ON IDENTIFIABILITY OF NONLINEAR ODE MODELS AND APPLICATIONS IN VIRAL DYNAMICS

PubMed Central

MIAO, HONGYU; XIA, XIAOHUA; PERELSON, ALAN S.; WU, HULIN

2011-01-01

Ordinary differential equations (ODE) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last 2 decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determing unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past one to two decades, including structural identifiability analysis, practical identifiability analysis and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV, influenza and hepatitis viruses are given to illustrate how to apply these identifiability analysis methods in practice. PMID:21785515

In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis.

PubMed

Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

2015-01-01

There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone's overall intradialytic mass transfer rate coefficient, km ; and, methadone's removal rate, j ME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. The ODE/PDE model revealed a significant increase in the change of methadone's mass transfer with increased dialysate flow rate, %Δkm =18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone's mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone's removal during dialysis. The absolute value of the prediction errors for methadone's extraction and throughput were less than 2%. ODE/PDE modeling of methadone's hemodialysis is a new approach to study methadone's removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone's mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans.

Independence screening for high dimensional nonlinear additive ODE models with applications to dynamic gene regulatory networks.

PubMed

Xue, Hongqi; Wu, Shuang; Wu, Yichao; Ramirez Idarraga, Juan C; Wu, Hulin

2018-05-02

Mechanism-driven low-dimensional ordinary differential equation (ODE) models are often used to model viral dynamics at cellular levels and epidemics of infectious diseases. However, low-dimensional mechanism-based ODE models are limited for modeling infectious diseases at molecular levels such as transcriptomic or proteomic levels, which is critical to understand pathogenesis of diseases. Although linear ODE models have been proposed for gene regulatory networks (GRNs), nonlinear regulations are common in GRNs. The reconstruction of large-scale nonlinear networks from time-course gene expression data remains an unresolved issue. Here, we use high-dimensional nonlinear additive ODEs to model GRNs and propose a 4-step procedure to efficiently perform variable selection for nonlinear ODEs. To tackle the challenge of high dimensionality, we couple the 2-stage smoothing-based estimation method for ODEs and a nonlinear independence screening method to perform variable selection for the nonlinear ODE models. We have shown that our method possesses the sure screening property and it can handle problems with non-polynomial dimensionality. Numerical performance of the proposed method is illustrated with simulated data and a real data example for identifying the dynamic GRN of Saccharomyces cerevisiae. Copyright © 2018 John Wiley & Sons, Ltd.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation

PubMed Central

Zimmer, Christoph

2016-01-01

Background Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. Methods The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. Results The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models. PMID:27583802

A Two-Stage Estimation Method for Random Coefficient Differential Equation Models with Application to Longitudinal HIV Dynamic Data.

PubMed

Fang, Yun; Wu, Hulin; Zhu, Li-Xing

2011-07-01

We propose a two-stage estimation method for random coefficient ordinary differential equation (ODE) models. A maximum pseudo-likelihood estimator (MPLE) is derived based on a mixed-effects modeling approach and its asymptotic properties for population parameters are established. The proposed method does not require repeatedly solving ODEs, and is computationally efficient although it does pay a price with the loss of some estimation efficiency. However, the method does offer an alternative approach when the exact likelihood approach fails due to model complexity and high-dimensional parameter space, and it can also serve as a method to obtain the starting estimates for more accurate estimation methods. In addition, the proposed method does not need to specify the initial values of state variables and preserves all the advantages of the mixed-effects modeling approach. The finite sample properties of the proposed estimator are studied via Monte Carlo simulations and the methodology is also illustrated with application to an AIDS clinical data set.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

PubMed

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks.

PubMed

Flassig, R J; Sundmacher, K

2012-12-01

Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs). In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning. An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html. flassig@mpi-magdeburg.mpg.de Supplementary data are are available at Bioinformatics online.

Robust estimation for ordinary differential equation models.

