing a thermoelectric module has been constructed. This model has been used to establish conditions under which, when fulfilled, the heat-insulating layer can serve as a thermostating coating for an object with a given fixed temperature under convective-radiative heat exchange on the outer surface of the fragment under consideration. The results of the qualitative analysis of the proposed model are presented.
Generalized Mathematical Model Predicting the Mechanical Processing Topography
NASA Astrophysics Data System (ADS)
Leonov, S. L.; Markov, A. M.; Belov, A. B.; Sczygol, N.
2016-04-01
We propose a unified approach for the construction of mathematical models for the formation of surface topography and calculation of its roughness parameters for different methods of machining processes. The approach is based on a process of geometric copy tool in the material which superimposes plastico-elastic deformation, oscillatory occurrences in processing and random components of the profile. The unified approach makes it possible to reduce the time forcreation of simulated stochastic model for a specific type of processing and guarantee the accuracy of geometric parameters calculation of the surface. We make an application example of generalized model for calculation of roughness density distribution Ra in external sharpening.
Simakov, David S. A.; Pérez-Mercader, Juan
2013-01-01
Oscillating chemical reactions are common in biological systems and they also occur in artificial non-biological systems. Generally, these reactions are subject to random fluctuations in environmental conditions which translate into fluctuations in the values of physical variables, for example, temperature. We formulate a mathematical model for a nonisothermal minimal chemical oscillator containing a single negative feedback loop and study numerically the effects of stochastic fluctuations in temperature in the absence of any deterministic limit cycle or periodic forcing. We show that noise in temperature can induce sustained limit cycle oscillations with a relatively narrow frequency distribution and some characteristic frequency. These properties differ significantly depending on the noise correlation. Here, we have explored white and colored (correlated) noise. A plot of the characteristic frequency of the noise induced oscillations as a function of the correlation exponent shows a maximum, therefore indicating the existence of autonomous stochastic resonance, i.e. coherence resonance. PMID:23929212
ECO: A Generic Eutrophication Model Including Comprehensive Sediment-Water Interaction
Smits, Johannes G. C.; van Beek, Jan K. L.
2013-01-01
The content and calibration of the comprehensive generic 3D eutrophication model ECO for water and sediment quality is presented. Based on a computational grid for water and sediment, ECO is used as a tool for water quality management to simulate concentrations and mass fluxes of nutrients (N, P, Si), phytoplankton species, detrital organic matter, electron acceptors and related substances. ECO combines integral simulation of water and sediment quality with sediment diagenesis and closed mass balances. Its advanced process formulations for substances in the water column and the bed sediment were developed to allow for a much more dynamic calculation of the sediment-water exchange fluxes of nutrients as resulting from steep concentration gradients across the sediment-water interface than is possible with other eutrophication models. ECO is to more accurately calculate the accumulation of organic matter and nutrients in the sediment, and to allow for more accurate prediction of phytoplankton biomass and water quality in response to mitigative measures such as nutrient load reduction. ECO was calibrated for shallow Lake Veluwe (The Netherlands). Due to restoration measures this lake underwent a transition from hypertrophic conditions to moderately eutrophic conditions, leading to the extensive colonization by submerged macrophytes. ECO reproduces observed water quality well for the transition period of ten years. The values of its process coefficients are in line with ranges derived from literature. ECO’s calculation results underline the importance of redox processes and phosphate speciation for the nutrient return fluxes. Among other things, the results suggest that authigenic formation of a stable apatite-like mineral in the sediment can contribute significantly to oligotrophication of a lake after a phosphorus load reduction. PMID:23844160
ECO: a generic eutrophication model including comprehensive sediment-water interaction.
Smits, Johannes G C; van Beek, Jan K L
2013-01-01
The content and calibration of the comprehensive generic 3D eutrophication model ECO for water and sediment quality is presented. Based on a computational grid for water and sediment, ECO is used as a tool for water quality management to simulate concentrations and mass fluxes of nutrients (N, P, Si), phytoplankton species, detrital organic matter, electron acceptors and related substances. ECO combines integral simulation of water and sediment quality with sediment diagenesis and closed mass balances. Its advanced process formulations for substances in the water column and the bed sediment were developed to allow for a much more dynamic calculation of the sediment-water exchange fluxes of nutrients as resulting from steep concentration gradients across the sediment-water interface than is possible with other eutrophication models. ECO is to more accurately calculate the accumulation of organic matter and nutrients in the sediment, and to allow for more accurate prediction of phytoplankton biomass and water quality in response to mitigative measures such as nutrient load reduction. ECO was calibrated for shallow Lake Veluwe (The Netherlands). Due to restoration measures this lake underwent a transition from hypertrophic conditions to moderately eutrophic conditions, leading to the extensive colonization by submerged macrophytes. ECO reproduces observed water quality well for the transition period of ten years. The values of its process coefficients are in line with ranges derived from literature. ECO's calculation results underline the importance of redox processes and phosphate speciation for the nutrient return fluxes. Among other things, the results suggest that authigenic formation of a stable apatite-like mineral in the sediment can contribute significantly to oligotrophication of a lake after a phosphorus load reduction.
Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills
ERIC Educational Resources Information Center
Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven
2015-01-01
How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…
Mathematical Modelling of Cation Transport and Regulation in Yeast.
Kahm, Matthiasé; Kschischo, Maik
2016-01-01
Mathematical modelling of ion transport is a strategy to understand the complex interplay between various ionic species and their transporters. Such models should provide new insights and suggest new interesting experiments. Two essential variables in models for ion transport and control are the membrane potential and the intracellular pH, which generates an additional layer of complexity absent from many other models of biochemical reaction pathways. The aim of this text is to introduce the reader to the basic principles and assumptions of modelling in this field. A simplified model of potassium transport will be used as an example and will be derived in a step by step manner. This forms the basis for understanding the advantages and limitations of more complex models. These are briefly reviewed at the end of this chapter.
NASA Astrophysics Data System (ADS)
Cook, D. P.; Evans, J. W.
1995-02-01
This first of two related articles describes a mathematical model for electromagnetic casting in three dimensions, i.e., where the dependent variables are functions of all three spatial coordinates. It is shown how the method of inductances can be extended to three dimensions in order to solve Maxwell's equations for the electromagnetic field in and around the caster. The principal task here is the calculation of the inductances between loops of irregular shape, and the method by which this is done is described. The computations are self-consistent ones in that the free surface of the molten metal is adjusted in response to the supporting electromagnetic forces which are themselves dependent on the shape of that surface. The computed electromagnetic forces are input into a second phase of the calculation where melt flow is computed in three dimensions using the finite element package FIDAP.
Mathematical modeling of the neuron morphology using two dimensional images.
Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja
2016-02-01
In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.
Analyzing electrical activities of pancreatic β cells using mathematical models.
Cha, Chae Young; Powell, Trevor; Noma, Akinori
2011-11-01
Bursts of repetitive action potentials are closely related to the regulation of glucose-induced insulin secretion in pancreatic β cells. Mathematical studies with simple β-cell models have established the central principle that the burst-interburst events are generated by the interaction between fast membrane excitation and slow cytosolic components. Recently, a number of detailed models have been developed to simulate more realistic β cell activity based on expanded findings on biophysical characteristics of cellular components. However, their complex structures hinder our intuitive understanding of the underlying mechanisms, and it is becoming more difficult to dissect the role of a specific component out of the complex network. We have recently developed a new detailed model by incorporating most of ion channels and transporters recorded experimentally (the Cha-Noma model), yet the model satisfies the charge conservation law and reversible responses to physiological stimuli. Here, we review the mechanisms underlying bursting activity by applying mathematical analysis tools to representative simple and detailed models. These analyses include time-based simulation, bifurcation analysis and lead potential analysis. In addition, we introduce a new steady-state I-V (ssI-V) curve analysis. We also discuss differences in electrical signals recorded from isolated single cells or from cells maintaining electrical connections within multi-cell preparations. Towards this end, we perform simulations with our detailed pancreatic β-cell model.
A generic set of HF antennas for use with spherical model expansions
NASA Astrophysics Data System (ADS)
Katal, Nedim
1990-03-01
An antenna engineering handbook and database program has been constructed by engineers at the Lawrence Livermore National Laboratory (LLNL) using the Numerical Electromagnetics Code (NEC) antenna modeling program to prepare data performance on tactical field communication antennas used by the Army. It is desirable to have this information installed on a personnel computer (PC), using relational database techniques to select antennas based on performance criteria. This thesis obtains and analyses current distributions and radiation pattern data by using NEC for the following set of four (4) high frequency (HF) tactical generic antennas to be used in future spherical mode expansion work: a quarter wavelength basic whip, a one-wavelength horizontal quad Loop, a 564-foot longwire, and a sloping vee beam dipole. The results of this study show that the basic whip antenna provides good groundwave communication, but it has poor near vertical incident skywave (NVIS) performance. The current distribution has the characteristics of standing waves. The horizontal quad loop antenna is good for night vision imaging systems (NVIS) and medium range skywave communications. The current distribution is sinusoidal and continuous around the loop. The long wire antenna allows short, medium and long range communications and a standing wave current distribution occurs along the antenna axis due to non-termination. The sloping vee beam antenna favors long range communication and the current distribution is mainly that of travelling sinusoidal waves. Because of their well-known efficiency, the basic whip and quad loop can be used as reference standards for the spherical mode expansion work. The longwire and sloping vee beam antenna are unwieldy, but they are effective as base station antennas.