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.
Nonlinear mathematical model for a biaxial MOEMS scanning mirror
NASA Astrophysics Data System (ADS)
Ma, Yunfei; Davis, Wyatt O.; Ellis, Matt; Brown, Dean
2010-02-01
In this paper, a nonlinear mathematic model for Microvision's MOEMS scanning mirror is presented. The pixel placement accuracy requirement for scanned laser spot displays translates into a roughly 80dB signal to noise ratio, noise being a departure from the ideal trajectory. To provide a tool for understanding subtle nonidealities, a detailed nonlinear mathematical model is derived, using coefficients derived from physics, finite element analysis, and experiments. Twelve degrees of freedom parameterize the motion of a gimbal plate and a suspended micromirror; a thirteenth is the device temperature. Illustrations of the application of the model to capture subtleties about the device dynamics and transfer functions are presented.
Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit
NASA Astrophysics Data System (ADS)
Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie
2015-09-01
The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity
The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.
Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin
2016-07-01
Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data.
1998-09-11
34Evolution of Bloch electrons with Applied Electromagnetic Fields: the Semiclassical Equations ", European Jour- nal of Applied Mathematics (1996...establishment (with Jalal Shatah) of the existence of homoclinic orbits with complex spa- tial structure for perturbed NLS equations . This existence...a very small amount of diffraction. (v) McLaughlin (with T. Ueda) have in progress a study of precursors for model nonlinear wave equations . This
NASA Astrophysics Data System (ADS)
Saranya, J.; Rajendran, L.; Wang, L.; Fernandez, C.
2016-10-01
For the first time a mathematical modelling of the enzymatic glucose membraneless fuel cell with direct electron transfer has been reported. The niche of this mathematical modelling is the description of the new Homotopy perturbation method to solve the nonlinear differential equations that describes glucose concentration and hydrogen ions respectively. The analytical results of an enzymatic fuel cell should be used, while developing fuel cell, to estimate its various kinetic parameters to attain the highest power value. Our analytical results are compared with limiting case results and satisfactory agreement is noted. The influence of parameters on the concentrations are discussed.
1994-01-03
August, 1991. Thesis - "Applications of the Inverse Spectral Transform to a Korteweg - DeVries Equation with a Kuramoto-Sivashinsky-Type Perturbation... equations , the mathematical theory of nematic optics involves strong coupling between the electromagnetic and nematic director (molecular orientation... equations for the electric field E coupled to a nonlinear parabolic equation for the director n, a field of unit vectors which describes the local molecular
A non-linear mathematical model for a three species ecosystem: Hippos in Lake Edward.
Bologna, Mauro; Chandía, Kristopher J; Flores, J C
2016-01-21
In this work we study a non-linear mathematical model based on three different interacting species. We apply our model to Lake Edward ecosystem consisting in hippos, tilapia fishes and human inhabitants. In this case, we estimate the values of the key parameters using actual data and show the reliability of the proposed model as a predictive tool. We also show, via numerical calculations and parameter values that the ecosystem associated to the lake is very far from reaching a stable equilibrium. Through our analysis we provide the conditions for a possible coexistence among the three species.
Mathematical Modeling and Control of Nonlinear Oscillators with Shape Memory Alloys
NASA Astrophysics Data System (ADS)
Bendame, Mohamed
Shape memory alloys (SMAs) belong to an interesting type of materials that have attracted the attention of scientists and engineers over the last few decades. They have some interesting properties that made them the subject of extensive research to find the best ways to utilize them in different engineering, biomedical, and scientific applications. In this thesis, we develop a mathematical model and analyze the behavior of SMAs by considering a one degree of freedom nonlinear oscillator consisting of a mass connected to a fixed frame through a viscous damping and a shape memory alloy device. Due to the nonlinear and dissipative nature of shape memory alloys, optimal control and Lyapunov stability theories are used to design a controller to stabilize the response of the one degree of freedom nonlinear oscillator. Since SMAs exist in two phases, martensite and austenite, and their phase transformations are dependent on stress and temperature, this work is presented in two parts. The first part deals with the nonlinear oscillator system in its two separate phases by considering a temperature where the SMA exists in only one of the phases. A model for each phase is developed based on Landau-Ginzburg-Devonshire theory that defines the free energy in a polynomial form enabling us to describe the SMAs shape memory effect and pseudoelasticity. However, due to the phenomenon of hysteresis in SMAs, the response of the nonlinear oscillator with a SMA element, in either phase, is chaotic and unstable. In order to stabilize the chaotic behavior, an optimal linear quadratic regulator controller is designed around a stable equilibrium for the martensitic and the austenitic phases. The closed-loop response for each phase is then simulated and computational results are presented. The second part of the thesis deals with the entire system in its dynamics by combining the two phases and taking into account the effect of temperature on the response of the system. Governing equations
Nonlinear Gompertz Curve Models of Achievement Gaps in Mathematics and Reading
ERIC Educational Resources Information Center
Cameron, Claire E.; Grimm, Kevin J.; Steele, Joel S.; Castro-Schilo, Laura; Grissmer, David W.
2015-01-01
This study examined achievement trajectories in mathematics and reading from school entry through the end of middle school with linear and nonlinear growth curves in 2 large longitudinal data sets (National Longitudinal Study of Youth--Children and Young Adults and Early Childhood Longitudinal Study--Kindergarten Cohort [ECLS-K]). The S-shaped…
Bifurcation and Resonance of a Mathematical Model for Non-Linear Motion of a Flooded Ship in Waves
NASA Astrophysics Data System (ADS)
Murashige, S.; Aihara, K.; Komuro, M.
1999-02-01
A flooded ship can exhibit undesirable non-linear roll motion even in waves of moderate amplitude. In order to understand the mechanism of this non-linear phenomenon, the non-linearly coupled dynamics of a ship and flood water are considered using a mathematical model for the simplified motion of a flooded ship in regular beam waves. This paper describes bifurcation and resonance of this coupled system. A bifurcation diagram shows that large-amplitude subharmonic motion exists in a wide range of parameters, and that the Hopf bifurcation is observed due to the dynamic effects of flood water. Resonance frequencies can be determined by linearization of this model. Comparison between the resonant points and the bifurcation curves suggests that non-linear resonance of this model can bring about large-amplitude subharmonic motion, even if it is in the non-resonate state of the linearized system.
Petros, O.; Kuhn, S.; Popa, G.
1982-06-01
A new, efficient method for investigating and optimizing the ion-nitriding process in a glow-discharge plasma is proposed and worked out in detail for the mass kinetics of Rp-3 steel. This method, which is based on the concepts of experiment planning, mathematical modelling, and nonlinear optimization, is quite general and potentially applicable to a wide class of technological and other processes depending on several parameters.
Peluso, Paul R; Liebovitch, Larry S; Gottman, John M; Norman, Michael D; Su, Jessica
2012-01-01
Mathematical models, such as the one developed by Gottman et al. (1998, 2000, 2002) to understand the interaction between husbands and wives, can provide novel insights into the dynamics of the therapeutic relationship. A set of nonlinear equations were used to model the changing emotional state of a therapist and client. The results suggest: (1) The person that is most responsive to the other achieves the most positive state, (2) the emotional state of the client oscillates before reaching its final state, (3) therapy is least successful when the therapist starts from a negative state, and (4) there is an inverse relationship between models that change only the influence parameter and models that change only the inertia parameter, creating a series of four basic models to work with. These theoretical models require further, empirical investigation to test the derived parameters. If validated, or revised based on observations of therapist-client relationships in development, they could provide specific direction in creating successful therapeutic relationships for training clinicians and those already in practice.
Terry, Emmanuelle; Marvel, Jacqueline; Arpin, Christophe; Gandrillon, Olivier; Crauste, Fabien
2012-08-01
The primary CD8 T cell immune response, due to a first encounter with a pathogen, happens in two phases: an expansion phase, with a fast increase of T cell count, followed by a contraction phase. This contraction phase is followed by the generation of memory cells. These latter are specific of the antigen and will allow a faster and stronger response when encountering the antigen for the second time. We propose a nonlinear mathematical model describing the T CD8 immune response to a primary infection, based on three nonlinear ordinary differential equations and one nonlinear age-structured partial differential equation, describing the evolution of CD8 T cell count and pathogen amount. We discuss in particular the roles and relevance of feedback controls that regulate the response. First we reduce our system to a system with a nonlinear differential equation with a distributed delay. We study the existence of two steady states, and we analyze the asymptotic stability of these steady states. Second we study the system with a discrete delay, and analyze global asymptotic stability of steady states. Finally, we show some simulations that we can obtain from the model and confront them to experimental data.
NASA Astrophysics Data System (ADS)
Fenili, André
2012-11-01
In this paper the author investigates the angular position and vibration control of a nonlinear rigid-flexible two link robotic manipulator considering fast angular maneuvers. The nonlinear control technique named State-Dependent Riccati Equation (SDRE) is used here to achieve these aims. In a more realistic approach, it is considered that some states can be measured and some states cannot be measured. The states not measured are estimated in order to be used for the SDRE control. These states are all the angular velocities and the velocity of deformation of the flexible link. A state-dependent Riccati equation-based estimator is used here. Not only different initial conditions between the system to be controlled (here named "real" system) and the estimator but also a different mathematical model is considered as the estimation model in order to verify the limitations of the proposed estimation and control techniques. The mathematical model that emulates the real system to be controlled considers two modes expansion and the estimation model considers only one mode expansion. The results for the different approaches are compared and discussed.
NASA Technical Reports Server (NTRS)
Suit, W. T.
1986-01-01
Shuttle flight test data were used to determine values for the short-period parameters. The best identified, as judged by its estimated standard deviation, was the elevon effectiveness parameter C (sub m (sub sigma e squared)). However, the scatter about the preflight prediction of C (sub m (sub sigma e squared)) was large. Other investigators have suggested that adding nonlinear terms to the mathematical model used to identify C (sub m (sub sigma e)) could reduce the scatter. The results of this investigation show that C (sub m (sub sigma e squared)) is the only identifiable nonlinear parameter applicable and that the changes in C (sub m (sub sigma e)) values when C (sub m (sub sigma e squared)) is included are in the order of ten percent for the data estimated.
[Mathematical models of hysteresis
Mayergoyz, I.D.
1991-01-01
The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories''. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.
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 Modeling and Nonlinear Dynamical Analysis of Cell Growth in Response to Antibiotics
NASA Astrophysics Data System (ADS)
Jin, Suoqin; Niu, Lili; Wang, Gang; Zou, Xiufen
2015-06-01
This study is devoted to the revelation of the dynamical mechanisms of cell growth in response to antibiotics. We establish a mathematical model of ordinary differential equations for an antibiotic-resistant growth system with one positive feedback loop. We perform a dynamical analysis of the behavior of this model system. We present adequate sets of conditions that can guarantee the existence and stability of biologically-reasonable steady states. Using bifurcation analysis and numerical simulation, we show that the relative growth rate, which is defined as the ratio of the cell growth rate to the basal cell growth rate in the absence of antibiotics, can exhibit bistable behavior in an extensive range of parameters that correspond to a growth state and a nongrowth state in biology. We discover that both antibiotic and antibiotic resistance genes can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to the onset of bistability. These results would contribute to a better understanding of not only the evolution of antibiotics but also the emergence of drug resistance in other diseases.
ERIC Educational Resources Information Center
Scheidt, Douglas M.
1995-01-01
Reviews three functions of the "Scientist" software package useful for the social sciences: nonlinear curve fitting, parameter estimation, and data/regression plotting. Social scientists are likely to find limitations and unfamiliar procedures in "Scientist". Its value lies in its visual presentation of data and regression curves and the…
NASA Astrophysics Data System (ADS)
Chavarette, Fábio Roberto; Balthazar, José Manoel; Peruzzi, Nelson José; Rafikov, Marat
2009-03-01
The Fitzhugh-Nagumo (FH) mathematical model is considered a simplification of the Hodgkin-Huxley (HH) model. This paper analyzes the non-linear dynamics of the Fitzhugh-Nagumo (FN) mathematical model, and still presents some modifications in the governing equations of the system in order to transform it into a non-ideal one (taking into account that an energy source has limited power supply). We also developed an optimal linear control design and used Sinhas's theory for the membrane's action potential in order to stabilize the variation of this potential.
PREFACE: Physics and Mathematics of Nonlinear Phenomena 2013 (PMNP2013)
NASA Astrophysics Data System (ADS)
Konopelchenko, B. G.; Landolfi, G.; Martina, L.; Vitolo, R.
2014-03-01
Modern theory of nonlinear integrable equations is nowdays an important and effective tool of study for numerous nonlinear phenomena in various branches of physics from hydrodynamics and optics to quantum filed theory and gravity. It includes the study of nonlinear partial differential and discrete equations, regular and singular behaviour of their solutions, Hamitonian and bi- Hamitonian structures, their symmetries, associated deformations of algebraic and geometrical structures with applications to various models in physics and mathematics. The PMNP 2013 conference focused on recent advances and developments in Continuous and discrete, classical and quantum integrable systems Hamiltonian, critical and geometric structures of nonlinear integrable equations Integrable systems in quantum field theory and matrix models Models of nonlinear phenomena in physics Applications of nonlinear integrable systems in physics The Scientific Committee of the conference was formed by Francesco Calogero (University of Rome `La Sapienza', Italy) Boris A Dubrovin (SISSA, Italy) Yuji Kodama (Ohio State University, USA) Franco Magri (University of Milan `Bicocca', Italy) Vladimir E Zakharov (University of Arizona, USA, and Landau Institute for Theoretical Physics, Russia) The Organizing Committee: Boris G Konopelchenko, Giulio Landolfi, Luigi Martina, Department of Mathematics and Physics `E De Giorgi' and the Istituto Nazionale di Fisica Nucleare, and Raffaele Vitolo, Department of Mathematics and Physics `E De Giorgi'. A list of sponsors, speakers, talks, participants and the conference photograph are given in the PDF. Conference photograph
NASA Technical Reports Server (NTRS)
Glukharev, K. K.; Morozova, N. I.; Potemkin, B. A.; Solovyev, V. S.; Frolov, K. V.
1973-01-01
A mathematical model of the human body was constructed, under the action of harmonic vibrations, in the 2.5-7 Hz frequency range. In this frequency range, the model of the human body as a vibrating system, with concentrated parameters is considered. Vertical movements of the seat and vertical components of vibrations of the human body are investigated.
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.
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…
NASA Astrophysics Data System (ADS)
Özgüven, H. N.
1991-03-01
A six-degree-of-freedom non-linear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the non-linear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the "static transmission error method" developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.
NASA Technical Reports Server (NTRS)
Ozguven, H. Nevzat
1991-01-01
A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.
NASA Astrophysics Data System (ADS)
Duxbury, N. S.; Romanovsky, V. E.; Romanovskii, N. N.; Garagulya, L. S.; Brouchkov, A. V.; Komarov, I. A.; Roman, L. T.; Tipenko, G. S.; Buldovich, S. N.; Maximova, L. N.
2012-12-01
We have developed coupled permafrost - carbon physical and numerical models, where carbon is in the form of methane clathrate hydrate ( CH4*6H2O ) in a porous subsurface environment. The driving force for the subsurface temperature field dynamics is climate variations on the Earth's surface. This is an upper boundary condition for the nonlinear evolutionary system of partial differential equations (PDEs) describing subsurface heat transfer (parabolic PDEs) in a generalized Stefan formulation. The developed numerical model is a valuable computational tool to quantitatively study nonlinear dynamical thermal processes with phase transitions in terrestrial and Martian subsurfaces. Our model is multifrontal and therefore allows one to perform computations for a problem with any number of emerging/vanishing phase transition interfaces (both in methane gas hydrate deposits and in permafrost), since the model treats these fronts implicitly in an enthalpy formulation and in corresponding finite-difference scheme. This model takes into account the pressure (and therefore the depth) dependence of the phase transition temperature for methane clathrate hydrate. We have performed model computations using the thermophysical characteristics (heat capacity, density/porosity, thermal conductivity) for the Siberian subsurface. It can be used as a terrestrial analog for the Martian subsurface (e.g., Duxbury et al., 2001). Also, thermophysical coefficients from laboratory experiments for methane clathrate hydrate were used in our model. In addition, our model takes into account the dependence of subsurface thermophysical characteristics on temperature and spatial coordinates. The results of our computations and their interpretation will be presented. References. N. S. Duxbury, I. A. Zotikov, K. H. Nealson, V. E. Romanovsky, F. D. Carsey (2001). A numerical model for an alternative origin of Lake Vostok and its exobiological implications for Mars, Journal of Geophysical Research
Teaching Mathematical Modelling.
ERIC Educational Resources Information Center
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Mathematical modeling in neuroendocrinology.
Bertram, Richard
2015-04-01
Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.
ERIC Educational Resources Information Center
Fox, William
2012-01-01
The purpose of our modeling effort is to predict future outcomes. We assume the data collected are both accurate and relatively precise. For our oscillating data, we examined several mathematical modeling forms for predictions. We also examined both ignoring the oscillations as an important feature and including the oscillations as an important…
ADMET: ADipocyte METabolism mathematical model.
Micheloni, Alessio; Orsi, Gianni; De Maria, Carmelo; Vozzi, Giovanni
2015-01-01
White fat cells have an important physiological role in maintaining triglyceride and free fatty acid levels due to their fundamental storage property, as well as determining insulin resistance. ADipocyte METabolism is a mathematical model that mimics the main metabolic pathways of human white fat cell, connecting inputs (composition of culture medium) to outputs (glycerol and free fatty acid release). It is based on a set of nonlinear differential equations, implemented in Simulink® and controlled by cellular energetic state. The validation of this model is based on a comparison between the simulation results and a set of experimental data collected from the literature.
Mathematical models of bipolar disorder
NASA Astrophysics Data System (ADS)
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
Mathematical Modeling: A Structured Process
ERIC Educational Resources Information Center
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Richardson, mathematical modeller
NASA Astrophysics Data System (ADS)
Vreugdenhil, C. B.
1994-03-01
On the occasion of the 70th anniversary of Richardson's book Weather Prediction by Numerical Process (Cambridge University Press, Cambridge), a review is given of Richardson's scientific work. He made lasting contributions to very diverse fields of interest, such as finite-difference methods and related numerical methods, weather forecasting by computer, turbulence, international relations, and fractals. Although he was an original experimenter, the main present-day interest is in his mathematical modelling work.
ERIC Educational Resources Information Center
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
Generalized Nonlinear Yule Models
NASA Astrophysics Data System (ADS)
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
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…
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 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…
Mathematical models of vaccination.
Scherer, Almut; McLean, Angela
2002-01-01
Mathematical models of epidemics have a long history of contributing to the understanding of the impact of vaccination programmes. Simple, one-line models can predict target vaccination coverage that will eradicate an infectious agent, whilst other questions require complex simulations of stochastic processes in space and time. This review introduces some simple ordinary differential equation models of mass vaccination that can be used to address important questions about the predicted impact of vaccination programmes. We show how to calculate the threshold vaccination coverage rate that will eradicate an infection, explore the impact of vaccine-induced immunity that wanes through time, and study the competitive interactions between vaccine susceptible and vaccine resistant strains of infectious agent.
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…
Teaching and Assessing Mathematical Modelling.
ERIC Educational Resources Information Center
Lingefjard, T.
2002-01-01
Reports on the observed actions of prospective Swedish secondary mathematics teachers as they were working in a modeling situation. Discusses the way the students tackled the modeling situation and their strategies and attitudes as well as the difficulties in assessing mathematical modeling performance. (KHR)
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 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.
Identifying nonlinear biomechanical models by multicriteria analysis
NASA Astrophysics Data System (ADS)
Srdjevic, Zorica; Cveticanin, Livija
2012-02-01
In this study, the methodology developed by Srdjevic and Cveticanin (International Journal of Industrial Ergonomics 34 (2004) 307-318) for the nonbiased (objective) parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n-degree of freedom (DOF) nonlinear biomechanical models. The dynamic performance of the n-DOF nonlinear model is described in terms of response functions in the frequency domain, such as the driving-point mechanical impedance and seat-to-head transmissibility function. For randomly generated parameters of the model, nonlinear equations of motion are solved using the Runge-Kutta method. The appropriate data transformation from the time-to-frequency domain is performed by a discrete Fourier transformation. Squared deviations of the response functions from the target values are used as the model performance evaluation criteria, thus shifting the problem into the multicriteria framework. The objective weights of criteria are obtained by applying the Shannon entropy concept. The suggested methodology is programmed in Pascal and tested on a 4-DOF nonlinear lumped parameter biomechanical model. The identification process over the 2000 generated sets of parameters lasts less than 20 s. The model response obtained with the imbedded identified parameters correlates well with the target values, therefore, justifying the use of the underlying concept and the mathematical instruments and numerical tools applied. It should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model.
Purpura, David J; Logan, Jessica A R
2015-12-01
Both mathematical language and the approximate number system (ANS) have been identified as strong predictors of early mathematics performance. Yet, these relations may be different depending on a child's developmental level. The purpose of this study was to evaluate the relations between these domains across different levels of ability. Participants included 114 children who were assessed in the fall and spring of preschool on a battery of academic and cognitive tasks. Children were 3.12 to 5.26 years old (M = 4.18, SD = .58) and 53.6% were girls. Both mixed-effect and quantile regressions were conducted. The mixed-effect regressions indicated that mathematical language, but not the ANS, nor other cognitive domains, predicted mathematics performance. However, the quantile regression analyses revealed a more nuanced relation among domains. Specifically, it was found that mathematical language and the ANS predicted mathematical performance at different points on the ability continuum. These dual nonlinear relations indicate that different mechanisms may enhance mathematical acquisition dependent on children's developmental abilities.
Mathematical modelling in developmental biology.
Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier
2013-06-01
In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.