PubMed

Cao, J; Wang, L; Xu, J

2011-12-01

Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a nonparametric function, which is a linear combination of basis functions. The nonparametric function is estimated by a robust penalized smoothing method. The penalty term is defined with the parametric ODE model, which controls the roughness of the nonparametric function and maintains the fidelity of the nonparametric function to the ODE model. The basis coefficients and ODE parameters are estimated in two nested levels of optimization. The coefficient estimates are treated as an implicit function of ODE parameters, which enables one to derive the analytic gradients for optimization using the implicit function theorem. Simulation studies show that the robust method gives satisfactory estimates for the ODE parameters from noisy data with outliers. The robust method is demonstrated by estimating a predator-prey ODE model from real ecological data. © 2011, The International Biometric Society.

A system of recurrent neural networks for modularising, parameterising and dynamic analysis of cell signalling networks.

PubMed

Samarasinghe, S; Ling, H

In this paper, we show how to extend our previously proposed novel continuous time Recurrent Neural Networks (RNN) approach that retains the advantage of continuous dynamics offered by Ordinary Differential Equations (ODE) while enabling parameter estimation through adaptation, to larger signalling networks using a modular approach. Specifically, the signalling network is decomposed into several sub-models based on important temporal events in the network. Each sub-model is represented by the proposed RNN and trained using data generated from the corresponding ODE model. Trained sub-models are assembled into a whole system RNN which is then subjected to systems dynamics and sensitivity analyses. The concept is illustrated by application to G1/S transition in cell cycle using Iwamoto et al. (2008) ODE model. We decomposed the G1/S network into 3 sub-models: (i) E2F transcription factor release; (ii) E2F and CycE positive feedback loop for elevating cyclin levels; and (iii) E2F and CycA negative feedback to degrade E2F. The trained sub-models accurately represented system dynamics and parameters were in good agreement with the ODE model. The whole system RNN however revealed couple of parameters contributing to compounding errors due to feedback and required refinement to sub-model 2. These related to the reversible reaction between CycE/CDK2 and p27, its inhibitor. The revised whole system RNN model very accurately matched dynamics of the ODE system. Local sensitivity analysis of the whole system model further revealed the most dominant influence of the above two parameters in perturbing G1/S transition, giving support to a recent hypothesis that the release of inhibitor p27 from Cyc/CDK complex triggers cell cycle stage transition. To make the model useful in a practical setting, we modified each RNN sub-model with a time relay switch to facilitate larger interval input data (≈20min) (original model used data for 30s or less) and retrained them that produced parameters and protein concentrations similar to the original RNN system. Results thus demonstrated the reliability of the proposed RNN method for modelling relatively large networks by modularisation for practical settings. Advantages of the method are its ability to represent accurate continuous system dynamics and ease of: parameter estimation through training with data from a practical setting, model analysis (40% faster than ODE), fine tuning parameters when more data are available, sub-model extension when new elements and/or interactions come to light and model expansion with addition of sub-models. Copyright © 2017 Elsevier B.V. All rights reserved.

In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

PubMed Central

Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

2015-01-01

Background There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). Methodology We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δkm=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value of the prediction errors for methadone’s extraction and throughput were less than 2%. Conclusion ODE/PDE modeling of methadone’s hemodialysis is a new approach to study methadone’s removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone’s mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans. PMID:26229501

Hybrid regulatory models: a statistically tractable approach to model regulatory network dynamics.

PubMed

Ocone, Andrea; Millar, Andrew J; Sanguinetti, Guido

2013-04-01

Computational modelling of the dynamics of gene regulatory networks is a central task of systems biology. For networks of small/medium scale, the dominant paradigm is represented by systems of coupled non-linear ordinary differential equations (ODEs). ODEs afford great mechanistic detail and flexibility, but calibrating these models to data is often an extremely difficult statistical problem. Here, we develop a general statistical inference framework for stochastic transcription-translation networks. We use a coarse-grained approach, which represents the system as a network of stochastic (binary) promoter and (continuous) protein variables. We derive an exact inference algorithm and an efficient variational approximation that allows scalable inference and learning of the model parameters. We demonstrate the power of the approach on two biological case studies, showing that the method allows a high degree of flexibility and is capable of testable novel biological predictions. http://homepages.inf.ed.ac.uk/gsanguin/software.html. Supplementary data are available at Bioinformatics online.

ODE constrained mixture modelling: a method for unraveling subpopulation structures and dynamics.

PubMed

Hasenauer, Jan; Hasenauer, Christine; Hucho, Tim; Theis, Fabian J

2014-07-01

Functional cell-to-cell variability is ubiquitous in multicellular organisms as well as bacterial populations. Even genetically identical cells of the same cell type can respond differently to identical stimuli. Methods have been developed to analyse heterogeneous populations, e.g., mixture models and stochastic population models. The available methods are, however, either incapable of simultaneously analysing different experimental conditions or are computationally demanding and difficult to apply. Furthermore, they do not account for biological information available in the literature. To overcome disadvantages of existing methods, we combine mixture models and ordinary differential equation (ODE) models. The ODE models provide a mechanistic description of the underlying processes while mixture models provide an easy way to capture variability. In a simulation study, we show that the class of ODE constrained mixture models can unravel the subpopulation structure and determine the sources of cell-to-cell variability. In addition, the method provides reliable estimates for kinetic rates and subpopulation characteristics. We use ODE constrained mixture modelling to study NGF-induced Erk1/2 phosphorylation in primary sensory neurones, a process relevant in inflammatory and neuropathic pain. We propose a mechanistic pathway model for this process and reconstructed static and dynamical subpopulation characteristics across experimental conditions. We validate the model predictions experimentally, which verifies the capabilities of ODE constrained mixture models. These results illustrate that ODE constrained mixture models can reveal novel mechanistic insights and possess a high sensitivity.

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models.

PubMed

Brouwer, Andrew F; Meza, Rafael; Eisenberg, Marisa C

2017-07-01

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes. © 2016 Society for Risk Analysis.

ODE Constrained Mixture Modelling: A Method for Unraveling Subpopulation Structures and Dynamics

PubMed Central

Hasenauer, Jan; Hasenauer, Christine; Hucho, Tim; Theis, Fabian J.

2014-01-01

Functional cell-to-cell variability is ubiquitous in multicellular organisms as well as bacterial populations. Even genetically identical cells of the same cell type can respond differently to identical stimuli. Methods have been developed to analyse heterogeneous populations, e.g., mixture models and stochastic population models. The available methods are, however, either incapable of simultaneously analysing different experimental conditions or are computationally demanding and difficult to apply. Furthermore, they do not account for biological information available in the literature. To overcome disadvantages of existing methods, we combine mixture models and ordinary differential equation (ODE) models. The ODE models provide a mechanistic description of the underlying processes while mixture models provide an easy way to capture variability. In a simulation study, we show that the class of ODE constrained mixture models can unravel the subpopulation structure and determine the sources of cell-to-cell variability. In addition, the method provides reliable estimates for kinetic rates and subpopulation characteristics. We use ODE constrained mixture modelling to study NGF-induced Erk1/2 phosphorylation in primary sensory neurones, a process relevant in inflammatory and neuropathic pain. We propose a mechanistic pathway model for this process and reconstructed static and dynamical subpopulation characteristics across experimental conditions. We validate the model predictions experimentally, which verifies the capabilities of ODE constrained mixture models. These results illustrate that ODE constrained mixture models can reveal novel mechanistic insights and possess a high sensitivity. PMID:24992156

Energy-based operator splitting approach for the time discretization of coupled systems of partial and ordinary differential equations for fluid flows: The Stokes case

NASA Astrophysics Data System (ADS)

Carichino, Lucia; Guidoboni, Giovanna; Szopos, Marcela

2018-07-01

The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The proposed algorithm is based on a semi-discretization in time based on operator splitting, whose design is guided by the rationale of ensuring that the physical energy balance is maintained at the discrete level. As a result, unconditional stability with respect to the time step choice is ensured by the implicit treatment of interface conditions within the Stokes substeps, whereas the coupling between Stokes and ODE substeps is enforced via appropriate initial conditions for each substep. Notably, unconditional stability is attained without the need of subiterating between Stokes and ODE substeps. Stability and convergence properties of the proposed algorithm are tested on three specific examples for which analytical solutions are derived.