Model updating of nonlinear structures from measured FRFs
NASA Astrophysics Data System (ADS)
Canbaloğlu, Güvenç; Özgüven, H. Nevzat
2016-12-01
There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by using experimental measurements in order to have a more accurate model. Most of the model updating methods used in structural dynamics are for linear systems. However, in real life applications most of the structures have nonlinearities, which restrict us applying model updating techniques available for linear structures, unless they work in linear range. Well-established frequency response function (FRF) based model updating methods would easily be extended to a nonlinear system if the FRFs of the underlying linear system (linear FRFs) could be experimentally measured. When frictional type of nonlinearity co-exists with other types of nonlinearities, it is not possible to obtain linear FRFs experimentally by using low level forcing. In this study a method (named as Pseudo Receptance Difference (PRD) method) is presented to obtain linear FRFs of a nonlinear structure having multiple nonlinearities including friction type of nonlinearity. PRD method, calculates linear FRFs of a nonlinear structure by using FRFs measured at various forcing levels, and simultaneously identifies all nonlinearities in the system. Then, any model updating method can be used to update the linear part of the mathematical model. In this present work, PRD method is used to predict the linear FRFs from measured nonlinear FRFs, and the inverse eigensensitivity method is employed to update the linear finite element (FE) model of the nonlinear structure. The proposed method is validated with different case studies using nonlinear lumped single-degree of freedom system, as well as a continuous system. Finally, a real nonlinear T-beam test structure is used to show the application and the accuracy of the proposed method. The accuracy of the updated nonlinear model of the
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.
Mathew, Shibin; Bartels, John; Banerjee, Ipsita; Vodovotz, Yoram
2014-10-07
The precise inflammatory role of the cytokine interleukin (IL)-6 and its utility as a biomarker or therapeutic target have been the source of much debate, presumably due to the complex pro- and anti-inflammatory effects of this cytokine. We previously developed a nonlinear ordinary differential equation (ODE) model to explain the dynamics of endotoxin (lipopolysaccharide; LPS)-induced acute inflammation and associated whole-animal damage/dysfunction (a proxy for the health of the organism), along with the inflammatory mediators tumor necrosis factor (TNF)-α, IL-6, IL-10, and nitric oxide (NO). The model was partially calibrated using data from endotoxemic C57Bl/6 mice. Herein, we investigated the sensitivity of the area under the damage curve (AUCD) to the 51 rate parameters of the ODE model for different levels of simulated LPS challenges using a global sensitivity approach called Random Sampling High Dimensional Model Representation (RS-HDMR). We explored sufficient parametric Monte Carlo samples to generate the variance-based Sobol' global sensitivity indices, and found that inflammatory damage was highly sensitive to the parameters affecting the activity of IL-6 during the different stages of acute inflammation. The AUCIL6 showed a bimodal distribution, with the lower peak representing healthy response and the higher peak representing sustained inflammation. Damage was minimal at low AUCIL6, giving rise to a healthy response. In contrast, intermediate levels of AUCIL6 resulted in high damage, and this was due to the insufficiency of damage recovery driven by anti-inflammatory responses from IL-10 and the activation of positive feedback sustained by IL-6. At high AUCIL6, damage recovery was interestingly restored in some population of simulated animals due to the NO-mediated anti-inflammatory responses. These observations suggest that the host's health status during acute inflammation depends in a nonlinear fashion on the magnitude of the inflammatory stimulus
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…
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.
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.
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…
Nonlinear Dynamic Models in Advanced Life Support
NASA Technical Reports Server (NTRS)
Jones, Harry
2002-01-01
To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.
NASA Astrophysics Data System (ADS)
Ge, Hao; Qian, Hong
2017-01-01
This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with N species, M reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical thermodynamics under G. N. Lewis' kinetic law of entire equilibrium (detailed balance in nonlinear chemical kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. The kinetic models are represented by a Markovian jumping process. A generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink are the major discoveries. The proof is based on the large deviation principle of this type of Markov processes. A general fluctuation dissipation theorem for stochastic reaction kinetics is also proved. The mathematical theory illustrates how a novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a multi-scale system.
Mathematical Modeling in Continuum Mechanics
NASA Astrophysics Data System (ADS)
Temam, Roger; Miranville, Alain
2005-06-01
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
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…
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…
ASTP ranging system mathematical model
NASA Technical Reports Server (NTRS)
Ellis, M. R.; Robinson, L. H.
1973-01-01
A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.
The mathematics of non-linear metrics for nested networks
NASA Astrophysics Data System (ADS)
Wu, Rui-Jie; Shi, Gui-Yuan; Zhang, Yi-Cheng; Mariani, Manuel Sebastian
2016-10-01
Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness-complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness-complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.
Mathematical Modeling: A Bridge to STEM Education
ERIC Educational Resources Information Center
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…
The 24-Hour Mathematical Modeling Challenge
ERIC Educational Resources Information Center
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
Mathematical 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.
A nonlinear biomathematical model for the study of intracranial aneurysms.
Nieto, J J; Torres, A
2000-08-01
The formation and rupture of aneurysms is a significant medical problem, but is not clearly understood. Most intracranial aneurysm are located in the circle of Willis. We consider a nonlinear mathematical model that simulates the blood flow inside the aneurysm, one of the relevant factors in the evolution of an aneurysm. Different techniques from nonlinear analysis are used in order to obtain, from the model, several consequences that would help to understand some medical aspects of aneurysms of the circle of Willis.
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…
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 Modelling with Young Children
ERIC Educational Resources Information Center
English, Lyn D.; Watters, James J.
2004-01-01
This paper addresses the first year of a three-year, longitudinal study which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third-graders (8 years of age) and their teachers participated in the first year of the program, which involved several preliminary modeling…
Mathematical modeling of biological ensembles
Harlow, F.H.; Sandoval, D.L.; Ruppel, H.M.
1986-07-01
Mathematical models are proposed for three distinctly different aspects of biophysical dynamics: mental dynamics, mob dynamics, and the evolution of species. Each section is self-contained, but the approaches are unified by the employment of stochastic equations for the interactive dynamics of numerous discrete entities.
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…
Nonlinear Modeling by Assembling Piecewise Linear Models
NASA Technical Reports Server (NTRS)
Yao, Weigang; Liou, Meng-Sing
2013-01-01
To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.
Piezomagnetoelastic broadband energy harvester: Nonlinear modeling and characterization
NASA Astrophysics Data System (ADS)
Aravind Kumar, K.; Ali, S. F.; Arockiarajan, A.
2015-11-01
Piezomagnetoelastic energy harvesters are one among the widely explored configurations to improve the broadband characteristics of vibration energy harvesters. Such nonlinear harvesters follow a Moon beam model with two magnets at the base and one at the tip of the beam. The present article develops a geometric nonlinear mathematical model for the broadband piezomagnetoelastic energy harvester. The electromechanical coupling and the nonlinear magnetic potential equations are developed from the dimensional system parameters to describe the nonlinear dynamics exhibited by the system. The developed model is capable of characterizing the monostable, bistable and tristable operating regimes of the piezomagnetoelastic energy harvester, which are not explicit in the Duffing representation of the system. Bifurcations and attractor motions are analyzed as nonlinear functions of the distance between base magnets and the field strength of the tip magnet. The model is further used to characterize the potential wells and stable states, with due focus on the performance of the system in broadband energy harvesting.
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.
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…
Mathematical Modeling in the High School Curriculum
ERIC Educational Resources Information Center
Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary
2016-01-01
In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…
Problem Posing and Solving with Mathematical Modeling
ERIC Educational Resources Information Center
English, Lyn D.; Fox, Jillian L.; Watters, James J.
2005-01-01
Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.
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…
NASA Technical Reports Server (NTRS)
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
Daly, Edoardo; Porporato, Amilcare
2004-11-01
Similarity solutions of the shallow-water equation with a generalized resistance term are studied for open channel flows when both inertial and gravity forces are negligible. The resulting model encompasses various particular cases that appear, in addition to mathematical hydraulics, in diverse physical phenomena, such as gravity currents, creeping flows of Newtonian and non-Newtonian fluids, thin films, and nonlinear Fokker-Planck equations. Solutions of both source-type and dam-break problems are analyzed. Closed-form solutions are discussed, when possible, along with a qualitative study of two phase-plane formulations based on two different variable transformations.
Fallacies of composition in nonlinear marketing models
NASA Astrophysics Data System (ADS)
Bischi, Gian Italo; Cerboni Baiardi, Lorenzo
2015-01-01
In this paper we consider some nonlinear discrete-time dynamic models proposed in the literature to represent marketing competition, and we use these models to critically discuss the statement, often made in economic literature, that identical agents behave identically and quasi-identical ones behave in a similar way. We show, through examples and some general mathematical statements, that the one-dimensional model of a representative agent, whose dynamics summarize the common behavior of identical interacting agents, may be misleading. In order to discuss these topics some simple methods for the study of local stability and bifurcations are employed, as well as numerical examples where some results taken from the literature on chaos synchronization are applied to two-dimensional marketing models that exhibit riddling, blowout and other global phenomena related to the existence of measure-theoretic attractors.
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.
Employment of CB models for non-linear dynamic analysis
NASA Technical Reports Server (NTRS)
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Mathematical modeling of drug delivery.
Siepmann, J; Siepmann, F
2008-12-08
Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design
Summer Camp of Mathematical Modeling in China
ERIC Educational Resources Information Center
Tian, Xiaoxi; Xie, Jinxing
2013-01-01
The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…
Mathematical Modelling of Folate Metabolism
Panetta, John C.; Paugh, Steven W.
2013-01-01
Folate metabolism is a complex biological process that is influenced by many variables including transporters, co-factors and enzymes. Mathematical models provide a useful tool to evaluate this complex system and to elucidate hypotheses that would be otherwise untenable to test in vitro or in vivo. Forty years of model development and refinement along with enhancements in technology have led to systematic improvement in our biological understanding from these models. However, increased complexity does not always lead to increased understanding, and a balanced approach to modelling the system is often advantageous. This approach should address questions about sensitivity of the model to variation and incorporate genomic data. The folate model is a useful platform for investigating the effects of antifolates on the folate pathway. The utility of the model is demonstrated through interrogation of drug resistance, drug-drug interactions, drug selectivity, and drug doses and schedules. Mathematics can be used to create models with the ability to design and improve rationale therapeutic interventions. PMID:23703958
Corrigendum and addendum. Modeling weakly nonlinear acoustic wave propagation
Christov, Ivan; Christov, C. I.; Jordan, P. M.
2014-12-18
This article presents errors, corrections, and additions to the research outlined in the following citation: Christov, I., Christov, C. I., & Jordan, P. M. (2007). Modeling weakly nonlinear acoustic wave propagation. The Quarterly Journal of Mechanics and Applied Mathematics, 60(4), 473-495.
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. PMID:23852667
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 models in medicine: Diseases and epidemics
Witten, M.
1987-01-01
This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling.
Mathematical Models Of Turbulence In Hypersonic Flow
NASA Technical Reports Server (NTRS)
Marvin, J. G.; Coakley, T. J.
1991-01-01
Report discusses mathematical models of turbulence used in numerical simulations of complicated viscous, hypersonic flows. Includes survey of essential features of models and their statuses in applications.
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 model of nonlinear electrodynamics
Kruglov, S.I.
2015-02-15
A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.
Nonlinear Statistical Modeling of Speech
NASA Astrophysics Data System (ADS)
Srinivasan, S.; Ma, T.; May, D.; Lazarou, G.; Picone, J.
2009-12-01
Contemporary approaches to speech and speaker recognition decompose the problem into four components: feature extraction, acoustic modeling, language modeling and search. Statistical signal processing is an integral part of each of these components, and Bayes Rule is used to merge these components into a single optimal choice. Acoustic models typically use hidden Markov models based on Gaussian mixture models for state output probabilities. This popular approach suffers from an inherent assumption of linearity in speech signal dynamics. Language models often employ a variety of maximum entropy techniques, but can employ many of the same statistical techniques used for acoustic models. In this paper, we focus on introducing nonlinear statistical models to the feature extraction and acoustic modeling problems as a first step towards speech and speaker recognition systems based on notions of chaos and strange attractors. Our goal in this work is to improve the generalization and robustness properties of a speech recognition system. Three nonlinear invariants are proposed for feature extraction: Lyapunov exponents, correlation fractal dimension, and correlation entropy. We demonstrate an 11% relative improvement on speech recorded under noise-free conditions, but show a comparable degradation occurs for mismatched training conditions on noisy speech. We conjecture that the degradation is due to difficulties in estimating invariants reliably from noisy data. To circumvent these problems, we introduce two dynamic models to the acoustic modeling problem: (1) a linear dynamic model (LDM) that uses a state space-like formulation to explicitly model the evolution of hidden states using an autoregressive process, and (2) a data-dependent mixture of autoregressive (MixAR) models. Results show that LDM and MixAR models can achieve comparable performance with HMM systems while using significantly fewer parameters. Currently we are developing Bayesian parameter estimation and
Nonlinear, discrete flood event models, 2. Assessment of statistical nonlinearity
NASA Astrophysics Data System (ADS)
Bates, Bryson C.
1988-05-01
The first paper (Part 1) of this series presented a Bayesian procedure for the estimation of parameters in nonlinear, discrete flood event models. Part 2 begins with a discussion of the concept of nonlinearity in parameter estimation, its consequences, and the need to assess its extent. Three measures of nonlinearity are considered. They are Beale's measure , a bias calculation , and maximum curvature measures . A case study is presented, using the model and data described in Part 1. The results show quite clearly that care is required in the application of all three measures to calibrated flood models, and in the interpretation of the measured values. Devised by Bates and Watts, 1980.
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.
Research in Applied Mathematics Related to Nonlinear System Theory.
1981-09-01
control systems", Journal of Mathematical Analysis and Applications , 58: 98-112. R. E. KALMAN [1976] "Realization theory of linear dynamical systems...Theory. [19801 "Some remarks on the reachability of infinite- dimensional linear systems", Journal of Mathematical Analysis and Applications , 74: 568-577
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.
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…
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.
On a nonlinear viscoelastic model of Hunt-Crossley impact
NASA Astrophysics Data System (ADS)
Dyagel, R. V.; Lapshin, V. V.
2011-10-01
We consider a nonlinear viscoelastic model of the impact of a body on a stationary Hunt-Crossley obstacle. We obtain the first integral of the equation of motion and determine the coefficient of restitution, the kinetic energy lost at the impact, and their dependence on the impact velocity. We find the solution of the equation of motion of the body in terms of integrals by using the Lambert W-function and present the results of mathematical modeling.
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.
Constructing a Model of Mathematical Literacy.
ERIC Educational Resources Information Center
Pugalee, David K.
1999-01-01
Discusses briefly the call for mathematical literacy and the need for a model that articulates the fluid and dynamic nature of this form of literacy. Presents such a model which uses two concentric circles, one depicting the four processes of mathematical literacy (representing, manipulating, reasoning, and problem solving) and enablers that…
Mathematical Modelling as a Professional Task
ERIC Educational Resources Information Center
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Mathematical Modelling of Data: Software for Pedagogy.
ERIC Educational Resources Information Center
Bellomonte, L.; Sperandeo-Mineo, R. M.
1993-01-01
Discussion of mathematical modeling, particularly for high school physics curricula, focuses on software that is connected with laboratory work and the inference of mathematical models based on measurements of physical quantities. Fitting procedures are described, and user interface is explained. (Contains nine references.) (LRW)
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 of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
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.
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
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.
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.
Children's Intuitive Mathematics: The Development of Knowledge about Nonlinear Growth
ERIC Educational Resources Information Center
Ebersbach, Mirjam; Wilkening, Friedrich
2007-01-01
This study is concerned with the development of children's intuitive understanding of nonlinear processes. The ability to estimate linear and exponential growth was examined in 7-, 9-, 11-, and 13-year-old children and adults (N=160). Whereas linear growth was judged correctly at all ages, estimations of exponential growth were in line with…
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…
Modeling Nonlinear Acoustical Blast Waves Outdoors: A Research Summary
1991-09-01
Porous Surfaces. 5 David Gottlieb and Eli Turkel, "Dissipative Two-Four Methods for Time Dependent Problems," Mathematical Comnputation, No. 30 (1976...or structure factor, which Attenborough relates to the tortuosity. The local reaction assumption is inhereptly built into this model of the porous...k Waves in the Atmosphere," Journal of the Acoustical Socidy of America, No. 74 (1983). pp 1514-1517. David T. Blackstone., "Nonlinear Acoustics
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)
Mathematical Existence Results for the Doi-Edwards Polymer Model
NASA Astrophysics Data System (ADS)
Chupin, Laurent
2017-01-01
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.
ERIC Educational Resources Information Center
Purpura, David J.; Logan, Jessica A. R.
2015-01-01
Both mathematical language and the approximate number system (ANS) have been identified as strong predictors of early mathematics performance. Yet, these relations may be different depending on a child's developmental level. The purpose of this study was to evaluate the relations between these domains across different levels of ability.…
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,…
NASA Technical Reports Server (NTRS)
Blum, P. W.; Harris, I.
1973-01-01
The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all the nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In part 1 the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analysed.
Development of a mathematical model of the human circulatory system.
Conlon, Martin J; Russell, Donald L; Mussivand, Tofy
2006-09-01
A mathematical lumped parameter model of the human circulatory system (HCS) has been developed to complement in vitro testing of ventricular assist devices. Components included in this model represent the major parts of the systemic HCS loop, with all component parameters based on physiological data available in the literature. Two model configurations are presented in this paper, the first featuring elements with purely linear constitutive relations, and the second featuring nonlinear constitutive relations for the larger vessels. Three different aortic compliance functions are presented, and a pressure-dependent venous flow resistance is used to simulate venous collapse. The mathematical model produces reasonable systemic pressure and flow behaviour, and graphs of this data are included.
Study of Photovoltaic Cells Engineering Mathematical Model
NASA Astrophysics Data System (ADS)
Zhou, Jun; Yu, Zhengping; Lu, Zhengyi; Li, Chenhui; Zhang, Ruilan
2016-11-01
The characteristic curve of photovoltaic cells is the theoretical basis of PV Power, which simplifies the existing mathematical model, eventually, obtains a mathematical model used in engineering. The characteristic curve of photovoltaic cells contains both exponential and logarithmic calculation. The exponential and logarithmic spread out through Taylor series, which includes only four arithmetic and use single chip microcontroller as the control center. The result shows that: the use of single chip microcontroller for calculating exponential and logarithmic functions, simplifies mathematical model of PV curve, also can meet the specific conditions’ requirement for engineering applications.
Sayyar-Rodsari, Bijan; Schweiger, Carl; Hartman, Eric
2007-10-07
The difficult problems being tackled in the accelerator community are those that are nonlinear, substantially unmodeled, and vary over time. Such problems are ideal candidates for model-based optimization and control if representative models of the problem can be developed that capture the necessary mathematical relations and remain valid throughout the operation region of the system, and through variations in system dynamics. The goal of this proposal is to develop the methodology and the algorithms for building high-fidelity mathematical representations of complex nonlinear systems via constrained training of combined first-principles and neural network models.
Establishing an Explanatory Model for Mathematics Identity.
Cribbs, Jennifer D; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M
2015-04-01
This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence in mathematics directly impact their identity as a "math person," findings indicate that students' self-perceptions related to competence and performance have an indirect effect on their mathematics identity, primarily by association with students' interest and external recognition in mathematics. Thus, the model indicates that students' competence and performance beliefs are not sufficient for their mathematics identity development, and it highlights the roles of interest and recognition.
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 as Problem Solving for Children in the Singapore Mathematics Classrooms
ERIC Educational Resources Information Center
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
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)
ERIC Educational Resources Information Center
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
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.
Mathematical model of one-man air revitalization system
NASA Technical Reports Server (NTRS)
1976-01-01
A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.
Mathematical model of depolarization mechanism of conducted vasoreactivity
NASA Astrophysics Data System (ADS)
Neganova, Anastasiia Y.; Stiukhina, Elena S.; Postnov, Dmitry E.
2015-03-01
We address the problem of conducted vasodilation, the phenomenon which is also known as functional hyperemia. Specifically, we test the mechanism of nondecremental propagation of electric signals along endothelial cell layer recently hypothesized by Figueroa et al. By means of functional modeling we focus on possible nonlinear mechanisms that can underlie such regenerative pulse transmission (RPT). Since endothelial cells (EC) are generally known as electrically inexcitable, the possible role of ECs in RPT mechanisms is not evident. By means of mathematical modeling we check the dynamical self-consistency of Figueroa's hypothesis, as well as estimate the possible contribution of specific ionic currents to the suggested RPT mechanism.
A 6DOF mathematical model of parachute in Mars EDL
NASA Astrophysics Data System (ADS)
Shen, Ganghui; Xia, Yuanqing; Sun, Haoran
2015-04-01
The base of the dynamics characteristic research on the parachute and vehicle system is to establish a dynamics model, during the parachute descent phase, which can accurately display the relationship among the velocity, altitude and attitude angles as well as the variation of time. This paper starts with a new tracking law - ADRC in Mars entry guidance, which affects the initial states of the parachute deployment point and determines precision landing capability. Then, the influence of unsteady resistance to the parachute in Martian air is considered as the added mass, and a 6DOF nonlinear mathematical model of the parachute and vehicle system is established.
Modelling Mathematical Reasoning in Physics Education
NASA Astrophysics Data System (ADS)
Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche
2012-04-01
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 tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.
Mathematical Modeling of Circadian and Homeostatic Interaction
2011-11-16
REM ) sleep , and non- REM ( NREM ) sleep states. Using this mathematical modeling framework, the Pis conducted modeling studies on several...The model network exhibits realistic polyphasic sleep -wake behavior consisting of wake, rapid eye movement ( REM ) sleep , and non- REM ( NREM ) sleep ...states. In addition, the model captures stereotypical sleep patterning including cycling between NREM and REM sleep . Using this
Bakshi, S; de Lange, EC; Danhof, M; Peletier, LA
2016-01-01
In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase‐planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor‐pool model with positive feedback is used to demonstrate the power of mathematical analysis. This model is nonlinear and exhibits multiple steady states, the stability of which is analyzed. The analysis offers insight into model behavior and suggests useful parameter regions, which simulations alone could not. PMID:27405001
Bilinear modeling and nonlinear estimation
NASA Technical Reports Server (NTRS)
Dwyer, Thomas A. W., III; Karray, Fakhreddine; Bennett, William H.
1989-01-01
New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.
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…
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
Zbiek, Rose Mary; Conner, Annamarie
2006-01-01
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…
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.
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…
Battery electrochemical nonlinear/dynamic SPICE model
Glass, M.C.
1996-12-31
An Integrated Battery Model has been produced which accurately represents DC nonlinear battery behavior together with transient dynamics. The NiH{sub 2} battery model begins with a given continuous-function electrochemical math model. The math model for the battery consists of the sum of two electrochemical process DC currents, which are a function of the battery terminal voltage. This paper describes procedures for realizing a voltage-source SPICE model which implements the electrochemical equations using behavioral sources. The model merges the essentially DC non-linear behavior of the electrochemical model, together with the empirical AC dynamic terminal impedance from measured data. Thus the model integrates the short-term linear impedance behavior, with the long-term nonlinear DC resistance behavior. The long-duration non-Faradaic capacitive behavior of the battery is represented by a time constant. Outputs of the model include battery voltage/current, state-of-charge, and charge-current efficiency.
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…
Nonlinear modeling of thermoacoustically driven energy cascade
NASA Astrophysics Data System (ADS)
Gupta, Prateek; Scalo, Carlo; Lodato, Guido
2016-11-01
We present an investigation of nonlinear energy cascade in thermoacoustically driven high-amplitude oscillations, from the initial weakly nonlinear regime to the shock wave dominated limit cycle. We develop a first principle based quasi-1D model for nonlinear wave propagation in a canonical minimal unit thermoacoustic device inspired by the experimental setup of Biwa et al.. Retaining up to quadratic nonlinear terms in the governing equations, we develop model equations for nonlinear wave propagation in the proximity of differentially heated no-slip boundaries. Furthermore, we discard the effects of acoustic streaming in the present study and focus on nonlinear energy cascade due to high amplitude wave propagation. Our model correctly predicts the observed exponential growth of the thermoacoustically amplified second harmonic, as well as the energy transfer rate to higher harmonics causing wave steepening. Moreover, we note that nonlinear coupling of local pressure with heat transfer reduces thermoacoustic amplification gradually thus causing the system to reach limit cycle exhibiting shock waves. Throughout, we verify the results from the quasi-1D model with fully compressible Navier-Stokes simulations.
A mathematical model of a cloud
NASA Astrophysics Data System (ADS)
Wang, A. P.
1980-07-01
The model under consideration is a pencil of radiation incident on a cloud, and the problem is to determine the reflection and transmitted radiation. Based on the method of 'principle of invariance', three mathematical models are constructed. The first is the basic model, which describes the radiation system completely. The second is the flux integral model, in which the integral average intensity is considered. The third is the diffusion model, which gives the most important information about the diffused radiation field.
Cheviakov, A F; Ganghoffer, J-F
2016-05-01
The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures.
About a mathematical model of market
NASA Astrophysics Data System (ADS)
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
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 Model For Scattering From Mirrors
NASA Technical Reports Server (NTRS)
Wang, Yaujen
1988-01-01
Additional terms account for effects of particulate contamination. Semiempirical mathematical model of scattering of light from surface of mirror gives improved account of effects of particulate contamination. Models that treated only scattering by microscopic irregularities in surface gave bidirectional reflectance distribution functions differing from measured scattering intensities over some ranges of angles.
Assessment of Galileo modal test results for mathematical model verification
NASA Technical Reports Server (NTRS)
Trubert, M.
1984-01-01
The modal test program for the Galileo Spacecraft was completed at the Jet Propulsion Laboratory in the summer of 1983. The multiple sine dwell method was used for the baseline test. The Galileo Spacecraft is a rather complex 2433 kg structure made of a central core on which seven major appendages representing 30 percent of the total mass are attached, resulting in a high modal density structure. The test revealed a strong nonlinearity in several major modes. This nonlinearity discovered in the course of the test necessitated running additional tests at the unusually high response levels of up to about 21 g. The high levels of response were required to obtain a model verification valid at the level of loads for which the spacecraft was designed. Because of the high modal density and the nonlinearity, correlation between the dynamic mathematical model and the test results becomes a difficult task. Significant changes in the pre-test analytical model are necessary to establish confidence in the upgraded analytical model used for the final load verification. This verification, using a test verified model, is required by NASA to fly the Galileo Spacecraft on the Shuttle/Centaur launch vehicle in 1986.
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.
Mathematical modeling relevant to closed artificial ecosystems.
DeAngelis, Donald 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.
Application of a nonlinear slug test model
McElwee, C.D.
2001-01-01
Knowledge of the hydraulic conductivity distribution is of utmost importance in understanding the dynamics of an aquifer and in planning the consequences of any action taken upon that aquifer. Slug tests have been used extensively to measure hydraulic conductivity in the last 50 years since Hvorslev's (1951) work. A general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the wellbore, and a Hvorslev model for the aquifer has been implemented in this work. The nonlinear model has three parameters: ??, which is related primarily to radius changes in the water column; A, which is related to the nonlinear head losses; and K, the hydraulic conductivity. An additional parameter has been added representing the initial velocity of the water column at slug initiation and is incorporated into an analytical solution to generate the first time step before a sequential numerical solution generates the remainder of the time solution. Corrections are made to the model output for acceleration before it is compared to the experimental data. Sensitivity analysis and least squares fitting are used to estimate the aquifer parameters and produce some diagnostic results, which indicate the accuracy of the fit. Finally, an example of field data has been presented to illustrate the application of the model to data sets that exhibit nonlinear behavior. Multiple slug tests should be taken at a given location to test for nonlinear effects and to determine repeatability.
Clinical Trials: Spline Modeling is Wonderful for Nonlinear Effects.
Cleophas, Ton J
2016-01-01
Traditionally, nonlinear relationships like the smooth shapes of airplanes, boats, and motor cars were constructed from scale models using stretched thin wooden strips, otherwise called splines. In the past decades, mechanical spline methods have been replaced with their mathematical counterparts. The objective of the study was to study whether spline modeling can adequately assess the relationships between exposure and outcome variables in a clinical trial and also to study whether it can detect patterns in a trial that are relevant but go unobserved with simpler regression models. A clinical trial assessing the effect of quantity of care on quality of care was used as an example. Spline curves consistent of 4 or 5 cubic functions were applied. SPSS statistical software was used for analysis. The spline curves of our data outperformed the traditional curves because (1) unlike the traditional curves, they did not miss the top quality of care given in either subgroup, (2) unlike the traditional curves, they, rightly, did not produce sinusoidal patterns, and (3) unlike the traditional curves, they provided a virtually 100% match of the original values. We conclude that (1) spline modeling can adequately assess the relationships between exposure and outcome variables in a clinical trial; (2) spline modeling can detect patterns in a trial that are relevant but may go unobserved with simpler regression models; (3) in clinical research, spline modeling has great potential given the presence of many nonlinear effects in this field of research and given its sophisticated mathematical refinement to fit any nonlinear effect in the mostly accurate way; and (4) spline modeling should enable to improve making predictions from clinical research for the benefit of health decisions and health care. We hope that this brief introduction to spline modeling will stimulate clinical investigators to start using this wonderful method.
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
Lewis, Jennifer
2012-10-15
This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. The goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.
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…
Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming
Colins, Andrea; Gerdtzen, Ziomara P.; Nuñez, Marco T.; Salgado, J. Cristian
2017-01-01
Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex
Nonlinear modeling of an aerospace object dynamics
NASA Astrophysics Data System (ADS)
Davydov, I. E.; Davydov, E. I.
2017-01-01
Here are presented the scientific results, obtained by motion modeling of complicated technical systems of aerospace equipment with consideration of nonlinearities. Computerized panel that allows to measure mutual influence of the system's motion and stabilization device with consideration of its real characteristics has been developed. Analysis of motion stability of a system in general has been carried out and time relationships of the system's motion taking in account nonlinearities are presented.
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.
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
[Mathematical models of hysteresis]. Progress report No. 4, [January 1, 1991--December 31, 1991
Mayergoyz, I.D.
1991-12-31
The research described in this proposal is currently being supported by the US Department of Energy under the contract ``Mathematical Models of Hysteresis``. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with ``nonlocal memories``. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.
To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling
ERIC Educational Resources Information Center
Lingefjard, Thomas; Holmquist, Mikael
2005-01-01
Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…
Mathematical Modeling of Wildfire Dynamics
NASA Astrophysics Data System (ADS)
Del Bene, Kevin; Drew, Donald
2012-11-01
Wildfires have been a long-standing problem in today's society. In this paper, we derive and solve a fluid dynamics model to study a specific type of wildfire, namely, a two dimensional flow around a rising plume above a concentrated heat source, modeling a fire line. This flow assumes a narrow plume of hot gas rising and entraining the surrounding air. The surrounding air is assumed to have constant density and is irrotational far from the fire line. The flow outside the plume is described by a Biot-Savart integral with jump conditions across the position of the plume. The plume model describes the unsteady evolution of the mass, momentum, energy, and vorticity inside the plume, with sources derived to model mixing in the style of Morton, et al. 1956]. The fire is then modeled using a conservation derivation, allowing the fire to propagate, coupling back to the plume model. The results show that this model is capable of capturing the complex interaction of the plume with the surrounding air and fuel layer. Funded by NSF GRFP.
Establishing an Explanatory Model for Mathematics Identity
ERIC Educational Resources Information Center
Cribbs, Jennifer D.; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M.
2015-01-01
This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…
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.
Melatonin in Epilepsy: A New Mathematical Model of Diurnal Secretion
Kijonka, Marek; Pęcka, Marcin; Sokół, Maria
2016-01-01
Purpose. The main objective of the study was to create a mathematical model that describes the melatonin circadian secretion and, then the functionality of the model was tested by a comparison of the melatonin secretions in children with and without epilepsy. Material and Methods. The patients were divided into the epilepsy group (EG, n = 52) and the comparison group (CG, n = 30). The melatonin level was assessed by a radioimmunoassay method. The diurnal melatonin secretion was described using a nonlinear least squares method. Spearman's rank correlation coefficient was chosen to estimate the dependence of the acquired data. The model reproduces blood concentration profiles and its parameters were statistically analyzed using the Mann-Whitney-Wilcoxon test and logistic regression. Results. The correlation analysis performed for the EG and CG groups showed moderate correlations between age and the melatonin secretion model parameters. Patients with epilepsy are characterized by an increased phase shift of melatonin release. PMID:27478439
Linear theory for filtering nonlinear multiscale systems with model error
Berry, Tyrus; Harlim, John
2014-01-01
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure
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.
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.
Modeling of the vibrating beam accelerometer nonlinearities
NASA Astrophysics Data System (ADS)
Romanowski, P. A.; Knop, R. C.
Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.
propulsion machinery dynamics and the ship equations of motion. The model couples the ship propulsion dynamics equations with nonlinear maneuvering...This report describes an analog computer maneuvering simulation of a destroyer study ship. The mathematical model which is used includes the ship
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.
Mathematical models for principles of gyroscope theory
NASA Astrophysics Data System (ADS)
Usubamatov, Ryspek
2017-01-01
Gyroscope devices are primary units for navigation and control systems that have wide application in engineering. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which known mathematical models have been formulated on the law of kinetic energy conservation and the change in the angular momentum. The gyroscope theory is represented by numerous publications, which mathematical models do not match the actual torques and motions in these devices.. The nature of gyroscope effects is more complex than represented in known publications. Recent investigations in this area have demonstrated that on a gyroscope can act until eleven internal torques simultaneously and interdependently around two axes. These gyroscope torques are generated by spinning rotor's mass-elements and by the gyroscope center-mass based on action of several inertial forces. The change in the angular momentum does not play first role for gyroscope motions. The external load generates several internal torques which directions may be distinguished. This situation leads changing of the angular velocities of gyroscope motions around two axes. Formulated mathematical models of gyroscope internal torques are representing the fundamental principle of gyroscope theory. In detail, the gyroscope is experienced the resistance torque generated by the centrifugal and Coriolis forces of the spinning rotor and the precession torque generated by the common inertial forces and the change in the angular momentum. The new mathematical models for the torques and motions of the gyroscope confirmed for most unsolvable problems. The mathematical models practically tested and the results are validated the theoretical approach.
Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling
ERIC Educational Resources Information Center
Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan
2012-01-01
The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…
ERIC Educational Resources Information Center
Bukova-Guzel, Esra
2011-01-01
This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…
Nonlinear damping and quasi-linear modelling.
Elliott, S J; Ghandchi Tehrani, M; Langley, R S
2015-09-28
The mechanism of energy dissipation in mechanical systems is often nonlinear. Even though there may be other forms of nonlinearity in the dynamics, nonlinear damping is the dominant source of nonlinearity in a number of practical systems. The analysis of such systems is simplified by the fact that they show no jump or bifurcation behaviour, and indeed can often be well represented by an equivalent linear system, whose damping parameters depend on the form and amplitude of the excitation, in a 'quasi-linear' model. The diverse sources of nonlinear damping are first reviewed in this paper, before some example systems are analysed, initially for sinusoidal and then for random excitation. For simplicity, it is assumed that the system is stable and that the nonlinear damping force depends on the nth power of the velocity. For sinusoidal excitation, it is shown that the response is often also almost sinusoidal, and methods for calculating the amplitude are described based on the harmonic balance method, which is closely related to the describing function method used in control engineering. For random excitation, several methods of analysis are shown to be equivalent. In general, iterative methods need to be used to calculate the equivalent linear damper, since its value depends on the system's response, which itself depends on the value of the equivalent linear damper. The power dissipation of the equivalent linear damper, for both sinusoidal and random cases, matches that dissipated by the nonlinear damper, providing both a firm theoretical basis for this modelling approach and clear physical insight. Finally, practical examples of nonlinear damping are discussed: in microspeakers, vibration isolation, energy harvesting and the mechanical response of the cochlea.
Evaluation of nonlinearity and validity of nonlinear modeling for complex time series
NASA Astrophysics Data System (ADS)
Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo
2007-10-01
Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.
Mathematical modeling the radiation effects on humoral immunity
NASA Astrophysics Data System (ADS)
Smirnova, O. A.
A mathematical model of humoral immune response in nonirradiated and irradiated mammals is developed. It is based on conventional theories and experimental facts in this field. The model is a system of nonlinear differential equations which describe the dynamics of concentrations of antibody and antigen molecules, immunocompetent B lymphocytes, and the rest blood lymphocytes, as well as the bone-marrow lymphocyte precursors. The interaction of antigen molecules with antibodies and with antibody-like receptors on immunocompetent cells is also incorporated. The model quantitatively reproduces the dynamics of the humoral immune response to the T-independent antigen (capsular antigen of plague microbe) in nonirradiated mammals (CBA mice). It describes the peculiarities of the humoral immune response in CBA mice exposed to acute radiation before or after introducing antigen. The model predicts an adaptation of humoral immune system to low dose rate chronic irradiation in the result of which the intensity of immune response relaxes to a new, lower than normal, stable level. The mechanisms of this phenomenon are revealed. The results obtained show that the developed model, after the appropriate identification, can be used to predict the effects of acute and low-level long-term irradiation on the system of humoral immunity in humans. Employment of the mathematical model identified in the proper way should be important in estimating the radiation risk for cosmonauts and astronauts on long space missions such as a voyage to Mars or a lunar colony.
Mathematical modeling of HIV-like particle assembly in vitro.
Liu, Yuewu; Zou, Xiufen
2017-02-22
In vitro, the recombinant HIV-1 Gag protein can generate spherical particles with a diameter of 25-30 nm in a fully defined system. It has approximately 80 building blocks, and its intermediates for assembly are abundant in geometry. Accordingly, there are a large number of nonlinear equations in the classical model. Therefore, it is difficult to compute values of geometry parameters for intermediates and make the mathematical analysis using the model. In this work, we develop a new model of HIV-like particle assembly in vitro by using six-fold symmetry of HIV-like particle assembly to decrease the number of geometry parameters. This method will greatly reduce computational costs and facilitate the application of the model. Then, we prove the existence and uniqueness of the positive equilibrium solution for this model with 79 nonlinear equations. Based on this model, we derive the interesting result that concentrations of all intermediates at equilibrium are independent of three important parameters, including two microscopic on-rate constants and the size of nucleating structure. Before equilibrium, these three parameters influence the concentration variation rates of all intermediates. We also analyze the relationship between the initial concentration of building blocks and concentrations of all intermediates. Furthermore, the bounds of concentrations of free building blocks and HIV-like particles are estimated. These results will be helpful to guide HIV-like particle assembly experiments and improve our understanding of the assembly dynamics of HIV-like particles in vitro.
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
Development of Mathematical Models to Estimate Animal Performance and Feed Biological Values
Technology Transfer Automated Retrieval System (TEKTRAN)
Mathematical modeling in nutrition is important because the human mind is able to formulate concepts and hypothesis but lack the ability to track quantitative relationships of complex, nonlinear, and dynamic systems. It provides us with a tool to analyze huge amounts of data and information about nu...
Nonlinear friction model for servo press simulation
NASA Astrophysics Data System (ADS)
Ma, Ninshu; Sugitomo, Nobuhiko; Kyuno, Takunori; Tamura, Shintaro; Naka, Tetsuo
2013-12-01
The friction coefficient was measured under an idealized condition for a pulse servo motion. The measured friction coefficient and its changing with both sliding distance and a pulse motion showed that the friction resistance can be reduced due to the re-lubrication during unloading process of the pulse servo motion. Based on the measured friction coefficient and its changes with sliding distance and re-lubrication of oil, a nonlinear friction model was developed. Using the newly developed the nonlinear friction model, a deep draw simulation was performed and the formability was evaluated. The results were compared with experimental ones and the effectiveness was verified.
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.…
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.…
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)
An Improved ((G'/G))-expansion Method for Solving Nonlinear PDEs in Mathematical Physics
Zayed, Elsayed M. E.; Al-Joudi, Shorog
2010-09-30
In the present article, we construct the traveling wave solutions of the (1+1)-dimensional coupled Hirota-Satsuma-KdV equations and the (1+1)-dimensional variant coupled Boussinesq system of equations by using an improved ((G'/G))-expansion method, where G satisfies the second order linear ordinary differential equation. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.
Voters' Fickleness:. a Mathematical Model
NASA Astrophysics Data System (ADS)
Boccara, Nino
This paper presents a spatial agent-based model in order to study the evolution of voters' choice during the campaign of a two-candidate election. Each agent, represented by a point inside a two-dimensional square, is under the influence of its neighboring agents, located at a Euclidean distance less than or equal to d, and under the equal influence of both candidates seeking to win its support. Moreover, each agent located at time t at a given point moves at the next timestep to a randomly selected neighboring location distributed normally around its position at time t. Besides their location in space, agents are characterized by their level of awareness, a real a ∈ [0, 1], and their opinion ω ∈ {-1, 0, +1}, where -1 and +1 represent the respective intentions to cast a ballot in favor of one of the two candidates while 0 indicates either disinterest or refusal to vote. The essential purpose of the paper is qualitative; its aim is to show that voters' fickleness is strongly correlated to the level of voters' awareness and the efficiency of candidates' propaganda.
Mathematical 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.
Mathematical Models of College Myopia
Greene, Peter R.; Grill, Zachary W.; Medina, Antonio
2015-01-01
Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/−0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia. PMID:26709316
Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS
Bolker, Benjamin M.; Gardner, Beth; Maunder, Mark; Berg, Casper W.; Brooks, Mollie; Comita, Liza; Crone, Elizabeth; Cubaynes, Sarah; Davies, Trevor; de Valpine, Perry; Ford, Jessica; Gimenez, Olivier; Kéry, Marc; Kim, Eun Jung; Lennert-Cody, Cleridy; Magunsson, Arni; Martell, Steve; Nash, John; Nielson, Anders; Regentz, Jim; Skaug, Hans; Zipkin, Elise
2013-01-01
1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.
Mathematical Models Of Turbulence In Transonic Flow
NASA Technical Reports Server (NTRS)
Rubesin, Morris W.; Viegas, John R.
1989-01-01
Predictions of several models compared with measurements of well-documented flow. Report reviews performances of variety of mathematical models of turbulence in transonic flow. Predictions of models compared with measurements of flow in wind tunnel along outside of cylinder having axisymmetric bump of circular-arc cross section in meridional plane. Review part of continuing effort to calibrate and verify computer codes for prediction of transonic flows about airfoils. Johnson-and-King model proved superior in predicting transonic flow over bumpy cylinder.
Nonlinear ARMA models for the D(st) index and their physical interpretation
NASA Technical Reports Server (NTRS)
Vassiliadis, D.; Klimas, A. J.; Baker, D. N.
1996-01-01
Time series models successfully reproduce or predict geomagnetic activity indices from solar wind parameters. A method is presented that converts a type of nonlinear filter, the nonlinear Autoregressive Moving Average (ARMA) model to the nonlinear damped oscillator physical model. The oscillator parameters, the growth and decay, the oscillation frequencies and the coupling strength to the input are derived from the filter coefficients. Mathematical methods are derived to obtain unique and consistent filter coefficients while keeping the prediction error low. These methods are applied to an oscillator model for the Dst geomagnetic index driven by the solar wind input. A data set is examined in two ways: the model parameters are calculated as averages over short time intervals, and a nonlinear ARMA model is calculated and the model parameters are derived as a function of the phase space.
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)
Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites
NASA Technical Reports Server (NTRS)
Turner, Travis L.
2004-01-01
A constitutive mathematical model has been developed that predicts the nonlinear thermomechanical behaviors of shape-memory-alloys (SMAs) and of shape-memory-alloy hybrid composite (SMAHC) structures, which are composite-material structures that contain embedded SMA actuators. SMAHC structures have been investigated for their potential utility in a variety of applications in which there are requirements for static or dynamic control of the shapes of structures, control of the thermoelastic responses of structures, or control of noise and vibrations. The present model overcomes deficiencies of prior, overly simplistic or qualitative models that have proven ineffective or intractable for engineering of SMAHC structures. The model is sophisticated enough to capture the essential features of the mechanics of SMAHC structures yet simple enough to accommodate input from fundamental engineering measurements and is in a form that is amenable to implementation in general-purpose structural analysis environments.
Mathematical modeling of vertebrate limb development.
Zhang, Yong-Tao; Alber, Mark S; Newman, Stuart A
2013-05-01
In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.
Determining critical load in the multispan beams with the nonlinear model
NASA Astrophysics Data System (ADS)
DemÑ-r, D. Dönmez; Sinir, B. G.; Usta, L.
2017-01-01
The beams which are one of the most commonly used structural members are quite important for many researchers. Mathematical models determining the response of beams under external loads are concluded from elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. In this study, the derivation of the nonlinear model is introduced to determine the critical load in the multispan beams. Since the engineering practice of this kind of problems is very common, determining the critical load is quite important. For this purpose, the nonlinear mathematical model of the multispan Euler-Bernoulli beam is firstly obtained. To be able to obtain the independent of the material and the geometry, the present model are became dimensionless. Then, the critical axial load can be determined via the nonlinear solution of the governing equation.