Semiparametric mixed-effects analysis of PK/PD models using differential equations.

PubMed

Wang, Yi; Eskridge, Kent M; Zhang, Shunpu

2008-08-01

Motivated by the use of semiparametric nonlinear mixed-effects modeling on longitudinal data, we develop a new semiparametric modeling approach to address potential structural model misspecification for population pharmacokinetic/pharmacodynamic (PK/PD) analysis. Specifically, we use a set of ordinary differential equations (ODEs) with form dx/dt = A(t)x + B(t) where B(t) is a nonparametric function that is estimated using penalized splines. The inclusion of a nonparametric function in the ODEs makes identification of structural model misspecification feasible by quantifying the model uncertainty and provides flexibility for accommodating possible structural model deficiencies. The resulting model will be implemented in a nonlinear mixed-effects modeling setup for population analysis. We illustrate the method with an application to cefamandole data and evaluate its performance through simulations.

NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations.

PubMed

Prague, Mélanie; Commenges, Daniel; Guedj, Jérémie; Drylewicz, Julia; Thiébaut, Rodolphe

2013-08-01

Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

An epidemic model to evaluate the homogeneous mixing assumption

NASA Astrophysics Data System (ADS)

Turnes, P. P.; Monteiro, L. H. A.

2014-11-01

Many epidemic models are written in terms of ordinary differential equations (ODE). This approach relies on the homogeneous mixing assumption; that is, the topological structure of the contact network established by the individuals of the host population is not relevant to predict the spread of a pathogen in this population. Here, we propose an epidemic model based on ODE to study the propagation of contagious diseases conferring no immunity. The state variables of this model are the percentages of susceptible individuals, infectious individuals and empty space. We show that this dynamical system can experience transcritical and Hopf bifurcations. Then, we employ this model to evaluate the validity of the homogeneous mixing assumption by using real data related to the transmission of gonorrhea, hepatitis C virus, human immunodeficiency virus, and obesity.

Regularized Semiparametric Estimation for Ordinary Differential Equations

PubMed Central

Li, Yun; Zhu, Ji; Wang, Naisyin

2015-01-01

Ordinary differential equations (ODEs) are widely used in modeling dynamic systems and have ample applications in the fields of physics, engineering, economics and biological sciences. The ODE parameters often possess physiological meanings and can help scientists gain better understanding of the system. One key interest is thus to well estimate these parameters. Ideally, constant parameters are preferred due to their easy interpretation. In reality, however, constant parameters can be too restrictive such that even after incorporating error terms, there could still be unknown sources of disturbance that lead to poor agreement between observed data and the estimated ODE system. In this paper, we address this issue and accommodate short-term interferences by allowing parameters to vary with time. We propose a new regularized estimation procedure on the time-varying parameters of an ODE system so that these parameters could change with time during transitions but remain constants within stable stages. We found, through simulation studies, that the proposed method performs well and tends to have less variation in comparison to the non-regularized approach. On the theoretical front, we derive finite-sample estimation error bounds for the proposed method. Applications of the proposed method to modeling the hare-lynx relationship and the measles incidence dynamic in Ontario, Canada lead to satisfactory and meaningful results. PMID:26392639

Symmetries and solutions of the non-autonomous von Bertalanffy equation

NASA Astrophysics Data System (ADS)

Edwards, Maureen P.; Anderssen, Robert S.

2015-05-01

For growth in a closed environment, which is indicative of the situation in laboratory experiments, autonomous ODE models do not necessarily capture the dynamics under investigation. The importance and impact of a closed environment arise when the question under examination relates, for example, to the number of the surviving microbes, such as in a study of the spoilage and contamination of food, the gene silencing activity of fungi or the production of a chemical compound by bacteria or fungi. Autonomous ODE models are inappropriate as they assume that only the current size of the population controls the growth-decay dynamics. This is reflected in the fact that, asymptotically, their solutions can only grow or decay monotonically or asymptote. Non-autonomous ODE models are not so constrained. A natural strategy for the choice of non-autonomous ODEs is to take appropriate autonomous ones and change them to be non-autonomous through the introduction of relevant non-autonomous terms. This is the approach in this paper with the focus being the von Bertalanffy equation. Since this equation has independent importance in relation to practical applications in growth modelling, it is natural to explore the deeper relationships between the introduced non-autonomous terms through a symmetry analysis, which is the purpose and goal of the current paper. Infinitesimals are derived which allow particular forms of the non-autonomous von Bertalanffy equation to be transformed into autonomous forms for which some new analytic solutions have been found.