ERIC Educational Resources Information Center
Jurow, A. Susan
2004-01-01
Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The…
ERIC Educational Resources Information Center
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…
Mathematical modelling of the lower urinary tract.
Paya, Antonio Soriano; Fernandez, Daniel Ruiz; Gil, David; Garcia Chamizo, Juan Manuel; Perez, Francisco Macia
2013-03-01
The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.
Frey Law, Laura A; Shields, Richard K
2005-01-01
Background Mathematical muscle models may be useful for the determination of appropriate musculoskeletal stresses that will safely maintain the integrity of muscle and bone following spinal cord injury. Several models have been proposed to represent paralyzed muscle, but there have not been any systematic comparisons of modelling approaches to better understand the relationships between model parameters and muscle contractile properties. This sensitivity analysis of simulated muscle forces using three currently available mathematical models provides insight into the differences in modelling strategies as well as any direct parameter associations with simulated muscle force properties. Methods Three mathematical muscle models were compared: a traditional linear model with 3 parameters and two contemporary nonlinear models each with 6 parameters. Simulated muscle forces were calculated for two stimulation patterns (constant frequency and initial doublet trains) at three frequencies (5, 10, and 20 Hz). A sensitivity analysis of each model was performed by altering a single parameter through a range of 8 values, while the remaining parameters were kept at baseline values. Specific simulated force characteristics were determined for each stimulation pattern and each parameter increment. Significant parameter influences for each simulated force property were determined using ANOVA and Tukey's follow-up tests (α ≤ 0.05), and compared to previously reported parameter definitions. Results Each of the 3 linear model's parameters most clearly influence either simulated force magnitude or speed properties, consistent with previous parameter definitions. The nonlinear models' parameters displayed greater redundancy between force magnitude and speed properties. Further, previous parameter definitions for one of the nonlinear models were consistently supported, while the other was only partially supported by this analysis. Conclusion These three mathematical models use
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.
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.
On mathematical modelling of flameless combustion
Mancini, Marco; Schwoeppe, Patrick; Weber, Roman; Orsino, Stefano
2007-07-15
A further analysis of the IFRF semi-industrial-scale experiments on flameless (mild) combustion of natural gas is carried out. The experimental burner features a strong oxidizer jet and two weak natural gas jets. Numerous publications have shown the inability of various RANS-based mathematical models to predict the structure of the weak jet. We have proven that the failure is in error predictions of the entrainment and therefore is not related to any chemistry submodels, as has been postulated. (author)
Mathematical model for estimation of meteoroid dark flight trajectory
NASA Astrophysics Data System (ADS)
Vinnikov, V. V.; Gritsevich, M. I.; Turchak, L. I.
2016-10-01
This paper is concerned with mathematical model for numerical simulation of meteoroid dynamics. The simulations of bolide ballistics are carried out via hard sphere approximation. System of differential equations for movement and heat transfer is solved in Lagrange variables via Runge-Kutta methods. The drag force of atmospheric air is computed via Henderson formula, valid for wide ranges of Reynolds and Mach numbers. The parameters of surrounding gas are obtained from standard atmosphere model. The impact pressure is computed taking into account entropy jump through bow head shockwave and consequent isentropic deceleration of the flow in the vicinity of streamlined sphere. Meteoroid fragmentation is modeled as sequential division of parent body into two parts using random weighting coefficient for parent mass. The condition for fragmentation event occur when the hemisphere-averaged value of impact pressure exceeds the threshold of relative body strength, which nonlinearly depends on ration of initial meteoroid mass to current mass of considered fragment. To compute trajectory divergence for newly-formed splinters we introduce the repulsive force, dependent on impact pressure, cross sectional areas of mutually repulsing bodies and distances between them. The set of mathematical models is implemented as the program complex. Preliminary computational results show that fragmentation altitude, terminal velocities and maximum splinter masses are in good agreement with corresponding observations and measurements.
Nonlinear Modeling of Joint Dominated Structures
NASA Technical Reports Server (NTRS)
Chapman, J. M.
1990-01-01
The development and verification of an accurate structural model of the nonlinear joint-dominated NASA Langley Mini-Mast truss are described. The approach is to characterize the structural behavior of the Mini-Mast joints and struts using a test configuration that can directly measure the struts' overall stiffness and damping properties, incorporate this data into the structural model using the residual force technique, and then compare the predicted response with empirical data taken by NASA/LaRC during the modal survey tests of the Mini-Mast. A new testing technique, referred to as 'link' testing, was developed and used to test prototype struts of the Mini-Masts. Appreciable nonlinearities including the free-play and hysteresis were demonstrated. Since static and dynamic tests performed on the Mini-Mast also exhibited behavior consistent with joints having free-play and hysteresis, nonlinear models of the Mini-Mast were constructed and analyzed. The Residual Force Technique was used to analyze the nonlinear model of the Mini-Mast having joint free-play and hysteresis.
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 Programming Model for Fighter Training Squadron Pilot Scheduling
2007-03-01
of Defense, or the United States Government. AFIT/GOR/ENS/07-17 MATHEMATICAL PROGAMMING MODEL FOR...March 2007 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT/GOR/ENS/07-17 MATHEMATICAL PROGAMMING MODEL FOR FIGHTER...80 x MATHEMATICAL PROGAMMING MODEL FOR FIGHTER TRAINING SQUADRON PILOT
Nonlinear GARCH model and 1 / f noise
NASA Astrophysics Data System (ADS)
Kononovicius, A.; Ruseckas, J.
2015-06-01
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.
Nonlinear kinetic modeling of stimulated Raman scattering
NASA Astrophysics Data System (ADS)
Benisti, Didier
2011-10-01
Despite its importance for many applications, such as or Raman amplification or inertial confinement fusion, deriving a nonlinear estimate of Raman reflectivity in a plasma has remained quite a challenge for decades. This is mainly due to the nonlinear modification of the electron distribution function induced by the plasma wave (EPW), which, in turn, modifies the propagation of this wave. In this paper is derived an envelope equation for the EPW valid in 3D and which accounts for the nonlinear change of its collisionless (Landau-like) damping rate, group velocity, coupling to the electromagnetic drive, frequency and wave number. Our theoretical predictions for each of these terms are carefully compared against results from Vlasov simulations of stimulated Raman scattering (SRS), as well as with other theories. Moreover, our envelope model shows to be as accurate as a Vlasov code in predicting Raman threshold in 1D. Making comparisons with experimental results nevertheless requires including transverse dimensions and letting Raman start from noise. To this end, we performed a completely new derivation of the electrostatic fluctuations in a plasma, which accounts nonlinear effects. Moreover, based on our Multi-D simulations of Raman scattering with our envelope code BRAMA, we discuss the effect on SRS of wave front bowing, transverse detrapping and of a completely new defocussing effect due to the local change in the direction of the EPW group velocity induced by the nonlinear decrease of Landau damping.
Biology by numbers: mathematical modelling in developmental biology.
Tomlin, Claire J; Axelrod, Jeffrey D
2007-05-01
In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.
ERIC Educational Resources Information Center
Costellano, Janet; Scaffa, Matthew
The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…
Dynamical effects of overparametrization in nonlinear models
NASA Astrophysics Data System (ADS)
Aguirre, Luis Antonio; Billings, S. A.
1995-01-01
This paper is concemed with dynamical reconstruction for nonlinear systems. The effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated. It is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns. The complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters. In this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes. Moreover, some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels. In order to precisely quantify the complexity of the reconstructions, global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks.
The development of a mathematical model of a hybrid airship
NASA Astrophysics Data System (ADS)
Abdul Ghaffar, Alia Farhana
The mathematical model of a winged hybrid airship is developed for the analysis of its dynamic stability characteristics. A full nonlinear equation of motion that describes the dynamics of the hybrid airship is determined and for completeness, some of the components in the equations are estimated using the appropriate methods that has been established and used in the past. Adequate assumptions are made in order to apply any relevant computation and estimation methods. While this hybrid airship design is unique, its modeling and stability analysis were done according to the typical procedure of conventional airships and aircrafts. All computations pertaining to the hybrid airship's equation of motion are carried out and any issues related to the integration of the wing to the conventional airship design are discussed in this thesis. The design of the hybrid airship is also slightly modified to suit the demanding requirement of a complete and feasible mathematical model. Then, linearization is performed under a chosen trim condition, and eigenvalue analysis is carried out to determine the general dynamic stability characteristics of the winged hybrid airship. The result shows that the winged hybrid airship possesses dynamic instability in longitudinal pitch motion and lateral-directional slow roll motion. This is due to the strong coupling between the aerostatic lift from the buoyant gas and aerodynamic lift from the wing.
Nonlinear Walecka models and point-coupling relativistic models
Lourenco, O.; Amaral, R. L. P. G.; Dutra, M.; Delfino, A.
2009-10-15
We study hadronic nonlinear point-coupling (NLPC) models which reproduce numerically the binding energy, the incompressibility, and the nucleon effective mass at the nuclear matter saturation obtained by different nonlinear Walecka (NLW) models. We have investigated their behaviors as functions of the nuclear matter density to observe how they deviate from known NLW models. In our study we present a meson-exchange modified nonlinear Walecka model (MNLW) which exactly underlies a nonlinear point-coupling model (NLPC) presenting third- and fourth-order scalar density self-couplings. A discussion about naive dimensional analysis (NDA) and naturalness is also provided for a large class of NLW and NLPC models. At finite temperature, critical and flash parameters of both approaches are presented.
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.
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.
Prakash, J; Srinivasan, K
2009-07-01
In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.
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.
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…
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…
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.
Simplified Model of Nonlinear Landau Damping
N. A. Yampolsky and N. J. Fisch
2009-07-16
The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.
Non-compact nonlinear sigma models
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Tolley, Andrew J.; Zhou, Shuang-Yong
2016-09-01
The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there exist stable solutions in this class of models. This result also has important implications for Lorentz-invariant massive gravity: There exist stable nontrivial vacua in massive gravity that are free from any linear vDVZ-discontinuity and a Λ2 decoupling limit can be defined on these vacua.
Mathematical model of testing of pipeline integrity by thermal fields
Vaganova, Nataliia
2014-11-18
Thermal fields testing at the ground surface above a pipeline are considered. One method to obtain and investigate an ideal thermal field in different environments is a direct numerical simulation of heat transfer processes taking into account the most important physical factors. In the paper a mathematical model of heat propagation from an underground source is described with accounting of physical factors such as filtration of water in soil and solar radiation. Thermal processes are considered in 3D origin where the heat source is a pipeline with constant temperature and non-uniform isolated shell (with 'damages'). This problem leads to solution of heat diffusivity equation with nonlinear boundary conditions. Approaches to analysis of thermal fields are considered to detect damages.
Mathematical Modeling of an Oscillating Droplet
NASA Technical Reports Server (NTRS)
Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)
2000-01-01
Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.
Input-output analysis of mathematical models of ecosystems
Antonios, M.N.
1982-01-01
Necessary and sufficient conditions for the convergence of the solutions of linear and nonlinear time varying compartmental models described by systems of differential equations are reviewed. For continuous and discrete models, the concept of environ analysis is extended to advanced linear systems and for the first time to systems with time varying coefficient matrices A(t) and (A(t))/sup T/. Output and input environ partitioning flow and storage matrices for a two trophic level aquatic system are derived in the form of integral equations. As a step towards the important goal of controlling the eutrophication phenomenon, two phytoplankton population models in natural waters are presented. In the first model, a non-linear function general enough to include the effects of feeding saturation intraspecific consumer interference, and eutrophication phenomenon is used to present the transfer of material or energy from phytoplankton to zooplankton populations. The model using this grazing rate function is subjected to equilibrium and stability analysis to ascertain its mathematical implications. It is shown that, for a certain range of one of the parameters in this function all equilibrium points of the system become stable even with nutrient enrichment. In the second model, dynamics of both nitrogen and phosphorus cycles are combined. The influence of direct human control added to different aquatic models is studied in detail. Optimal control theory is used to obtain optimal strategies for the control of these models with several cost functions. It is found that the control program in each problem depends on the model considered and on the function to be optimized.
Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model
NASA Technical Reports Server (NTRS)
Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.
2009-01-01
Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.
Nonlinear traveling wave solution for the MJO skeleton model
NASA Astrophysics Data System (ADS)
Chen, S.; Stechmann, S. N.
2014-12-01
Recently, a minimal dynamical model is presented for capturing MJO's fundamental features. The model is a nonlinear oscillator model for the MJO skeleton and it involves interactions between convection, moisture and circulation. I will present the exact nonlinear traveling wave solutions for the model based on its energy conservation. The exact nonlinear solution provides for an explicit comparison of features between linear and nonlinear waves such as dispersion relations and traveling wave speeds. Moreover, the nonlinear solutions, compared with the linear ones, produce a narrow region of active convection and a wider region of suppressed convection. These predictions offer nonlinear MJO features that could potentially be targets of observational investigations.
Mathematical modelling of submarine landslide motion
NASA Astrophysics Data System (ADS)
Burminskij, A.
2012-04-01
Mathematical modelling of submarine landslide motion The paper presents a mathematical model to calculate dynamic parameters of a submarine landslide. The problem of estimation possible submarine landslides dynamic parameters and run-out distances as well as their effect on submarine structures becomes more and more actual because they can have significant impacts on infrastructure such as the rupture of submarine cables and pipelines, damage to offshore drilling platforms, cause a tsunami. In this paper a landslide is considered as a viscoplastic flow and is described by continuum mechanics equations, averaged over the flow depth. The model takes into account friction at the bottom and at the landslide-water boundary, as well as the involvement of bottom material in motion. A software was created and series of test calculations were performed. Calculations permitted to estimate the contribution of various model coefficients and initial conditions. Motion down inclined bottom was studied both for constant and variable slope angle. Examples of typical distributions of the flow velocity, thickness and density along the landslide body at different stages of motion are given.
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 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
Filtering nonlinear dynamical systems with linear stochastic models
NASA Astrophysics Data System (ADS)
Harlim, J.; Majda, A. J.
2008-06-01
2007 Proc. Natl Acad. Sci. 104 1124-9 Castronovo et al 2008 J. Comput. Phys. 227 3678-714) for the linear stochastically forced partial differential equations with constant coefficients such as in (Castronovo et al 2008 J. Comput. Phys. 227 3678-714), this Fourier diagonal decoupling is a natural approach provided that the system noise is chosen to be independent in the Fourier space; for a nonlinear problem, however, there is a strong mixing and correlations between different Fourier modes. Our strategy is to radically assume for the purposes of filtering that different Fourier modes are uncorrelated. In particular, we introduce physical model errors by replacing the nonlinearity in the original model with a suitable Ornstein-Uhlenbeck process. We show that even with this 'poor-man's' stochastic model, when the appropriate parametrization strategy is guided by mathematical offline test criteria, it is able to produce reasonably skilful filtered solutions. In the highly turbulent regime with infrequent observation time, this approach is at least as good as trusting the observations while the ensemble Kalman filter implemented in a perfect model scenario diverges. Since these Fourier diagonal linear filters have large model error compared with the nonlinear dynamics, an essential part of the study below is the interplay between this error and the mathematical criteria for a given linear filter in order to produce skilful filtered solutions through the radical strategy.
Mathematical modeling of the coating process.
Toschkoff, Gregor; Khinast, Johannes G
2013-12-05
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.
Predictive mathematical models of cancer signalling pathways.
Bachmann, J; Raue, A; Schilling, M; Becker, V; Timmer, J; Klingmüller, U
2012-02-01
Complex intracellular signalling networks integrate extracellular signals and convert them into cellular responses. In cancer cells, the tightly regulated and fine-tuned dynamics of information processing in signalling networks is altered, leading to uncontrolled cell proliferation, survival and migration. Systems biology combines mathematical modelling with comprehensive, quantitative, time-resolved data and is most advanced in addressing dynamic properties of intracellular signalling networks. Here, we introduce different modelling approaches and their application to medical systems biology, focusing on the identifiability of parameters in ordinary differential equation models and their importance in network modelling to predict cellular decisions. Two related examples are given, which include processing of ligand-encoded information and dual feedback regulation in erythropoietin (Epo) receptor signalling. Finally, we review the current understanding of how systems biology could foster the development of new treatment strategies in the context of lung cancer and anaemia.
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.
Simple nonlinear models suggest variable star universality
NASA Astrophysics Data System (ADS)
Lindner, John F.; Kohar, Vivek; Kia, Behnam; Hippke, Michael; Learned, John G.; Ditto, William L.
2016-02-01
Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes "golden" stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near -1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.
Mathematical model of laser PUVA psoriasis treatment
NASA Astrophysics Data System (ADS)
Medvedev, Boris A.; Tuchin, Valery V.; Yaroslavsky, Ilya V.
1991-05-01
In order to optimize laser PUVA psoriasis treatment we develop the mathematical model of the dynamics of cell processes within epidermis. We consider epidermis as a structure consisting of N cell monolayers. There are four kinds of cells that correspond to four epidermal strata. The different kinds of cells can exist within a given monolayer. We assume that the following cell processes take place: division, death and transition from one stratum to the following. Discrete transition of cells from stratum j to j + 1 approximates to real differentiation.
Mathematical modelling of risk reduction in reinsurance
NASA Astrophysics Data System (ADS)
Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.
2017-01-01
The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.
Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar
2014-09-25
Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.
Nonlinear structure formation in flat cosmological models
NASA Technical Reports Server (NTRS)
Martel, Hugo
1995-01-01
This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy
A mathematical model of aortic aneurysm formation
Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai
2017-01-01
Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412
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 aortic aneurysm formation.
Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R; Friedman, Avner; Zhu, Dai
2017-01-01
Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient's aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient's abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material.
Non-linear memristor switching model
NASA Astrophysics Data System (ADS)
Chernov, A. A.; Islamov, D. R.; Pik'nik, A. A.
2016-10-01
We introduce a thermodynamical model of filament growing when a current pulse via memristor flows. The model is the boundary value problem, which includes nonstationary heat conduction equation with non-linear Joule heat source, Poisson equation, and Shockley- Read-Hall equations taking into account strong electron-phonon interactions in trap ionization and charge transport processes. The charge current, which defines the heating in the model, depends on the rate of the oxygen vacancy generation. The latter depends on the local temperature. The solution of the introduced problem allows one to describe the kinetics of the switch process and the final filament morphology.
Mathematical models of tumor heterogeneity and drug resistance
NASA Astrophysics Data System (ADS)
Greene, James
In this dissertation we develop mathematical models of tumor heterogeneity and drug resistance in cancer chemotherapy. Resistance to chemotherapy is one of the major causes of the failure of cancer treatment. Furthermore, recent experimental evidence suggests that drug resistance is a complex biological phenomena, with many influences that interact nonlinearly. Here we study the influence of such heterogeneity on treatment outcomes, both in general frameworks and under specific mechanisms. We begin by developing a mathematical framework for describing multi-drug resistance to cancer. Heterogeneity is reflected by a continuous parameter, which can either describe a single resistance mechanism (such as the expression of P-gp in the cellular membrane) or can account for the cumulative effect of several mechanisms and factors. The model is written as a system of integro-differential equations, structured by the continuous "trait," and includes density effects as well as mutations. We study the limiting behavior of the model, both analytically and numerically, and apply it to study treatment protocols. We next study a specific mechanism of tumor heterogeneity and its influence on cell growth: the cell-cycle. We derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations, when the number of cells is large. The model is closely tied to experimental data of cell growth, and includes a novel implementation of
Model reduction of systems with localized nonlinearities.
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models
NASA Technical Reports Server (NTRS)
Hesse, Michael; Birn, Joachim
2011-01-01
Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.
A nonlinear dynamic analogue model of substorms
NASA Astrophysics Data System (ADS)
Klimas, A. J.; Baker, D. N.; Roberts, D. A.; Fairfield, D. H.; Büchner, J.
Linear prediction filter studies have shown that the magnetospheric response to energy transfer from the solar wind contains both directly driven and unloading components. These studies have also shown that the magnetospheric response is significantly nonlinear and, thus, the linear prediction filtering technique and other correlative techniques which assume a linear magnetospheric response cannot give a complete deacription of that response. Here, the solar wind-magnetosphere interaction is discussed within the framework of deterministic nonlinear dynamics. An earlier dripping faucet mechanical analogue to the magnetosphere is first reviewed and then the plasma physical counterpart to the mechanical model is constructed. A Faraday loop in the magnetotail is considered and the relationship of electric potentials on the loop to changes in the magnetic flux threading the loop is developed. This approach leads to a model of geomagnetic activity which is similar to the earlier mechanical model but described in terms of the geometry and plasma contents of the magnetotail. This Faraday loop response model contains analogues to both the directly driven and the storage-release magnetospheric responses and it includes, in a fundamental way, the inherent nonlinearity of the solar wind-magnetosphere system. It can be chancterized as a nonlinear, damped harmonic oscillator that is driven by the loading-unloading substorm cycle. The model is able to explain many of the features of the linear prediction filter results. In particular, at low geomagnetic activity levels the model exbibits the "regular dripping" response which provides an explanation for the unloading component at 1 hour lag in the linear prediction filters. Further, the model suggests that the disappearance of the unloading component in the linear prediction filters at high geomagnetic activity levels is due to a chaotic transition beyond which the loading-unloading mechanism becomes aperiodic. The model predicts
Automatic mathematical modeling for real time simulation program (AI application)
NASA Technical Reports Server (NTRS)
Wang, Caroline; Purinton, Steve
1989-01-01
A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.
Emerenini, Blessing O; Sonner, Stefanie; Eberl, Hermann J
2017-06-01
We analyze a mathematical model of quorum sensing induced biofilm dispersal. It is formulated as a system of non-linear, density-dependent, diffusion-reaction equations. The governing equation for the sessile biomass comprises two non-linear diffusion effects, a degeneracy as in the porous medium equation and fast diffusion. This equation is coupled with three semi-linear diffusion-reaction equations for the concentrations of growth limiting nutrients, autoinducers, and dispersed cells. We prove the existence and uniqueness of bounded non-negative solutions of this system and study the behavior of the model in numerical simulations, where we focus on hollowing effects in established biofilms.
A mathematical model of elastic fin micromotors
NASA Astrophysics Data System (ADS)
Lu, Pin; Lee, Kwok Hong; Piang Lim, Siak; Dong, Shuxiang; Zhong Lin, Wu
2000-08-01
In the present work, a simplified mathematical model of ultrasonic elastic fin micromotors has been developed. According to the operating principle of this type of motor, the motions of a rotor in each cycle of the stator vibration are divided into several stages based on whether the fin tip and the stator are in contact with slip, contact without slip or separation. The equations of motion of the rotor in each stage are derived. The valid range of the model has been discussed through numerical examples. This work provides an initial effort to construct a model for the elastic fin motor by considering the dynamical deformation of the rotor as well as the intermittent contacts.
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.
Developing mathematical models of neurobehavioral performance for the "real world".
Dean, Dennis A; Fletcher, Adam; Hursh, Steven R; Klerman, Elizabeth B
2007-06-01
Work-related operations requiring extended wake durations, night, or rotating shifts negatively affect worker neurobehavioral performance and health. These types of work schedules are required in many industries, including the military, transportation, and health care. These industries are increasingly using or considering the use of mathematical models of neurobehavioral performance as a means to predict the neurobehavioral deficits due to these operational demands, to develop interventions that decrease these deficits, and to provide additional information to augment existing decision-making processes. Recent advances in mathematical modeling have allowed its application to real-world problems. Developing application-specific expertise is necessary to successfully apply mathematical models, in part because development of new algorithms and methods linking the models to the applications may be required. During a symposium, "Modeling Human Neurobehavioral Performance II: Towards Operational Readiness," at the 2006 SIAM-SMB Conference on the Life Sciences, examples of the process of applying mathematical models, including model construction, model validation, or developing model-based interventions, were presented. The specific applications considered included refining a mathematical model of sleep/wake patterns of airline flight crew, validating a mathematical model using railroad operations data, and adapting a mathematical model to develop appropriate countermeasure recommendations based on known constraints. As mathematical models and their associated analytical methods continue to transition into operational settings, such additional development will be required. However, major progress has been made in using mathematical model outputs to inform those individuals making schedule decisions for their workers.
Mathematical model of acoustic speech production with mobile walls of the vocal tract
NASA Astrophysics Data System (ADS)
Lyubimov, N. A.; Zakharov, E. V.
2016-03-01
A mathematical speech production model is considered that describes acoustic oscillation propagation in a vocal tract with mobile walls. The wave field function satisfies the Helmholtz equation with boundary conditions of the third kind (impedance type). The impedance mode corresponds to a threeparameter pendulum oscillation model. The experimental research demonstrates the nonlinear character of how the mobility of the vocal tract walls influence the spectral envelope of a speech signal.
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.…
Nonlinear dynamical model of human gait
NASA Astrophysics Data System (ADS)
West, Bruce J.; Scafetta, Nicola
2003-05-01
We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.
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.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.
2015-09-15
Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.
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…
Teaching Mathematical Modelling for Earth Sciences via Case Studies
NASA Astrophysics Data System (ADS)
Yang, Xin-She
2010-05-01
Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).
Using a Functional Model to Develop a Mathematical Formula
ERIC Educational Resources Information Center
Otto, Charlotte A.; Everett, Susan A.; Luera, Gail R.
2008-01-01
The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…
Non-linear modelling and optimal control of a hydraulically actuated seismic isolator test rig
NASA Astrophysics Data System (ADS)
Pagano, Stefano; Russo, Riccardo; Strano, Salvatore; Terzo, Mario
2013-02-01
This paper investigates the modelling, parameter identification and control of an unidirectional hydraulically actuated seismic isolator test rig. The plant is characterized by non-linearities such as the valve dead zone and frictions. A non-linear model is derived and then employed for parameter identification. The results concerning the model validation are illustrated and they fully confirm the effectiveness of the proposed model. The testing procedure of the isolation systems is based on the definition of a target displacement time history of the sliding table and, consequently, the precision of the table positioning is of primary importance. In order to minimize the test rig tracking error, a suitable control system has to be adopted. The system non-linearities highly limit the performances of the classical linear control and a non-linear one is therefore adopted. The test rig mathematical model is employed for a non-linear control design that minimizes the error between the target table position and the current one. The controller synthesis is made by taking no specimen into account. The proposed approach consists of a non-linear optimal control based on the state-dependent Riccati equation (SDRE). Numerical simulations have been performed in order to evaluate the soundness of the designed control with and without the specimen under test. The results confirm that the performances of the proposed non-linear controller are not invalidated because of the presence of the specimen.
UH-60A Black Hawk engineering simulation program. Volume 1: Mathematical model
NASA Technical Reports Server (NTRS)
Howlett, J. J.
1981-01-01
A nonlinear mathematical model of the UR-60A Black Hawk helicopter was developed. This mathematical model, which was based on the Sikorsky General Helicopter (Gen Hel) Flight Dynamics Simulation, provides NASA with an engineering simulation for performance and handling qualities evaluations. This mathematical model is total systems definition of the Black Hawk helicopter represented at a uniform level of sophistication considered necessary for handling qualities evaluations. The model is a total force, large angle representation in six rigid body degrees of freedom. Rotor blade flapping, lagging, and hub rotational degrees of freedom are also represented. In addition to the basic helicopter modules, supportive modules were defined for the landing interface, power unit, ground effects, and gust penetration. Information defining the cockpit environment relevant to pilot in the loop simulation is presented.
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
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.
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.
Modelling of nonlinear filtering Poisson time series
NASA Astrophysics Data System (ADS)
Bochkarev, Vladimir V.; Belashova, Inna A.
2016-08-01
In this article, algorithms of non-linear filtering of Poisson time series are tested using statistical modelling. The objective is to find a representation of a time series as a wavelet series with a small number of non-linear coefficients, which allows distinguishing statistically significant details. There are well-known efficient algorithms of non-linear wavelet filtering for the case when the values of a time series have a normal distribution. However, if the distribution is not normal, good results can be expected using the maximum likelihood estimations. The filtration is studied according to the criterion of maximum likelihood by the example of Poisson time series. For direct optimisation of the likelihood function, different stochastic (genetic algorithms, annealing method) and deterministic optimization algorithms are used. Testing of the algorithm using both simulated series and empirical data (series of rare words frequencies according to the Google Books Ngram data were used) showed that filtering based on the criterion of maximum likelihood has a great advantage over well-known algorithms for the case of Poisson series. Also, the most perspective methods of optimisation were selected for this problem.
Mathematical model of tumor-immune surveillance.
Mahasa, Khaphetsi Joseph; Ouifki, Rachid; Eladdadi, Amina; Pillis, Lisette de
2016-09-07
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.
The use of mathematical models in teaching wastewater treatment engineering.
Morgenroth, E; Arvin, E; Vanrolleghem, P
2002-01-01
Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available.
Nonlinear Control of Wind Turbines with Hydrostatic Transmission Based on Takagi-Sugeno Model
NASA Astrophysics Data System (ADS)
Schulte, Horst; Georg, Soren
2014-06-01
A nonlinear model-based control concept for wind turbines with hydrostatic transmission is proposed. The complete mathematical model of a wind turbine drive train with variable displacement pump and variable displacement motor is presented. The controller design takes into consideration the nonlinearity of the aerodynamic maps and hydrostatic drive train by an convex combination of state space controller with measurable generator speed and hydraulic motor displacement as scheduling parameters. The objectives are the set point control of generator speed and tracking control of the rotor speed to reach the maximum power according to the power curve in the partial-load region.
Global Nonlinear Parametric Modeling with Application to F-16 Aerodynamics
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.
1998-01-01
A global nonlinear parametric modeling technique is described and demonstrated. The technique uses multivariate orthogonal modeling functions generated from the data to determine nonlinear model structure, then expands each retained modeling function into an ordinary multivariate polynomial. The final model form is a finite multivariate power series expansion for the dependent variable in terms of the independent variables. Partial derivatives of the identified models can be used to assemble globally valid linear parameter varying models. The technique is demonstrated by identifying global nonlinear parametric models for nondimensional aerodynamic force and moment coefficients from a subsonic wind tunnel database for the F-16 fighter aircraft. Results show less than 10% difference between wind tunnel aerodynamic data and the nonlinear parameterized model for a simulated doublet maneuver at moderate angle of attack. Analysis indicated that the global nonlinear parametric models adequately captured the multivariate nonlinear aerodynamic functional dependence.
From spiking neuron models to linear-nonlinear models.
Ostojic, Srdjan; Brunel, Nicolas
2011-01-20
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
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…
Mathematical Modelling: A Path to Political Reflection in the Mathematics Class
ERIC Educational Resources Information Center
Jacobini, Otavio Roberto; Wodewotzki, Maria Lucia L.
2006-01-01
This paper describes the construction of pedagogical environments in mathematics classes, centred on mathematical modelling and denominated "investigative scenarios", which stimulate students to investigation, to formulation of problems and to political reflection, as well as the sharing of acquired knowledge with other persons in the community.…
Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors
ERIC Educational Resources Information Center
Rash, Agnes M.; Zurbach, E. Peter
2004-01-01
The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…
ERIC Educational Resources Information Center
Lamb, Janeen; Kawakami, Takashi; Saeki, Akihiko; Matsuzaki, Akio
2014-01-01
The aim of this study was to investigate the use of the "dual mathematical modelling cycle framework" as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an "Oil Tank Task" that required them to develop two…
NASA Astrophysics Data System (ADS)
Rulevskiy, V. M.; Bukreev, V. G.; Shandarova, E. B.; Kuleshova, E. O.; Shandarov, S. M.; Vasilyeva, Yu Z.
2017-02-01
A modeling problem of the power system, which provides an AC power transmission to a submersible device over the conducting rope, was considered. The power supply system units and their parameters are described. The system multi-dimensional mathematical model in the variables state space with regard to the nonlinear characteristic of system elements is proposed.
Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
Mathematical foundations of the dendritic growth models.
Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos
2007-11-01
At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.
Mathematical modeling of plasma drifts over equatorial low latitude regions
NASA Astrophysics Data System (ADS)
Sundaresan, S.; Nageswara Rao, B.
2010-09-01
This paper presents a mathematical model to simulate ionospheric plasma drifts at equatorial low latitude regions by coupling of E- and F-regions. The governing non-linear differential equations (of elliptic and parabolic nature) are solved numerically through finite-difference schemes and obtained neutral winds and electric fields. The temperature and electron density profiles are generated utilizing MSIS-86 atmospheric model. The continuity equation is employed to obtain night-time E-region density profile using measured ionograms at Trivandrum (India). The computed vertical and zonal plasma drifts are comparable with measured Jacamarca plasma drifts with little variations during noon and evening times. The plasma drifts at Trivandrum (8.5° N, 76.5° E, dip 0.5° N) are compared with those of Jicamarca (12° S, 76.9° W, dip 2° N). Neutral wind simulations of present model agree well with those of horizontal wind model (HWM-93). The post-sunset enhancement and its reversal are also discussed.
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
Mathematical analysis of epidemiological models with heterogeneity
Van Ark, J.W.
1992-01-01
For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.
Mathematical Modeling of the Origins of Life
NASA Technical Reports Server (NTRS)
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Nonlinear energy principle for model current sheets
Yoon, Peter H.; Lui, Anthony T.Y.
2006-01-15
It is demonstrated on the basis of exact invariants of nonlinear Vlasov equation and model current sheets that the change in magnetic topology (i.e., reconnection) in a finite closed system leads to the conversion of magnetic-field energy to particle energy. It is also shown that the volume-averaged conversion efficiency diminishes as the spatial average is taken over larger and larger system size, while it increases when the system size becomes smaller. This finding may have an important implication for numerical simulation of reconnection processes under finite geometry.
Some Reflections on the Teaching of Mathematical Modeling
ERIC Educational Resources Information Center
Warwick, Jon
2007-01-01
This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve…
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.
The Aircraft Availability Model: Conceptual Framework and Mathematics
1983-06-01
THE AIRCRAFT AVAILABILITY MODEL: CONCEPTUAL FRAMEWORK AND MATHEMATICS June 1983 T. J. O’Malley Prepared pursuant to Department of Defense Contract No...OF REPORT & PERIOD COVERED The Aircraft Availability Model: Model Documentation Conceptual Framework and Mathematics 6. PERFORMING ORG. REPORT NUMBER
Model representation of the nonlinear step response in cardiac muscle
Chandra, Murali; Mamidi, Ranganath; Dong, Wenji; Campbell, Kenneth B.
2010-01-01
Motivated by the need for an analytical tool that can be used routinely to analyze data collected from isolated, detergent-skinned cardiac muscle fibers, we developed a mathematical model for representing the force response to step changes in muscle length (i.e., quick stretch and release). Our proposed model is reasonably simple, consisting of only five parameters representing: (1) the rate constant by which length change–induced distortion of elastic elements is dissipated; (2) the stiffness of the muscle fiber; (3) the amplitude of length-mediated recruitment of stiffness elements; (4) the rate constant by which this length-mediated recruitment takes place; and (5) the magnitude of the nonlinear interaction term by which distortion of elastic elements affects the number of recruited stiffness elements. Fitting this model to a family of force recordings representing responses to eight amplitudes of step length change (±2.0% baseline muscle length in 0.5% increments) enabled four things: (1) reproduction of all the identifiable features seen in a family of force responses to both positive and negative length changes; (2) close fitting of all records from the whole family of these responses with very little residual error; (3) estimation of all five model parameters with a great degree of certainty; and (4) importantly, ready discrimination between cardiac muscle fibers with different contractile regulatory proteins but showing only subtly different contractile function. We recommend this mathematical model as an analytic tool for routine use in studies of cardiac muscle fiber contractile function. Such model-based analysis gives novel insight to the contractile behavior of cardiac muscle fibers, and it is useful for characterizing the mechanistic effects that alterations of cardiac contractile proteins have on cardiac contractile function. PMID:20660660
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.
PREFACE: Physics-Based Mathematical Models for Nanotechnology
NASA Astrophysics Data System (ADS)
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
in the cross-disciplinary research area: low-dimensional semiconductor nanostructures. Since the main properties of two-dimensional heterostructures (such as quantum wells) are now quite well understood, there has been a consistently growing interest in the mathematical physics community to further dimensionality reduction of semiconductor structures. Experimental achievements in realizing one-dimensional and quasi-zero-dimensional heterostructures have opened new opportunities for theory and applications of such low-dimensional semiconductor nanostructures. One of the most important implications of this process has been a critical re-examining of assumptions under which traditional quantum mechanical models have been derived in this field. Indeed, the formation of LDSNs, in particular quantum dots, is a competition between the surface energy in the structure and strain energy. However, current models for bandstructure calculations use quite a simplified analysis of strain relaxation effects, although such effects are in the heart of nanostructure formation. By now, it has been understood that traditional models in this field may not be adequate for modeling realistic objects based on LDSNs due to neglecting many effects that may profoundly influence optoelectronic properties of the nanostructures. Among such effects are electromechanical effects, including strain relaxation, piezoelectric effect, spontaneous polarization, and higher order nonlinear effects. Up to date, major efforts have been concentrated on the analysis of idealized, isolated quantum dots, while a typical self-assembled semiconductor quantum dot nanostructure is an array (or a molecule) of many individual quantum dots sitting on the same `substrate' known as the wetting layer. Each such dot contains several hundred thousand atoms. In order to account for quantum effects accurately in a situation like that, attempts can be made to apply ab initio or atomistic methodologies, but then one would face a
Improving nonlinear modeling capabilities of functional link adaptive filters.
Comminiello, Danilo; Scarpiniti, Michele; Scardapane, Simone; Parisi, Raffaele; Uncini, Aurelio
2015-09-01
The functional link adaptive filter (FLAF) represents an effective solution for online nonlinear modeling problems. In this paper, we take into account a FLAF-based architecture, which separates the adaptation of linear and nonlinear elements, and we focus on the nonlinear branch to improve the modeling performance. In particular, we propose a new model that involves an adaptive combination of filters downstream of the nonlinear expansion. Such combination leads to a cooperative behavior of the whole architecture, thus yielding a performance improvement, particularly in the presence of strong nonlinearities. An advanced architecture is also proposed involving the adaptive combination of multiple filters on the nonlinear branch. The proposed models are assessed in different nonlinear modeling problems, in which their effectiveness and capabilities are shown.
Mathematical modeling plasma transport in tokamaks
Quiang, Ji
1997-01-01
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^{20}/m^{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%.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; ...
2015-09-15
Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less
Mathematical Model for the Mineralization of Bone
NASA Technical Reports Server (NTRS)
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
Mathematical Model for the Mineralization of Bone
NASA Technical Reports Server (NTRS)
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. The model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.
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 modelling of avascular-tumour growth.
Ward, J P; King, J R
1997-03-01
A system of nonlinear partial differential equations is proposed as a model for the growth of an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living or dead, and, depending on the concentration of a generic nutrient, the live cells may reproduce (expanding the tumour) or die (causing contraction). These volume changes resulting from cell birth and death generate a velocity field within the spheroid. Numerical solutions of the model reveal that after a period of time the variables settle to a constant profile propagating at a fixed speed. The travelling-wave limit is formulated and analytical solutions are found for a particular case. Numerical results for more general parameters compare well with these analytical solutions. Asymptotic techniques are applied to the physically relevant case of a small death rate, revealing two phases of growth retardation from the initial exponential growth, the first of which is due to nutrient-diffusion limitations and the second to contraction during necrosis. In this limit, maximal and "linear' phase growth speeds can be evaluated in terms of the model parameters.
ERIC Educational Resources Information Center
Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe
2016-01-01
Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…
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
NASA Astrophysics Data System (ADS)
Kharin, Stanislav; Sarsengeldin, Merey; Kassabek, Samat
2016-08-01
We represent mathematical models of electromagnetic field dynamics and heat transfer in closed symmetric and asymmetric electrical contacts including Thomson effect, which are essentially nonlinear due to the dependence of thermal and electrical conductivities on temperature. Suggested solutions are based on the assumption of identity of equipotentials and isothermal surfaces, which agrees with experimental data and valid for both linear and nonlinear cases. Well known Kohlrausch temperature-potential relation is analytically justified.
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.
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.
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.
Nonlinear modeling of chaotic time series: Theory and applications
NASA Astrophysics Data System (ADS)
Casdagli, M.; Eubank, S.; Farmer, J. D.; Gibson, J.; Desjardins, D.; Hunter, N.; Theiler, J.
We review recent developments in the modeling and prediction of nonlinear time series. In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases, it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years, methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics, and human speech.
Nonlinear modeling of chaotic time series: Theory and applications
Casdagli, M.; Eubank, S.; Farmer, J.D.; Gibson, J. Santa Fe Inst., NM ); Des Jardins, D.; Hunter, N.; Theiler, J. )
1990-01-01
We review recent developments in the modeling and prediction of nonlinear time series. In some cases apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics and human speech. 162 refs., 13 figs.
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.
Nonlinear structural finite element model updating and uncertainty quantification
NASA Astrophysics Data System (ADS)
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-04-01
This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.
Nonlinear models for estimating GSFC travel requirements
NASA Technical Reports Server (NTRS)
Buffalano, C.; Hagan, F. J.
1974-01-01
A methodology is presented for estimating travel requirements for a particular period of time. Travel models were generated using nonlinear regression analysis techniques on a data base of FY-72 and FY-73 information from 79 GSFC projects. Although the subject matter relates to GSFX activities, the type of analysis used and the manner of selecting the relevant variables would be of interest to other NASA centers, government agencies, private corporations and, in general, any organization with a significant travel budget. Models were developed for each of six types of activity: flight projects (in-house and out-of-house), experiments on non-GSFC projects, international projects, ART/SRT, data analysis, advanced studies, tracking and data, and indirects.
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…
Model Learner Outcomes for Mathematics Education.
ERIC Educational Resources Information Center
Halvorson, Judith K.; Stenglein, Sharon M.
Awareness of the need for essential reforms within mathematics education evolved fundamentally as the consequence of several national reports, culminating in the documentation of this need with "Everybody Counts" in January 1989. The publication of "Curriculum and Evaluation Standards for School Mathematics" by the National…
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…
Mathematical modeling of moving boundary problems in thermal energy storage
NASA Technical Reports Server (NTRS)
Solomon, A. D.
1980-01-01
The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.
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…
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…
Mathematical Models of the Value of Achievement Testing.
ERIC Educational Resources Information Center
Pinsky, Paul D.
The mathematical models of this paper were developed as an outgrowth of working with the Comprehensive Achievement Monitoring project (Project CAM) which was conceived as a model and application of sampling procedures such as those used in industrial quality control techniques to educational measurement. This paper explores mathematical modeling…
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 Modelling Research in Turkey: A Content Analysis Study
ERIC Educational Resources Information Center
Çelik, H. Coskun
2017-01-01
The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…
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.
Mathematical model I. Electron and quantum mechanics
NASA Astrophysics Data System (ADS)
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
A Mathematical Model of Forgetting and Amnesia
Murre, Jaap M. J.; Chessa, Antonio G.; Meeter, Martijn
2013-01-01
We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in strength (2) while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i) the temporal gradient of retrograde amnesia (Ribot’s Law), (ii) forgetting curves with and without anterograde amnesia, and (iii) learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff’s Disease, Alzheimer’s Dementia, Huntington’s Disease, and other disorders. PMID:23450438
Model of a nonlinear directional coupler in gallium arsenide
NASA Astrophysics Data System (ADS)
Gibbons, Wayne M.; Sarid, Dror
1987-08-01
We have calculated the response of a nonlinear directional coupler fabricated in an AlGaAs/GaAs structure using a realistic model for the optical nonlinearities. The model takes into account carrier-density-dependent index of refraction and absorption, and lateral carrier diffusion in each of the two coupled channel waveguides. Our results differ considerably from those obtained using a Kerr model for the optical nonlinearities.
Microwave heating and joining of ceramic cylinders: A mathematical model
NASA Technical Reports Server (NTRS)
Booty, Michael R.; Kriegsmann, Gregory A.
1994-01-01
A thin cylindrical ceramic sample is placed in a single mode microwave applicator in such a way that the electric field strength is allowed to vary along its axis. The sample can either be a single rod or two rods butted together. We present a simple mathematical model which describes the microwave heating process. It is built on the assumption that the Biot number of the material is small, and that the electric field is known and uniform throughout the cylinder's cross-section. The model takes the form of a nonlinear parabolic equation of reaction-diffusion type, with a spatially varying reaction term that corresponds to the spatial variation of the electromagnetic field strength in the waveguide. The equation is analyzed and a solution is found which develops a hot spot near the center of the cylindrical sample and which then propagates outwards until it stabilizes. The propagation and stabilization phenomenon concentrates the microwave energy in a localized region about the center where elevated temperatures may be desirable.