ShinyKGode: an interactive application for ODE parameter inference using gradient matching.

PubMed

Wandy, Joe; Niu, Mu; Giurghita, Diana; Daly, Rónán; Rogers, Simon; Husmeier, Dirk

2018-07-01

Mathematical modelling based on ordinary differential equations (ODEs) is widely used to describe the dynamics of biological systems, particularly in systems and pathway biology. Often the kinetic parameters of these ODE systems are unknown and have to be inferred from the data. Approximate parameter inference methods based on gradient matching (which do not require performing computationally expensive numerical integration of the ODEs) have been getting popular in recent years, but many implementations are difficult to run without expert knowledge. Here, we introduce ShinyKGode, an interactive web application to perform fast parameter inference on ODEs using gradient matching. ShinyKGode can be used to infer ODE parameters on simulated and observed data using gradient matching. Users can easily load their own models in Systems Biology Markup Language format, and a set of pre-defined ODE benchmark models are provided in the application. Inferred parameters are visualized alongside diagnostic plots to assess convergence. The R package for ShinyKGode can be installed through the Comprehensive R Archive Network (CRAN). Installation instructions, as well as tutorial videos and source code are available at https://joewandy.github.io/shinyKGode. Supplementary data are available at Bioinformatics online.

Antiviral Evaluation of Octadecyloxyethyl Esters of (S)-3-Hydroxy-2-(phosphonomethoxy)propyl Nucleosides Against Herpesviruses and Orthopoxviruses≠

PubMed Central

Valiaeva, Nadejda; Prichard, Mark N.; Buller, R. Mark; Beadle, James R.; Hartline, Caroll B.; Keith, Kathy A.; Schriewer, Jill; Trahan, Julissa; Hostetler, Karl Y.

2009-01-01

Our previous studies showed that esterification of (S)-3-hydroxy-2-(phosphono-methoxy)propyl]adenine (HPMPA) or 1-(S)-[3-hydroxy-2-(phosphonomethoxy)-propyl]cytosine (HPMPC) with alkoxyalkyl groups such as hexadecyloxypropyl (HDP) or octadecyloxyethyl (ODE) resulted in large increases in antiviral activity and oral bioavailability. The HDP- and ODE- esters of HPMPA were shown to be active in cells infected with human immunodeficiency virus, type 1 (HIV-1), while HPMPA itself was virtually inactive. To explore this approach in greater detail, we synthesized four new compounds in this series, the ODE esters of 9-(S)-[3-hydroxy-2-(phosphonomethoxy)-propyl]guanine (HPMPG), 1-(S)-[3-hydroxy-2-(phosphono-methoxy)propyl]thymine (HPMPT), 9-(S)-[3-hydroxy-2-(phosphonomethoxy)propyl]-2,6-diaminopurine (HPMPDAP) and 9-(S)-[3-hydroxy-2-(phosphonomethoxy)propyl]-2-amino-6-cyclopropylaminopurine. (HPMP-cPrDAP) and evaluated their antiviral activity against herpes simplex virus, type 1 (HSV-1), human cytomegalovirus (HCMV), and vaccinia, cowpox and ectromelia. Against HSV-1, subnanomolar EC50 values were observed with ODE-HPMPA and ODE-HPMPC while ODE-HPMPG had intermediate antiviral activity with an EC50 of 40 nanomolar. In HFF cells infected with HCMV, the lowest EC50 values were observed with ODE-HPMPC, 0.9 nanomolar. ODE -HPMPA was highly active with an EC50 of 3 nanomolar, while ODE-HPMPG and ODE-HPMPDAP were also highly active with EC50s of 22 and 77 nanomolar, respectively. Against vaccinia and cowpox viruses, ODE-HPMPG and ODE-HPMPDAP were the most active and selective compounds with EC50 values of 20 to 60 nanomolar and selectivity index values of 600 to 3,500. ODE-HPMPG was also active against ectromelia virus with an EC50 value of 410 nanomolar and a selectivity index value of 166. ODE-HPMPG and ODE-HPMPDAP are proposed for further preclinical evaluation as possible candidates for treatment of HSV, HCMV or orthopoxvirus diseases. PMID:19800369