Nonlinear Analysis and Modeling of Tires
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.
1996-01-01
The objective of the study was to develop efficient modeling techniques and computational strategies for: (1) predicting the nonlinear response of tires subjected to inflation pressure, mechanical and thermal loads; (2) determining the footprint region, and analyzing the tire pavement contact problem, including the effect of friction; and (3) determining the sensitivity of the tire response (displacements, stresses, strain energy, contact pressures and contact area) to variations in the different material and geometric parameters. Two computational strategies were developed. In the first strategy the tire was modeled by using either a two-dimensional shear flexible mixed shell finite elements or a quasi-three-dimensional solid model. The contact conditions were incorporated into the formulation by using a perturbed Lagrangian approach. A number of model reduction techniques were applied to substantially reduce the number of degrees of freedom used in describing the response outside the contact region. The second strategy exploited the axial symmetry of the undeformed tire, and uses cylindrical coordinates in the development of three-dimensional elements for modeling each of the different parts of the tire cross section. Model reduction techniques are also used with this strategy.
Structure-selection techniques applied to continuous-time nonlinear models
NASA Astrophysics Data System (ADS)
Aguirre, Luis A.; Freitas, Ubiratan S.; Letellier, Christophe; Maquet, Jean
2001-10-01
This paper addresses the problem of choosing the multinomials that should compose a polynomial mathematical model starting from data. The mathematical representation used is a nonlinear differential equation of the polynomial type. Some approaches that have been used in the context of discrete-time models are adapted and applied to continuous-time models. Two examples are included to illustrate the main ideas. Models obtained with and without structure selection are compared using topological analysis. The main differences between structure-selected models and complete structure models are: (i) the former are more parsimonious than the latter, (ii) a predefined fixed-point configuration can be guaranteed for the former, and (iii) the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models.
Mathematical Modeling Tools to Study Preharvest Food Safety.
Lanzas, Cristina; Chen, Shi
2016-08-01
This article provides an overview of the emerging field of mathematical modeling in preharvest food safety. We describe the steps involved in developing mathematical models, different types of models, and their multiple applications. The introduction to modeling is followed by several sections that introduce the most common modeling approaches used in preharvest systems. We finish the chapter by outlining potential future directions for the field.
Accounting for nonlinear material characteristics in modeling ferroresonant transformers
NASA Astrophysics Data System (ADS)
Voisine, J. T.
1985-04-01
A mathematical model relating core material properties, including nonlinear magnetization characteristics, to the performance of ferroresonant transformers has been developed. In accomplishing this, other factors such as fabrication destruction factors, leakage flux, air gap characteristics, loading, and coil resistances and self-inductances are also accounted for. From a material manufacturer's view, knowing such information facilitates isolating sources of performance variations between units of similar design and is therefore highly desirable. The model predicts the primary induction necessary to establish a specified secondary induction and determines peak induction at other points in the magnetic circuit. A study comparing the model with a transformer indicated that each predicted peak induction was within ±5% of the corresponding measured peak induction. A generalized 4-node magnetic circuit having two shunt paths was chosen and modeled. Such a circuit is easily modified facilitating the analyses of numerous other core designs. A computer program designed to run on an HP-41 programmable calculator was also developed and is briefly described.
Recovering map static nonlinearities from chaotic data using dynamical models
NASA Astrophysics Data System (ADS)
Aguirre, Luis Antonio
1997-02-01
This paper is concerned with the estimation from chaotic data of maps with static nonlinearities. A number of issues concerning model construction such as structure selection, over-parametrization and model validation are discussed in the light of the shape of the static non-linearities reproduced by the estimated maps. A new interpretation of term clusters and cluster coefficients of polynomial models is provided based on this approach. The paper discusses model limitations and some useful principles to select the structure of nonlinear maps. Some of the ideas have been tested using several nonlinear systems including a boost voltage regulator map and a set of real data from a chaotic circuit.
Mathematical models in biology: from molecules to life.
Kaznessis, Yiannis N
2011-01-01
A vexing question in the biological sciences is the following: can biological phenotypes be explained with mathematical models of molecules that interact according to physical laws? At the crux of the matter lies the doubt that humans can develop physically faithful mathematical representations of living organisms. We discuss advantages that synthetic biological systems confer that may help us describe life's distinctiveness with tractable mathematics that are grounded on universal laws of thermodynamics and molecular biology.
Mathematical models in biology: from molecules to life
Kaznessis, Yiannis N.
2011-01-01
A vexing question in the biological sciences is the following: can biological phenotypes be explained with mathematical models of molecules that interact according to physical laws? At the crux of the matter lies the doubt that humans can develop physically faithful mathematical representations of living organisms. We discuss advantages that synthetic biological systems confer that may help us describe life’s distinctiveness with tractable mathematics that are grounded on universal laws of thermodynamics and molecular biology. PMID:21472998
ERIC Educational Resources Information Center
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Jung, Kwan-Jin
2009-09-01
A mathematical model to regress the nonlinear blood oxygen level-dependent (BOLD) fMRI signal has been developed by incorporating the refractory effect into the linear BOLD model of the biphasic gamma variate function. The refractory effect was modeled as a relaxation of two separate BOLD capacities corresponding to the biphasic components of the BOLD signal in analogy with longitudinal relaxation of magnetization in NMR. When tested with the published fMRI data of finger tapping, the nonlinear BOLD model with the refractory effect reproduced the nonlinear BOLD effects such as reduced poststimulus undershoot and saddle pattern in a prolonged stimulation as well as the reduced BOLD signal for repetitive stimulation.
The roughness surface expressed by the mathematical model
NASA Astrophysics Data System (ADS)
Macurova, Anna
2010-07-01
The work investigates the effect of some characteristics of a cut surface and studies roughness of the cutting process. There is elaborated theoretical information and new aspects on calculation of the theoretical values of the roughness of the cut surface for the chosen materials are formulated. In the area of the experimental investigation, results on characteristics of the chosen materials are formulated in this work. Obtained results are fundamental for the mathematical modulation and mathematical analysis for the investigated dependencies for the cut surfaces. The mathematical model also represents the specific dependencies of the technological process. The characteristics of the observed parameters are approximated by characteristics of the quasi-linear models. The solution of this model offers acceptable results. The mathematical models of the roughness of the cut surface are a mathematical description of the dependency of the maximum roughness of the cut surface of the feed represented by the differential equation and by the integral curves.
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
Mathematical modelling for nanotube bundle oscillators
NASA Astrophysics Data System (ADS)
Thamwattana, Ngamta; Cox, Barry J.; Hill, James M.
2009-07-01
This paper investigates the mechanics of a gigahertz oscillator comprising a nanotube oscillating within the centre of a uniform concentric ring or bundle of nanotubes. The study is also extended to the oscillation of a fullerene inside a nanotube bundle. In particular, certain fullerene-nanotube bundle oscillators are studied, namely C60-carbon nanotube bundle, C60-boron nitride nanotube bundle, B36N36-carbon nanotube bundle and B36N36-boron nitride nanotube bundle. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the fullerene and the nanotube bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques which provides considerable insight into the underlying mechanisms. The paper presents a synopsis of the major results derived in detail by the present authors in [1, 2].
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)
Application of CFD techniques toward the validation of nonlinear aerodynamic models
NASA Technical Reports Server (NTRS)
Schiff, L. B.; Katz, J.
1985-01-01
Applications of Computational fluid dynamics (CFD) methods to determine the regimes of applicability of nonlinear models describing the unsteady aerodynamic responses to aircraft flight motions are described. The potential advantages of computational methods over experimental methods are discussed and the concepts underlying mathematical modeling are reviewed. The economic and conceptual advantages of the modeling procedure over coupled, simultaneous solutions of the gasdynamic equations and the vehicle's kinematic equations of motion are discussed. The modeling approach, when valid, eliminates the need for costly repetitive computation of flow field solutions. For the test cases considered, the aerodynamic modeling approach is shown to be valid.
Application of nonlinear time series models to driven systems
Hunter, N.F. Jr.
1990-01-01
In our laboratory we have been engaged in an effort to model nonlinear systems using time series methods. Our objectives have been, first, to understand how the time series response of a nonlinear system unfolds as a function of the underlying state variables, second, to model the evolution of the state variables, and finally, to predict nonlinear system responses. We hope to address the relationship between model parameters and system parameters in the near future. Control of nonlinear systems based on experimentally derived parameters is also a planned topic of future research. 28 refs., 15 figs., 2 tabs.
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.
2011-01-01
Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520
A Mathematical Model of Quorum Sensing Induced Biofilm Detachment
Emerenini, Blessing O.; Hense, Burkhard A.; Kuttler, Christina; Eberl, Hermann J.
2015-01-01
Background Cell dispersal (or detachment) is part of the developmental cycle of microbial biofilms. It can be externally or internally induced, and manifests itself in discrete sloughing events, whereby many cells disperse in an instance, or in continuous slower dispersal of single cells. One suggested trigger of cell dispersal is quorum sensing, a cell-cell communication mechanism used to coordinate gene expression and behavior in groups based on population densities. Method To better understand the interplay of colony growth and cell dispersal, we develop a dynamic, spatially extended mathematical model that includes biofilm growth, production of quorum sensing molecules, cell dispersal triggered by quorum sensing molecules, and re-attachment of cells. This is a highly nonlinear system of diffusion-reaction equations that we study in computer simulations. Results Our results show that quorum sensing induced cell dispersal can be an efficient mechanism for bacteria to control the size of a biofilm colony, and at the same time enhance its downstream colonization potential. In fact we find that over the lifetime of a biofilm colony the majority of cells produced are lost into the aqueous phase, supporting the notion of biofilms as cell nurseries. We find that a single quorum sensing based mechanism can explain both, discrete dispersal events and continuous shedding of cells from a colony. Moreover, quorum sensing induced cell dispersal affects the structure and architecture of the biofilm, for example it might lead to the formation of hollow inner regions in a biofilm colony. PMID:26197231
NASA Astrophysics Data System (ADS)
Průša, Vít; Řehoř, Martin; Tůma, Karel
2017-02-01
The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systems.
Mathematical manipulative models: in defense of "beanbag biology".
Jungck, John R; Gaff, Holly; Weisstein, Anton E
2010-01-01
Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.
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…
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…
The Berlin-White Integrated Science and Mathematics Model.
ERIC Educational Resources Information Center
Berlin, Donna F.; White, Arthur L.
1994-01-01
Discusses six aspects of the Berlin-White Integrated Science and Mathematics Model developed to address the need for a definition of the integration of science and mathematics education. These aspects are ways of learning; ways of knowing; process and thinking skills; content knowledge; attitudes and perceptions; and teaching strategies. (MKR)
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 Manipulative Models: In Defense of “Beanbag Biology”
Gaff, Holly; Weisstein, Anton E.
2010-01-01
Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. PMID:20810952
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…
Modelling Reality in Mathematics Classrooms: The Case of Word Problems.
ERIC Educational Resources Information Center
Greer, Brian
1997-01-01
Word problems as used within the culture of mathematics education often promote a suspension of sense making by the students. In the papers in this issue, an alternative conceptualization of word problems is proposed that calls for mathematical modelling that takes real world knowledge into account. (SLD)
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…
NASA Astrophysics Data System (ADS)
Coelho, Leandro dos Santos; Pessôa, Marcelo Wicthoff
2009-07-01
Most processes in industry are characterized by nonlinear and time-varying behavior. The identification of mathematical models typically nonlinear systems is vital in many fields of engineering. The developed mathematical models can be used to study the behavior of the underlying system as well as for supervision, fault detection, prediction, estimation of unmeasurable variables, optimization and model-based control purposes. A variety of system identification techniques are applied to the modeling of process dynamics. Recently, the identification of nonlinear systems by genetic programming (GP) approaches has been successfully applied in many applications. GP is a paradigm of evolutionary computation field based on a structure description method that applies the principles of natural evolution to optimization problems and its nature is a generalized hierarchy computer program description. GP adopts a tree structure code to describe an identification problem. Unlike the traditional approximation methods where the structure of an approximate model is fixed, the structure of the GP tree itself is modified and optimized and, thus, there is a possibility that GP trees could be more appropriate or accurate approximate models. This paper focuses the GP method for structure selection in a system identification applications. The proposed GP method combines different techniques for tuning of crossover and mutation probabilities with an orthogonal least-squares (OLS) algorithm to estimate the contribution of the branches of the tree to the accuracy of the discrete polynomial Nonlinear AutoRegressive with eXogenous inputs (NARX) model. The nonlinear system identification procedure, based on a NARX representation and GP, is applied to empirical case study of an experimental ball-and-tube system. The results demonstrate that the GP with OLS is a promising technique for NARX modeling.
Bond models in linear and nonlinear optics
NASA Astrophysics Data System (ADS)
Aspnes, D. E.
2015-08-01
Bond models, also known as polarizable-point or mechanical models, have a long history in optics, starting with the Clausius-Mossotti relation but more accurately originating with Ewald's largely forgotten work in 1912. These models describe macroscopic phenomena such as dielectric functions and nonlinear-optical (NLO) susceptibilities in terms of the physics that takes place in real space, in real time, on the atomic scale. Their strengths lie in the insights that they provide and the questions that they raise, aspects that are often obscured by quantum-mechanical treatments. Statics versions were used extensively in the late 1960's and early 1970's to correlate NLO susceptibilities among bulk materials. Interest in NLO applications revived with the 2002 work of Powell et al., who showed that a fully anisotropic version reduced by more than a factor of 2 the relatively large number of parameters necessary to describe secondharmonic- generation (SHG) data for Si(111)/SiO2 interfaces. Attention now is focused on the exact physical meaning of these parameters, and to the extent that they represent actual physical quantities.
ERIC Educational Resources Information Center
Wright, Vince
2014-01-01
Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…
Mathematical modeling in wound healing, bone regeneration and tissue engineering.
Geris, Liesbet; Gerisch, Alf; Schugart, Richard C
2010-12-01
The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.
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
Mathematical models and their applications in medicine and health.
Verma, B l; Ray, S K; Srivastava, R N
1981-01-01
Mathematical models have great potentialities as regards their utility in different disciplines of medicine and health. This paper attempts to elucidate their uses in the field. A brief mention of some models has also been made. Mathematical models are useful in epidemiologic research, planning and evaluation of preventive and control programmes, clinical trials, measurement of health, cost-benefit analysis, diagnosis of patients and in maximizing effectiveness of operations aimed at attaining specified goals within existing resources.
Nonlinear Growth Models in M"plus" and SAS
ERIC Educational Resources Information Center
Grimm, Kevin J.; Ram, Nilam
2009-01-01
Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the M"plus" structural modeling program and the nonlinear…
Applications of Nonlinear Models. AIR 1984 Annual Forum Paper.
ERIC Educational Resources Information Center
Stewart, Ian; Johnson, F. Craig
Some of the conceptual qualitative ideas needed to test nonlinear models empirically and to modify them are described. Relationships among these ideas and computer applications are also examined to elucidate the general process of nonlinear modeling. Two examples are presented along with a discussion of bifurcation, catastrophe, and maximum…
Effects of model sensitivity and nonlinearity on nonlinear regression of ground water flow
Yager, R.M.
2004-01-01
Nonlinear regression is increasingly applied to the calibration of hydrologic models through the use of perturbation methods to compute the Jacobian or sensitivity matrix required by the Gauss-Newton optimization method. Sensitivities obtained by perturbation methods can be less accurate than those obtained by direct differentiation, however, and concern has arisen that the optimal parameter values and the associated parameter covariance matrix computed by perturbation could also be less accurate. Sensitivities computed by both perturbation and direct differentiation were applied in nonlinear regression calibration of seven ground water flow models. The two methods gave virtually identical optimum parameter values and covariances for the three models that were relatively linear and two of the models that were relatively nonlinear, but gave widely differing results for two other nonlinear models. The perturbation method performed better than direct differentiation in some regressions with the nonlinear models, apparently because approximate sensitivities computed for an interval yielded better search directions than did more accurately computed sensitivities for a point. The method selected to avoid overshooting minima on the error surface when updating parameter values with the Gauss-Newton procedure appears for nonlinear models to be more important than the method of sensitivity calculation in controlling regression convergence.
Nonlinear lower hybrid modeling in tokamak plasmas
Napoli, F.; Schettini, G.; Castaldo, C.; Cesario, R.
2014-02-12
We present here new results concerning the nonlinear mechanism underlying the observed spectral broadening produced by parametric instabilities occurring at the edge of tokamak plasmas in present day LHCD (lower hybrid current drive) experiments. Low frequency (LF) ion-sound evanescent modes (quasi-modes) are the main parametric decay channel which drives a nonlinear mode coupling of lower hybrid (LH) waves. The spectrum of the LF fluctuations is calculated here considering the beating of the launched LH wave at the radiofrequency (RF) operating line frequency (pump wave) with the noisy background of the RF power generator. This spectrum is calculated in the frame of the kinetic theory, following a perturbative approach. Numerical solutions of the nonlinear LH wave equation show the evolution of the nonlinear mode coupling in condition of a finite depletion of the pump power. The role of the presence of heavy ions in a Deuterium plasma in mitigating the nonlinear effects is analyzed.
Mathematical modelling of the MAP kinase pathway using proteomic datasets.
Tian, Tianhai; Song, Jiangning
2012-01-01
The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.
Nonlinear q -voter model with inflexible zealots
NASA Astrophysics Data System (ADS)
Mobilia, Mauro
2015-07-01
We study the dynamics of the nonlinear q -voter model with inflexible zealots in a finite well-mixed population. In this system, each individual supports one of two parties and is either a susceptible voter or an inflexible zealot. At each time step, a susceptible adopts the opinion of a neighbor if this belongs to a group of q ≥2 neighbors all in the same state, whereas inflexible zealots never change their opinion. In the presence of zealots of both parties, the model is characterized by a fluctuating stationary state and, below a zealotry density threshold, the distribution of opinions is bimodal. After a characteristic time, most susceptibles become supporters of the party having more zealots and the opinion distribution is asymmetric. When the number of zealots of both parties is the same, the opinion distribution is symmetric and, in the long run, susceptibles endlessly swing from the state where they all support one party to the opposite state. Above the zealotry density threshold, when there is an unequal number of zealots of each type, the probability distribution is single-peaked and non-Gaussian. These properties are investigated analytically and with stochastic simulations. We also study the mean time to reach a consensus when zealots support only one party.
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.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying a series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less
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
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity
Pacini, Benjamin Robert; Mayes, Randall L.; Roettgen, Daniel R
2015-10-01
Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.
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 approaches to modeling of cortical spreading depression
NASA Astrophysics Data System (ADS)
Miura, Robert M.; Huang, Huaxiong; Wylie, Jonathan J.
2013-12-01
Migraine with aura (MwA) is a debilitating disease that afflicts about 25%-30% of migraine sufferers. During MwA, a visual illusion propagates in the visual field, then disappears, and is followed by a sustained headache. MwA was conjectured by Lashley to be related to some neurological phenomenon. A few years later, Leão observed electrophysiological waves in the brain that are now known as cortical spreading depression (CSD). CSD waves were soon conjectured to be the neurological phenomenon underlying MwA that had been suggested by Lashley. However, the confirmation of the link between MwA and CSD was not made until 2001 by Hadjikhani et al. [Proc. Natl. Acad. Sci. U.S.A. 98, 4687-4692 (2001)] using functional MRI techniques. Despite the fact that CSD has been studied continuously since its discovery in 1944, our detailed understandings of the interactions between the mechanisms underlying CSD waves have remained elusive. The connection between MwA and CSD makes the understanding of CSD even more compelling and urgent. In addition to all of the information gleaned from the many experimental studies on CSD since its discovery, mathematical modeling studies provide a general and in some sense more precise alternative method for exploring a variety of mechanisms, which may be important to develop a comprehensive picture of the diverse mechanisms leading to CSD wave instigation and propagation. Some of the mechanisms that are believed to be important include ion diffusion, membrane ionic currents, osmotic effects, spatial buffering, neurotransmitter substances, gap junctions, metabolic pumps, and synaptic connections. Discrete and continuum models of CSD consist of coupled nonlinear differential equations for the ion concentrations. In this review of the current quantitative understanding of CSD, we focus on these modeling paradigms and various mechanisms that are felt to be important for CSD.
Nonlinear ultrasound modelling and validation of fatigue damage
NASA Astrophysics Data System (ADS)
Fierro, G. P. Malfense; Ciampa, F.; Ginzburg, D.; Onder, E.; Meo, M.
2015-05-01
Nonlinear ultrasound techniques have shown greater sensitivity to microcracks and they can be used to detect structural damages at their early stages. However, there is still a lack of numerical models available in commercial finite element analysis (FEA) tools that are able to simulate the interaction of elastic waves with the materials nonlinear behaviour. In this study, a nonlinear constitutive material model was developed to predict the structural response under continuous harmonic excitation of a fatigued isotropic sample that showed anharmonic effects. Particularly, by means of Landau's theory and Kelvin tensorial representation, this model provided an understanding of the elastic nonlinear phenomena such as the second harmonic generation in three-dimensional solid media. The numerical scheme was implemented and evaluated using a commercially available FEA software LS-DYNA, and it showed a good numerical characterisation of the second harmonic amplitude generated by the damaged region known as the nonlinear response area (NRA). Since this process requires only the experimental second-order nonlinear parameter and rough damage size estimation as an input, it does not need any baseline testing with the undamaged structure or any dynamic modelling of the fatigue crack growth. To validate this numerical model, the second-order nonlinear parameter was experimentally evaluated at various points over the fatigue life of an aluminium (AA6082-T6) coupon and the crack propagation was measured using an optical microscope. A good correlation was achieved between the experimental set-up and the nonlinear constitutive model.
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,…
Key Concept Mathematics and Management Science Models
ERIC Educational Resources Information Center
Macbeth, Thomas G.; Dery, George C.
1973-01-01
The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)
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…
MAPCLUS: A Mathematical Programming Approach to Fitting the ADCLUS Model.
ERIC Educational Resources Information Center
Arabie, Phipps
1980-01-01
A new computing algorithm, MAPCLUS (Mathematical Programming Clustering), for fitting the Shephard-Arabie ADCLUS (Additive Clustering) model is presented. Details and benefits of the algorithm are discussed. (Author/JKS)
The Mathematical Concept of Set and the 'Collection' Model.
ERIC Educational Resources Information Center
Fischbein, Efraim; Baltsan, Madlen
1999-01-01
Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)
Model Predictive Control for Nonlinear Parabolic Partial Differential Equations
NASA Astrophysics Data System (ADS)
Hashimoto, Tomoaki; Yoshioka, Yusuke; Ohtsuka, Toshiyuki
In this study, the optimal control problem of nonlinear parabolic partial differential equations (PDEs) is investigated. Optimal control of nonlinear PDEs is an open problem with applications that include fluid, thermal, biological, and chemically-reacting systems. Model predictive control with a fast numerical solution method has been well established to solve the optimal control problem of nonlinear systems described by ordinary differential equations. In this study, we develop a design method of the model predictive control for nonlinear systems described by parabolic PDEs. Our approach is a direct infinite dimensional extension of the model predictive control method for finite-dimensional systems. The objective of this paper is to develop an efficient algorithm for numerically solving the model predictive control problem of nonlinear parabolic PDEs. The effectiveness of the proposed method is verified by numerical simulations.
Current algebra and the nonlinear σ-model
NASA Astrophysics Data System (ADS)
Ghosh, S.
2007-06-01
We present the current algebra of a particular form in the nonlinear σ-model. The algebra has a non-Abelian form with field-dependent structure functions. We comment on the connection of the model with noncommutative space.
Kac-Moody algebra and nonlinear sigma model
NASA Astrophysics Data System (ADS)
Ogura, Waichi; Hosoya, Akio
1985-12-01
We investigate the nonlinear sigma model over an arbitrary homogeneous space. Then it is shown that the sigma model realizes the Kac-Moody algebra as current algebra only if the homogeneous space is restricted to the group manifold.
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 on the closing and opening mechanism for venus flytrap.
Yang, Ruoting; Lenaghan, Scott C; Zhang, Mingjun; Xia, Lijin
2010-08-01
This paper investigates the opening and closing mechanism for the Venus Flytrap (Dionaea muscipula). A mathematical model has been proposed to explain how the flytrap transitions between open, semi-closed, and closed states. The model accounts for the charge accumulation of action potentials, which generated by mechanical stimulation of the sensitive trigger hairs on the lobes of the flytrap. Though many studies have been reported for the Venus flytrap opening and closing mechanism, this paper attempts to explain the mechanism from nonlinear dynamics and control perspective.
On the Reliability of Nonlinear Modeling using Enhanced Genetic Programming Techniques
NASA Astrophysics Data System (ADS)
Winkler, S. M.; Affenzeller, M.; Wagner, S.
The use of genetic programming (GP) in nonlinear system identification enables the automated search for mathematical models that are evolved by an evolutionary process using the principles of selection, crossover and mutation. Due to the stochastic element that is intrinsic to any evolutionary process, GP cannot guarantee the generation of similar or even equal models in each GP process execution; still, if there is a physical model underlying to the data that are analyzed, then GP is expected to find these structures and produce somehow similar results. In this paper we define a function for measuring the syntactic similarity of mathematical models represented as structure trees; using this similarity function we compare the results produced by GP techniques for a data set representing measurement data of a BMW Diesel engine.
Mathematical modeling of solidification phenomena in electromagnetically stirred melts
NASA Astrophysics Data System (ADS)
Poole, Gregory Michael
A methodology is presented to simulate the electromagnetic, heat transfer, and fluid flow phenomena for two dimensional electromagnetic solidification processes. For computation of the electromagnetic field, the model utilizes the mutual inductance technique to limit the solution domain to the molten metal and magnetic shields, commonly present in solidification systems. The temperature and velocity fields were solved using the control volume method in the metal domain. The developed model employs a two domain formulation for the mushy zone. Mathematical formulations are presented for turbulent flow in the bulk liquid and the suspended particle region, along with rheological behavior. An expression has been developed---for the first time---to describe damping of the flow in the suspended particle region as a result of the interactions between the particles and the turbulent eddies. The flow in the fixed particle region is described using Darcy's law. Calculations were carried out for globular and dendritic solidification morphologies of an electromagnetically-stirred melt in a bottom-chill mold. The coherency solid fraction for the globular solidification morphology was taken to be 0.5, while the coherency for dendritic morphology was 0.25. The results showed the flow intensity in the suspended particle region was reduced by an order of magnitude. The effect of the heat extraction rate on solidification time was investigated using three different heat transfer coefficients. The results showed that the decrease in solidification time is nonlinear with respect to increasing heat transfer coefficient. The influence of the final grain size on the damping of the flow in the suspended particle region was examined, and it was found that larger grain sizes reduce the extent of flow damping.
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…
Linear and Nonlinear Thinking: A Multidimensional Model and Measure
ERIC Educational Resources Information Center
Groves, Kevin S.; Vance, Charles M.
2015-01-01
Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…
A Nonlinear Mixed Effects Model for Latent Variables
ERIC Educational Resources Information Center
Harring, Jeffrey R.
2009-01-01
The nonlinear mixed effects model for continuous repeated measures data has become an increasingly popular and versatile tool for investigating nonlinear longitudinal change in observed variables. In practice, for each individual subject, multiple measurements are obtained on a single response variable over time or condition. This structure can be…
NASA Astrophysics Data System (ADS)
Song, Pengchao
Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) of the F-16 have provided good support to the long-standing hypothesis that this phenomenon involves a nonlinear structural damping. A potential mechanism for the appearance of nonlinearity in the damping are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is first on extending nonlinear reduced order modeling (ROM) methods to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An identification approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software. The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.
NASA Astrophysics Data System (ADS)
Yao, Ruo-Xia; Wang, Wei; Chen, Ting-Hua
2014-11-01
Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.
Mathematical modelling for the new millenium: medicine by numbers.
Smye, Stephen W; Clayton, Richard H
2002-11-01
Physicists, engineers and mathematicians are accustomed to the combination of elegance, rigour and utility that characterise mathematical models. They are familiar with the need to dip into their mathematical toolbox to select the technique of choice. However, medicine and biology have not been characterised, in general, by a mathematical formalism. The relative paucity of mathematical models in biology and medicine reflects in part the difficulty in making accurate and appropriate experimental measurements in the field. Signal noise, the lack of appropriate sensors, and uncertainty as to what constitutes the significant measurements are largely to blame for this. The purpose of this paper is to characterise a 'good' model, encourage the development and application of such models to new areas, and outline future developments in the field. It is proposed that a good model will be accurate, predictive, economical, unique and elegant. These principles will be illustrated with reference to four models: radiosensitisation of tumours, modelling solute clearance in haemodialysis, the myogenic response in reactive hyperaemia and cardiac electrical activity. It is suggested that, in the immediate future, the mathematical model will become a useful adjunct to laboratory experiment (and possibly clinical trial), and the provision of 'in silico' models will become routine.
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…
Takamizawa, K; Niu, S; Matsuda, T
1996-01-01
In vitro transanastomotic endothelialization was studied using a mathematical model with the Fisher equation. The Fisher equation is a nonlinear parabolic equation which has a cell migration term and a population growth term. The mathematical model was used to simulate recent experiments performed to investigate quantitatively the unidirectional formation of a bovine endothelial cell monolayer in vitro. The two parameters included in the equation were estimated using a trial and error method in which the calculated solutions of the various values of the two parameters are compared with the experimental data and the best fit pair is adopted: one parameter, D, which represents the unidirectional cell migration rate and the other, k, which represents the population growth rate. The calculated solutions fit the experimental data well. We also simulated the healing of a mechanically disrupted endothelial monolayer sheet. The significance of cellular biomechanics in tissue formation and design of tissue-engineered devices is discussed.
Nonlinear Model Predictive Control with Constraint Satisfactions for a Quadcopter
NASA Astrophysics Data System (ADS)
Wang, Ye; Ramirez-Jaime, Andres; Xu, Feng; Puig, Vicenç
2017-01-01
This paper presents a nonlinear model predictive control (NMPC) strategy combined with constraint satisfactions for a quadcopter. The full dynamics of the quadcopter describing the attitude and position are nonlinear, which are quite sensitive to changes of inputs and disturbances. By means of constraint satisfactions, partial nonlinearities and modeling errors of the control-oriented model of full dynamics can be transformed into the inequality constraints. Subsequently, the quadcopter can be controlled by an NMPC controller with the updated constraints generated by constraint satisfactions. Finally, the simulation results applied to a quadcopter simulator are provided to show the effectiveness of the proposed strategy.
Valuation of financial models with non-linear state spaces
NASA Astrophysics Data System (ADS)
Webber, Nick
2001-02-01
A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.
Evaluation of limb load asymmetry using two new mathematical models.
Kumar, Senthil N S; Omar, Baharudin; Joseph, Leonard H; Htwe, Ohnmar; Jagannathan, K; Hamdan, Nor M Y; Rajalakshmi, D
2014-09-25
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.
[Mathematical approach to modeling of the treatment of suppurative processes].
Men'shikov, D D; Enileev, R Kh
1989-03-01
Consideration of an inflammation focus as an "open system" provided analogy between microbiological processes in inflamed wounds and in systems of continuous cultivation of microorganisms. Mathematical modeling of such systems is widely used. Some of the methods for the mathematical modeling were applied to chemoprophylaxis and chemotherapy of postoperative wounds. In modeling continuous cultivation of microorganisms it is usually necessary to determine optimal conditions for the maximum yield of their biomass. In modeling of wound treatment the aim was to determine the process parameters providing the minimum biomass. The described simple models showed that there could be certain optimal flow rate of the washing fluid in the aspiration-washing procedure for wound treatment at which the drug was not completely washed out while the growth rate of the microbial population was minimal. Such mathematical models were shown valuable in optimizing the use of bactericidal and bacteriostatic antibiotics.
Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.
Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang
2016-10-31
Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.
Short- and Long-Term Optimal Control of a Mathematical Model for HIV Infection of CD4+T Cells.
Croicu, Ana-Maria
2015-11-01
The main goal of this study was to develop a theoretical short- and long-term optimal control treatment of HIV infection of [Formula: see text] cells. The aim of the mathematical model used herein is to make the free HIV virus particles in the blood decrease, while administering a treatment that is less toxic to patients. Pontryagin's classical control theory is applied to a mathematical model of HIV infection of [Formula: see text] cells characterized by a system of nonlinear differential equations with the following unknown functions: the concentration of susceptible [Formula: see text] cells, [Formula: see text] cells infected by the HIV viruses and free HIV virus particles in the blood.
Coupled and uncoupled dipole models of nonlinear scattering.
Balla, Naveen K; Yew, Elijah Y S; Sheppard, Colin J R; So, Peter T C
2012-11-05
Dipole models are one of the simplest numerical models to understand nonlinear scattering. Existing dipole model for second harmonic generation, third harmonic generation and coherent anti-Stokes Raman scattering assume that the dipoles which make up a scatterer do not interact with one another. Thus, this dipole model can be called the uncoupled dipole model. This dipole model is not sufficient to describe the effects of refractive index of a scatterer or to describe scattering at the edges of a scatterer. Taking into account the interaction between dipoles overcomes these short comings of the uncoupled dipole model. Coupled dipole model has been primarily used for linear scattering studies but it can be extended to predict nonlinear scattering. The coupled and uncoupled dipole models have been compared to highlight their differences. Results of nonlinear scattering predicted by coupled dipole model agree well with previously reported experimental results.
Mathematical modeling of physiological systems: an essential tool for discovery.
Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J
2014-08-28
Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?"
Mathematical modeling of physiological systems: An essential tool for discovery
Glynn, Patric; Unudurthi, Sathya D.; Hund, Thomas J.
2014-01-01
Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: “What is the value of a model?” PMID:25064823
Mathematical Models for Manpower and Personnel Planning, Research Report.
ERIC Educational Resources Information Center
Charnes, A.; And Others
Current work in mathematical modeling for manpower planning and personnel administration is reviewed with special reference to selected cases in the U.S. Navy. This included: (1) assignment models and their dynamic extensions, (2) Stochastic models with special reference to Markoff Processes, including the Office of Civilian Manpower and…
A Mathematical Model for the Middle Ear Ventilation
NASA Astrophysics Data System (ADS)
Molnárka, G.; Miletics, E. M.; Fücsek, M.
2008-09-01
The otitis media is one of the mostly existing illness for the children, therefore investigation of the human middle ear ventilation is an actual problem. In earlier investigations both experimental and theoretical approach one can find in ([l]-[3]). Here we give a new mathematical and computer model to simulate this ventilation process. This model able to describe the diffusion and flow processes simultaneously, therefore it gives more precise results than earlier models did. The article contains the mathematical model and some results of the simulation.
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 Nonlinear Viscoelastic Model for Ceramics at High Temperatures
NASA Technical Reports Server (NTRS)
Powers, Lynn M.; Panoskaltsis, Vassilis P.; Gasparini, Dario A.; Choi, Sung R.
2002-01-01
High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the nonlinear, asymmetric time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Element deletion has been implemented within ABAQUS. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. The analytical model is intended to be used to predict the creep rupture lives of ceramic parts in arbitrary stress conditions.
Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps
NASA Astrophysics Data System (ADS)
Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin
2016-11-01
In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 < 1, the disease may die out, and when R¯0 > 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.
Mathematical modeling in metal metabolism: overview and perspectives.
Curis, Emmanuel; Nicolis, Ioannis; Bensaci, Jalil; Deschamps, Patrick; Bénazeth, Simone
2009-10-01
A review of mathematical modeling in metal metabolism is presented. Both endogenous and exogenous metals are considered. Four classes of methods are considered: Petri nets, multi-agent systems, determinist models based on differential equations and stochastic models. For each, a basic theoretical background is given, then examples of applications are given, detailed and commented. Advantages and disadvantages of each class of model are presented. A special attention is given to determinist differential equation models, since almost all models belong to this class.
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.
Nonlinear damping model for flexible structures. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Zang, Weijian
1990-01-01
The study of nonlinear damping problem of flexible structures is addressed. Both passive and active damping, both finite dimensional and infinite dimensional models are studied. In the first part, the spectral density and the correlation function of a single DOF nonlinear damping model is investigated. A formula for the spectral density is established with O(Gamma(sub 2)) accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly. In the second part, the spectral density of a multi-DOF nonlinear damping model is investigated. In the third part, energy type nonlinear damping model in an infinite dimensional setting is studied.
Dilatonic non-linear sigma models and Ricci flow extensions
NASA Astrophysics Data System (ADS)
Carfora, M.; Marzuoli, A.
2016-09-01
We review our recent work describing, in terms of the Wasserstein geometry over the space of probability measures, the embedding of the Ricci flow in the renormalization group flow for dilatonic non-linear sigma models.
A new nonlinear model for pitch perception
NASA Astrophysics Data System (ADS)
Cartwright, Julyan H. E.; González, Diego L.; Piro, Oreste
The ability of the auditory system to perceive the fundamental frequency of a sound even when this frequency is removed from the stimulus is an interesting phenomenon related to the pitch of complex sounds. This capability is known as residue or virtual pitch perception and was first reported last century in the pioneering work of Seebeck. It is residue perception that allows one to listen to music with small transistor radios, which in general have a very poor and sometimes negligible response to low frequencies. The first attempt, due to von Helmholtz, to explain the residue as a nonlinear effect in the ear considered it to originate from difference combination tones. But later experiments showed that the residue does not coincide with a difference combination tone, and nonlinear theories were abandoned. However, in this paper we use recent results from the theory of nonlinear dynamical systems to show that physical frequencies produced by generic nonlinear oscillators acted upon by two independent periodic excitations can reproduce with great precision most of the experimental data about the residue.
A heuristic mathematical model for the dynamics of sensory conflict and motion sickness
NASA Technical Reports Server (NTRS)
Oman, C. M.
1982-01-01
By consideration of the information processing task faced by the central nervous system in estimating body spatial orientation and in controlling active body movement using an internal model referenced control strategy, a mathematical model for sensory conflict generation is developed. The model postulates a major dynamic functional role for sensory conflict signals in movement control, as well as in sensory-motor adaptation. It accounts for the role of active movement in creating motion sickness symptoms in some experimental circumstance, and in alleviating them in others. The relationship between motion sickness produced by sensory rearrangement and that resulting from external motion disturbances is explicitly defined. A nonlinear conflict averaging model is proposed which describes dynamic aspects of experimentally observed subjective discomfort sensation, and suggests resulting behaviours. The model admits several possibilities for adaptive mechanisms which do not involve internal model updating. Further systematic efforts to experimentally refine and validate the model are indicated.
A mathematical simulation model of the CH-47B helicopter, volume 2
NASA Technical Reports Server (NTRS)
Weber, J. M.; Liu, T. Y.; Chung, W.
1984-01-01
A nonlinear simulation model of the CH-47B helicopter, was adapted for use in a simulation facility. The model represents the specific configuration of the variable stability CH-47B helicopter. Modeling of the helicopter uses a total force approach in six rigid body degrees of freedom. Rotor dynamics are simulated using the Wheatley-Bailey equations, steady state flapping dynamics and included in the model of the option for simulation of external suspension, slung load equations of motion. Validation of the model was accomplished by static and dynamic data from the original Boeing Vertol mathematical model and flight test data. The model is appropriate for use in real time piloted simulation and is implemented on the ARC Sigma IX computer where it may be operated with a digital cycle time of 0.03 sec.
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
Chirkunov, Yu. A.
2015-10-15
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
Mathematical models to characterize early epidemic growth: A review
NASA Astrophysics Data System (ADS)
Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile
2016-09-01
There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.
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.
Nonlinear dynamical model and response of avian cranial kinesis.
Meekangvan, Preeda; A Barhorst, Alan; Burton, Thomas D; Chatterjee, Sankar; Schovanec, Lawrence
2006-05-07
All modern birds have kinetic skulls in which the upper bill can move relative to the braincase, but the biomechanics and motion dynamics of cranial kinesis in birds are poorly understood. In this paper, we model the dynamics of avian cranial kinesis, such as prokinesis and proximal rhynchokinesis in which the upper jaw pivots around the nasal-frontal (N-F) hinge. The purpose of this paper is to present to the biological community an approach that demonstrates the application of sophisticated predictive mathematical modeling tools to avian kinesis. The generality of the method, however, is applicable to the advanced study of the biomechanics of other skeletal systems. The paper begins with a review of the relevant biological literature as well as the essential morphology of avian kinesis, especially the mechanical coupling of the upper and lower jaw by the postorbital ligament. A planar model of the described bird jaw morphology is then developed that maintains the closed kinematic topology of the avian jaw mechanism. We then develop the full nonlinear equations of motion with the assumption that the M. protractor pterygoideus and M. depressor mandibulae act on the quadrate as a pure torque, and the nasal frontal hinge is elastic with damping. The mechanism is shown to be a single degree of freedom device due to the holonomic constraints present in the quadrate-jugal bar-upper jaw-braincase-quadrate kinematic chain as well as the quadrate-lower jaw-postorbital ligament-braincase-quadrate kinematic chain. The full equations are verified via simulation and animation using the parameters of a Grey Heron (Ardea cinerea). Next we develop a simplified analytical model of the equations by power series expansion. We demonstrate that this model reproduces the dynamics of the full model to a high degree of fidelity. We proceed to use the harmonic balance technique to develop the frequency response characteristics of the jaw mechanism. It is shown that this avian cranial
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
Mathematical modeling of renal hemodynamics in physiology and pathophysiology.
Sgouralis, Ioannis; Layton, Anita T
2015-06-01
In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease.
Mathematical Modeling of Primary Wood Processing
NASA Astrophysics Data System (ADS)
Szyszka, Barbara; Rozmiarek, Klaudyna
2008-09-01
This work presents a way of optimizing wood logs' conversion into semi-products. Calculating algorithms have been used in order to choose the cutting patterns and the number of logs needed to realize an order, including task specification. What makes it possible for the author's computer program TARPAK1 to be written is the visualization of the results, the generation pattern of wood logs' conversion for given entry parameters and prediction of sawn timber manufacture. This program has been created with the intention of being introduced to small and medium sawmills in Poland. The Project has been financed from government resources and written by workers of the Institute of Mathematics (Poznan University of Technology) and the Department of Mechanical Wood Technology (Poznan University of Life Sciences).
Nonlinear and Digital Man-machine Control Systems Modeling
NASA Technical Reports Server (NTRS)
Mekel, R.
1972-01-01
An adaptive modeling technique is examined by which controllers can be synthesized to provide corrective dynamics to a human operator's mathematical model in closed loop control systems. The technique utilizes a class of Liapunov functions formulated for this purpose, Liapunov's stability criterion and a model-reference system configuration. The Liapunov function is formulated to posses variable characteristics to take into consideration the identification dynamics. The time derivative of the Liapunov function generate the identification and control laws for the mathematical model system. These laws permit the realization of a controller which updates the human operator's mathematical model parameters so that model and human operator produce the same response when subjected to the same stimulus. A very useful feature is the development of a digital computer program which is easily implemented and modified concurrent with experimentation. The program permits the modeling process to interact with the experimentation process in a mutually beneficial way.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
ERIC Educational Resources Information Center
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Materials constitutive models for nonlinear analysis of thermally cycled structures
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hunt, L. E.
1982-01-01
Effects of inelastic materials models on computed stress-strain solutions for thermally loaded structures were studied by performing nonlinear (elastoplastic creep) and elastic structural analyses on a prismatic, double edge wedge specimen of IN 100 alloy that was subjected to thermal cycling in fluidized beds. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, and combined plus transient creep) were exercised for the problem by using the MARC nonlinear, finite element computer program. Maximum total strain ranges computed from the elastic and nonlinear analyses agreed within 5 percent. Mean cyclic stresses, inelastic strain ranges, and inelastic work were significantly affected by the choice of inelastic constitutive model. The computing time per cycle for the nonlinear analyses was more than five times that required for the elastic analysis.
A mathematical model of population dynamics for Batesian mimicry system.
Seno, Hiromi; Kohno, Takahiro
2012-01-01
We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.
Investigation of interaction femtosecond laser pulses with skin and eyes mathematical model
NASA Astrophysics Data System (ADS)
Rogov, P. U.; Smirnov, S. V.; Semenova, V. A.; Melnik, M. V.; Bespalov, V. G.
2016-08-01
We present a mathematical model of linear and nonlinear processes that takes place under the action of femtosecond laser radiation on the cutaneous covering. The study is carried out and the analytical solution of the set of equations describing the dynamics of the electron and atomic subsystems and investigated the processes of linear and nonlinear interaction of femtosecond laser pulses in the vitreous of the human eye, revealed the dependence of the pulse duration on the retina of the duration of the input pulse and found the value of the radiation power density, in which there is a self-focusing is obtained. The results of the work can be used to determine the maximum acceptable energy, generated by femtosecond laser systems, and to develop Russian laser safety standards for femtosecond laser systems.
The Mathematics Workshop Model: An Interview with Uri Treisman.
ERIC Educational Resources Information Center
Garland, May; Treisman, Uri
1993-01-01
Uri Treisman describes the development of his model to help minority students succeed and progress in mathematics, emphasizing group work and integrated instruction and student services. Explains his influences, core ideas informing the workshop model, structural impediments to success in the curriculum, existing programs, and other related…
Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.
Millat, Thomas; Winzer, Klaus
2017-03-01
Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the 'evolution' of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.
Mathematical and computational modeling simulation of solar drying Systems
Technology Transfer Automated Retrieval System (TEKTRAN)
Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...
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…
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.
Diagnostic Models for Procedural Bugs in Basic Mathematics Skills.
ERIC Educational Resources Information Center
Brown, John Seely; Burton, Richard R.
A new diagnostic modeling system for automatically synthesizing a deep structure model of a student's misconceptions or bugs in his/her basic mathematics skills provides a mechanism for explaining why a student is making a mistake as opposed to simply identifying the mistake. This report consists of four sections. The first provides examples of…
Mathematical model of glucose-insulin homeostasis in healthy rats.
Lombarte, Mercedes; Lupo, Maela; Campetelli, German; Basualdo, Marta; Rigalli, Alfredo
2013-10-01
According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat.
Mathematical modeling of steel fiber concrete under dynamic impact
NASA Astrophysics Data System (ADS)
Belov, N. N.; Yugov, N. T.; Kopanitsa, D. G.; Kopanitsa, G. D.; Yugov, A. A.; Shashkov, V. V.
2015-01-01
This paper introduces a continuum mechanics mathematical model that describes the processes of deformation and destruction of steel-fiber-concrete under a shock wave impact. A computer modeling method was applied to study the processes of shock wave impact of a steel cylindrical rod and concrete and steel fiber concrete plates. The impact speeds were within 100-500 m/s.
Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano-Anderson model
Longhi, Stefano
2007-05-01
The decay dynamics of a nonlinear impurity mode embedded in a linear structured continuum is theoretically investigated in the framework of a nonlinear Fano-Anderson model. A gradient flow dynamics for the survival probability is derived in the Van Hove ({lambda}{sup 2}t) limit by a multiple-scale asymptotic analysis, and the role of nonlinearity on the decay law is discussed. In particular, it is shown that the existence of bound states embedded in the continuum acts as transient trapping states which slow down the decay. The dynamical behavior predicted in the {lambda}{sup 2}t limit is studied in detail for a simple tight-binding one-dimensional lattice model, which may describe electron or photon transport in condensed matter or photonic systems. Numerical simulations of the underlying equations confirm, in particular, the trapping effect in the decay process due to bound states embedded in the continuum.
Mathematical modeling of moving contact lines in heat transfer applications
NASA Astrophysics Data System (ADS)
Ajaev, Vladimir S.; Klentzman, J.; Sodtke, C.; Stephan, P.
2007-10-01
We provide an overview of research on the mathematical modeling of apparent contact lines in non-isothermal systems conducted over the past several decades and report a number of recent developments in the field. The latter involve developing mathematical models of evaporating liquid droplets that account not only for liquid flow and evaporation, but also for unsteady heat conduction in the substrate. The droplet is placed on a flat heated solid substrate and is assumed to be in contact with a saturated vapor. Furthermore, we discuss a careful comparison between mathematical models and experimental work that involves simultaneous measurement of shapes of evaporating droplets and temperature profiles in the solid substrate. The latter is accomplished using thermochromic liquid crystals. Applications to new research areas, such as studies of the effect of evaporation on fingering instabilities in gravity-driven liquid films, are also discussed.
Hossein-Zadeh, Navid Ghavi
2016-08-01
The aim of this study was to compare seven non-linear mathematical models (Brody, Wood, Dhanoa, Sikka, Nelder, Rook and Dijkstra) to examine their efficiency in describing the lactation curves for milk fat to protein ratio (FPR) in Iranian buffaloes. Data were 43 818 test-day records for FPR from the first three lactations of Iranian buffaloes which were collected on 523 dairy herds in the period from 1996 to 2012 by the Animal Breeding Center of Iran. Each model was fitted to monthly FPR records of buffaloes using the non-linear mixed model procedure (PROC NLMIXED) in SAS and the parameters were estimated. The models were tested for goodness of fit using Akaike's information criterion (AIC), Bayesian information criterion (BIC) and log maximum likelihood (-2 Log L). The Nelder and Sikka mixed models provided the best fit of lactation curve for FPR in the first and second lactations of Iranian buffaloes, respectively. However, Wood, Dhanoa and Sikka mixed models provided the best fit of lactation curve for FPR in the third parity buffaloes. Evaluation of first, second and third lactation features showed that all models, except for Dijkstra model in the third lactation, under-predicted test time at which daily FPR was minimum. On the other hand, minimum FPR was over-predicted by all equations. Evaluation of the different models used in this study indicated that non-linear mixed models were sufficient for fitting test-day FPR records of Iranian buffaloes.
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 Modelling in the International Baccalaureate, Teacher Beliefs and Technology Usage.
ERIC Educational Resources Information Center
Brown, R.
2002-01-01
Investigates the introduction of mathematical modeling into the mathematics assessment program of the International Baccalaureate Diploma. Considers structured and open modeling in the pre-university mathematics program. Discusses influences of the use of hand-held technology on mathematical modeling and teacher and assessor beliefs about modeling…
Environmental factors in breast cancer invasion: a mathematical modelling review.
Simmons, Alex; Burrage, Pamela M; Nicolau, Dan V; Lakhani, Sunil R; Burrage, Kevin
2017-02-01
This review presents a brief overview of breast cancer, focussing on its heterogeneity and the role of mathematical modelling and simulation in teasing apart the underlying biophysical processes. Following a brief overview of the main known pathophysiological features of ductal carcinoma, attention is paid to differential equation-based models (both deterministic and stochastic), agent-based modelling, multi-scale modelling, lattice-based models and image-driven modelling. A number of vignettes are presented where these modelling approaches have elucidated novel aspects of breast cancer dynamics, and we conclude by offering some perspectives on the role mathematical modelling can play in understanding breast cancer development, invasion and treatment therapies.
The Mathematical Structure of Error Correction Models.
1985-05-01
The error correction model for a vector valued time series has been proposed and applied in the economic literature with the papers by Sargan (1964...the notion of cointegratedness of a vector process and showed the relation between cointegration and error correction models. This paper defines a...general error correction model, that encompasses the usual error correction model as well as the integral correction model by allowing a finite number of
Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.
Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C
2016-02-15
We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D-, A- and E-optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D-optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.
Model-based optimal design of experiments - semidefinite and nonlinear programming formulations
Duarte, Belmiro P.M.; Wong, Weng Kee; Oliveira, Nuno M.C.
2015-01-01
We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D–, A– and E–optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D–optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice. PMID:26949279
A general non-linear multilevel structural equation mixture model
Kelava, Augustin; Brandt, Holger
2014-01-01
In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh et al., 2004). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012; Kelava et al., 2014) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework. PMID:25101022
Mathematical construction of an engineering thermopiezoelastic model for smart composite shells
NASA Astrophysics Data System (ADS)
Yu, Wenbin; Hodges, Dewey H.
2005-02-01
An engineering model for composite piezoelectric shells under mechanical, thermal, and electrical loads has been constructed mathematically using the variational-asymptotic method. This work presents a unique formulation of the nonlinear, three-dimensional, one-way coupled, thermopiezoelasticity problem having the combined merits of both mathematical rigor and engineering simplicity. The variational-asymptotic method is used to rigorously split the three-dimensional problem into two problems: a nonlinear, two-dimensional, shell analysis over the reference surface to obtain the global response, and a linear analysis through the thickness to provide both the generalized shell constitutive model and recovery relations to approximate the original three-dimensional fields. The asymptotically correct electric enthalpy obtained herein is cast into the Reissner-Mindlin form to account for transverse shear deformation including the geometrical refinement due to initial curvatures. Recovery relations have been provided to obtain accurate stress distribution through the thickness. The present model is implemented into the computer program VAPAS. Results for several cases obtained from VAPAS are compared with exact thermopiezoelasticity solutions, classical lamination theory, and first-order shear-deformation theory. An excellent compromise between efficiency and accuracy for analyzing piezoelectric composite shells has been achieved. Part of this paper was presented at the 45th Structures, Structural Dynamics and Materials Conference, Palm Springs, California, April 19-22, 2004.
Computer modeling of batteries from non-linear circuit elements
NASA Technical Reports Server (NTRS)
Waaben, S.; Federico, J.; Moskowitz, I.
1983-01-01
A simple non-linear circuit model for battery behavior is given. It is based on time-dependent features of the well-known PIN change storage diode, whose behavior is described by equations similar to those associated with electrochemical cells. The circuit simulation computer program ADVICE was used to predict non-linear response from a topological description of the battery analog built from advice components. By a reasonable choice of one set of parameters, the circuit accurately simulates a wide spectrum of measured non-linear battery responses to within a few millivolts.
A model for the nonlinear mechanism responsible for cochlear amplification.
Fessel, Kimberly; Holmes, Mark H
2014-12-01
A nonlinear model for the mechanism responsible for the amplification of the sound wave in the ear is derived using the geometric and material properties of the system. The result is a nonlinear beam equation, with the nonlinearity appearing in a coefficient of the equation. Once derived, the beam problem is analyzed for various loading conditions. Based on this analysis it is seen that the mechanism is capable of producing a spatially localized gain, as required by any amplification mechanism, but it is also capable of increasing the spatial contrast in the signal.
Nonlinear analysis of lipid tubules by nonlocal beam model.
Shen, Hui-Shen
2011-05-07
Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for lipid tubules. The lipid tubule is modeled as a nonlocal micro/nano-beam which contains small scale effect. The material properties are assumed to be size-dependent. The governing equation is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of lipid tubules. In contrast, it increases the nonlinear to linear frequency ratios slightly for the lipid tubule with immovable end conditions.
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.
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.
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
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 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.
On mathematical modelling of insect flight dynamics in the context of micro air vehicles.
Zbikowski, Rafał; Ansari, Salman A; Knowles, Kevin
2006-06-01
to six types of fundamental manoeuvres, which we define as those flight conditions for which only one component of the translational and rotational body velocities is nonzero and constant. The second aspect of mathematical modelling for insect flight dynamics addressed here deals with the periodic character of the aerodynamic force and moment production. This leads to consideration of the types of solutions of nonlinear equations forced by nonlinear oscillations. In particular, the mechanism of synchronization seems relevant and should be investigated further.
Mathematical analysis and modeling of motion direction selectivity in the retina.
Escobar, María-José; Pezo, Danilo; Orio, Patricio
2013-11-01
Motion detection is one of the most important and primitive computations performed by our visual system. Specifically in the retina, ganglion cells producing motion direction-selective responses have been addressed by different disciplines, such as mathematics, neurophysiology and computational modeling, since the beginnings of vision science. Although a number of studies have analyzed theoretical and mathematical considerations for such responses, a clear picture of the underlying cellular mechanisms is only recently emerging. In general, motion direction selectivity is based on a non-linear asymmetric computation inside a receptive field differentiating cell responses between preferred and null direction stimuli. To what extent can biological findings match these considerations? In this review, we outline theoretical and mathematical studies of motion direction selectivity, aiming to map the properties of the models onto the neural circuitry and synaptic connectivity found in the retina. Additionally, we review several compartmental models that have tried to fill this gap. Finally, we discuss the remaining challenges that computational models will have to tackle in order to fully understand the retinal motion direction-selective circuitry.
NASA Astrophysics Data System (ADS)
Lasukov, V. V.; Rozhkova, S. V.; Abdrashitova, M. O.; Il'kin, E. E.; Novoselov, V. V.
2016-01-01
The nonlinear dynamics of the regular growth of the population of an aggregation of the Lemaitre-Friedmann primordial atoms has been investigated. It is analytically shown that there exists an asymptotic limit to the growth of the population of an aggregation of primordial atoms / galaxies. The nonlinear model, developed in this paper, of the information factor of the evolution of these primordial atoms can find wide application in biology, biological electronics, synthetic biology, in the mathematical history of the driving force of the noosphere, in cosmology, and in other areas of science and technology.
Batzel, Jerry; Baselli, Giuseppe; Mukkamala, Ramakrishna; Chon, Ki H
2009-01-01
Cardiovascular (CV) regulation is the result of a number of very complex control interactions. As computational power increases and new methods for collecting experimental data emerge, the potential for exploring these interactions through modelling increases as does the potential for clinical application of such models. Understanding these interactions requires the application of a diverse set of modelling techniques. Several recent mathematical modelling techniques will be described in this review paper. Starting from Granger's causality, the problem of closed-loop identification is recalled. The main aspects of linear identification and of grey-box modelling tailored to CV regulation analysis are summarized as well as basic concepts and trends for nonlinear extensions. Sensitivity analysis is presented and discussed as a potent tool for model validation and refinement. The integration of methods and models is fostered for a further physiological comprehension and for the development of more potent and robust diagnostic tools. PMID:19324714
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Energy transfer in nonlinear network models of proteins
NASA Astrophysics Data System (ADS)
Piazza, F.; Sanejouand, Y.-H.
2009-12-01
We investigate how nonlinearity and topological disorder affect the energy relaxation of local kicks in coarse-grained network models of proteins. We find that nonlinearity promotes long-range, coherent transfer of substantial energy to specific functional sites, while depressing transfer to generic locations. In some cases, transfer is mediated by the self-localization of discrete breathers at distant locations from the kick, acting as efficient energy-accumulating centers.
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
Generation of linear dynamic models from a digital nonlinear simulation
NASA Technical Reports Server (NTRS)
Daniele, C. J.; Krosel, S. M.
1979-01-01
The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.
NASA Astrophysics Data System (ADS)
Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.
2017-03-01
Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.
An ansatz for solving nonlinear partial differential equations in mathematical physics.
Akbar, M Ali; Ali, Norhashidah Hj Mohd
2016-01-01
In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.
Searching for spatial patterns in a pollinator-plant-herbivore mathematical model.
Sánchez-Garduño, Faustino; Breña-Medina, Víctor F
2011-05-01
This paper deals with the spatio-temporal dynamics of a pollinator-plant-herbivore mathematical model. The full model consists of three nonlinear reaction-diffusion-advection equations defined on a rectangular region. In view of analyzing the full model, we firstly consider the temporal dynamics of three homogeneous cases. The first one is a model for a mutualistic interaction (pollinator-plant), later on a sort of predator-prey (plant-herbivore) interaction model is studied. In both cases, the interaction term is described by a Holling response of type II. Finally, by considering that the plant population is the unique feeding source for the herbivores, a mathematical model for the three interacting populations is considered. By incorporating a constant diffusion term into the equations for the pollinators and herbivores, we numerically study the spatiotemporal dynamics of the first two mentioned models. For the full model, a constant diffusion and advection terms are included in the equation for the pollinators. For the resulting model, we sketch the proof of the existence, positiveness, and boundedness of solution for an initial and boundary values problem. In order to see the separated effect of the diffusion and advection terms on the final population distributions, a set of numerical simulations are included. We used homogeneous Dirichlet and Neumann boundary conditions.
An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics.
Ahmad, Jamshad; Mohyud-Din, Syed Tauseef
2014-01-01
In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature.
An Efficient Algorithm for Some Highly Nonlinear Fractional PDEs in Mathematical Physics
Ahmad, Jamshad; Mohyud-Din, Syed Tauseef
2014-01-01
In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature. PMID:25525804
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 damage in unidirectional composites
NASA Technical Reports Server (NTRS)
Goree, J. G.; Dharani, L. R.; Jones, W. F.
1981-01-01
A review of some approximate analytical models for damaged, fiber reinforced composite materials is presented. Using the classical shear lag stress displacement assumption, solutions are presented for a unidirectional laminate containing a notch, a rectangular cut-out, and a circular hole. The models account for longitudinal matrix yielding and splitting as well as transverse matrix yielding and fiber breakage. The constraining influence of a cover sheet on the unidirectional laminate is also modeled.
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.
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.
Unlocking the black box: teaching mathematical modeling with popular culture.
Lofgren, Eric T
2016-10-01
Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding.
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.
A Computational and Mathematical Model for Device Induced Thrombosis
NASA Astrophysics Data System (ADS)
Wu, Wei-Tao; Aubry, Nadine; Massoudi, Mehrdad; Antaki, James
2015-11-01
Based on the Sorenson's model of thrombus formation, a new mathematical model describing the process of thrombus growth is developed. In this model the blood is treated as a Newtonian fluid, and the transport and reactions of the chemical and biological species are modeled using CRD (convection-reaction-diffusion) equations. A computational fluid dynamic (CFD) solver for the mathematical model is developed using the libraries of OpenFOAM. Applying the CFD solver, several representative benchmark problems are studied: rapid thrombus growth in vivo by injecting Adenosine diphosphate (ADP) using iontophoretic method and thrombus growth in rectangular microchannel with a crevice which usually appears as a joint between components of devices and often becomes nidus of thrombosis. Very good agreements between the numerical and the experimental results validate the model and indicate its potential to study a host of complex and practical problems in the future, such as thrombosis in blood pumps and artificial lungs.
A Versatile Nonlinear Method for Predictive Modeling
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing; Yao, Weigang
2015-01-01
As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.
A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy.
Li, Xuefang; Xu, Jian-Xin
2016-10-07
Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon-γ (IFN-γ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013). The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model.
Nonlinear mixed models to study metabolizable energy utilization in broiler breeder hens.
Romero, L F; Zuidhof, M J; Renema, R A; Robinson, F E; Naeima, A
2009-06-01
This study developed mathematical models to overcome limitations of linear models of energy partitioning in hens. The fit of 1 linear and 2 nonlinear models of ME intake (MEI) were compared, using empirical data of 288 caged broiler breeder hens from 20 to 60 wk of age. Pullets were individually caged at 16 wk and assigned to 1 of 4 feed allocation groups. Three groups had feed allocated on a group basis with divergent target BW: standard (STD), HIGH (STD x 1.1), and LOW (STD x 0.9). The fourth group had individual-based feed allocation (IND) and followed the STD BW target. The linear model expressed MEI as a function of BW(0.75), ADG, egg mass (EM), and temperature. Nonlinear mixed models employed a normally distributed term associated with hen metabolic BW, and exponential terms of ADG and EM, or Cobb-Douglas form interactions between terms. Fit was evaluated with the Bayesian information criterion and systematic bias was analyzed through linear regressions of observed versus expected values. The linear model estimated energy partitioned to maintenance and retention in the range of reported values in the literature. However, this model had the poorest fit (R(2) = 0.64) and exhibited a slope bias of 0.91 (i.e., MEI was overestimated at low values and underestimated at high values). The first nonlinear mixed model indicated that MEI partitioned to ADG was a factor of ADG(1.15), whereas the ME partitioned to EM was a factor of EM(1.12). This model had improved fit (R(2) = 0.71) relative to the linear model. The second nonlinear mixed model indicated that the energy requirement for ADG increased by 0.60% and the EM energy requirement decreased by 2.07% for each 1% increment in BW. This model further improved fit (R(2) = 0.75). Nonlinear mixed models reduced estimation bias by accounting for individual variation in maintenance energy expenditure. These nonlinear mixed models may be used to analyze energy partitioning in animals, to develop prediction equations of MEI
Mathematical Model of Estuarial Sediment Transport.
1977-10-01
NUMBERS» Contract No. ^Ar DACW39-75-C-0080 ^^ 9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of Civil Engineering...The original model, SEDIMENT I, was verified by comparison with measurements in a recirculating flume. The modified model, SEDIMENT II, developed for... organic matter from contiguous drainage areas, and waste materials. Clay minerals are hydrated aluminum silicates in a layer lattice crystal
Mathematical Modelling of Laser/Material Interactions.
1983-11-25
translated to the model input. Even an experimental mode print can also be digitalised for the model. In trying to describe high order modes matliematically...4. Mazumder J. Steen W.M. "Welding of Ti 6al - 4V by continuous wave CO2 laser". Metal construction Sept. 1980 pp423 - 427. 5. Kogelnik H, Li.T Proc
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.
A mathematical model of intestinal oedema formation
Young, Jennifer; Rivière, Béatrice; Cox, Charles S.; Uray, Karen
2014-01-01
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. PMID:23036806
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…
Rotor systems research aircraft simulation mathematical model
NASA Technical Reports Server (NTRS)
Houck, J. A.; Moore, F. L.; Howlett, J. J.; Pollock, K. S.; Browne, M. M.
1977-01-01
An analytical model developed for evaluating and verifying advanced rotor concepts is discussed. The model was used during in both open loop and real time man-in-the-loop simulation during the rotor systems research aircraft design. Future applications include: pilot training, preflight of test programs, and the evaluation of promising concepts before their implementation on the flight vehicle.
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 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.
Program Helps Generate Boundary-Element Mathematical Models
NASA Technical Reports Server (NTRS)
Goldberg, R. K.
1995-01-01
Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).
A Mathematical Model of the Thermo-Anemometric Flowmeter.
Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman
2015-09-11
A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.
Aoki, Yasunori; Nordgren, Rikard; Hooker, Andrew C
2016-03-01
As the importance of pharmacometric analysis increases, more and more complex mathematical models are introduced and computational error resulting from computational instability starts to become a bottleneck in the analysis. We propose a preconditioning method for non-linear mixed effects models used in pharmacometric analyses to stabilise the computation of the variance-covariance matrix. Roughly speaking, the method reparameterises the model with a linear combination of the original model parameters so that the Hessian matrix of the likelihood of the reparameterised model becomes close to an identity matrix. This approach will reduce the influence of computational error, for example rounding error, to the final computational result. We present numerical experiments demonstrating that the stabilisation of the computation using the proposed method can recover failed variance-covariance matrix computations, and reveal non-identifiability of the model parameters.