Exact model reduction of combinatorial reaction networks

PubMed Central

Conzelmann, Holger; Fey, Dirk; Gilles, Ernst D

2008-01-01

Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks. PMID:18755034

Operator Factorization and the Solution of Second-Order Linear Ordinary Differential Equations

ERIC Educational Resources Information Center

Robin, W.

2007-01-01

The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…

Comparative analysis of Goodwin's business cycle models

NASA Astrophysics Data System (ADS)

Antonova, A. O.; Reznik, S.; Todorov, M. D.

2016-10-01

We compare the behavior of solutions of Goodwin's business cycle equation in the form of neutral delay differential equation with fixed delay (NDDE model) and in the form of the differential equations of 3rd, 4th and 5th orders (ODE model's). Such ODE model's (Taylor series expansion of NDDE in powers of θ) are proposed in N. Dharmaraj and K. Vela Velupillai [6] for investigation of the short periodic sawthooth oscillations in NDDE. We show that the ODE's of 3rd, 4th and 5th order may approximate the asymptotic behavior of only main Goodwin's mode, but not the sawthooth modes. If the order of the Taylor series expansion exceeds 5, then the approximate ODE becomes unstable independently of time lag θ.

MOCCASIN: converting MATLAB ODE models to SBML.

PubMed

Gómez, Harold F; Hucka, Michael; Keating, Sarah M; Nudelman, German; Iber, Dagmar; Sealfon, Stuart C

2016-06-15

MATLAB is popular in biological research for creating and simulating models that use ordinary differential equations (ODEs). However, sharing or using these models outside of MATLAB is often problematic. A community standard such as Systems Biology Markup Language (SBML) can serve as a neutral exchange format, but translating models from MATLAB to SBML can be challenging-especially for legacy models not written with translation in mind. We developed MOCCASIN (Model ODE Converter for Creating Automated SBML INteroperability) to help. MOCCASIN can convert ODE-based MATLAB models of biochemical reaction networks into the SBML format. MOCCASIN is available under the terms of the LGPL 2.1 license (http://www.gnu.org/licenses/lgpl-2.1.html). Source code, binaries and test cases can be freely obtained from https://github.com/sbmlteam/moccasin : mhucka@caltech.edu More information is available at https://github.com/sbmlteam/moccasin. © The Author 2016. Published by Oxford University Press.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

PubMed

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

Comparative Sensitivity Analysis of Muscle Activation Dynamics

PubMed Central

Günther, Michael; Götz, Thomas

2015-01-01

We mathematically compared two models of mammalian striated muscle activation dynamics proposed by Hatze and Zajac. Both models are representative for a broad variety of biomechanical models formulated as ordinary differential equations (ODEs). These models incorporate parameters that directly represent known physiological properties. Other parameters have been introduced to reproduce empirical observations. We used sensitivity analysis to investigate the influence of model parameters on the ODE solutions. In addition, we expanded an existing approach to treating initial conditions as parameters and to calculating second-order sensitivities. Furthermore, we used a global sensitivity analysis approach to include finite ranges of parameter values. Hence, a theoretician striving for model reduction could use the method for identifying particularly low sensitivities to detect superfluous parameters. An experimenter could use it for identifying particularly high sensitivities to improve parameter estimation. Hatze's nonlinear model incorporates some parameters to which activation dynamics is clearly more sensitive than to any parameter in Zajac's linear model. Other than Zajac's model, Hatze's model can, however, reproduce measured shifts in optimal muscle length with varied muscle activity. Accordingly we extracted a specific parameter set for Hatze's model that combines best with a particular muscle force-length relation. PMID:26417379

Mars approach for global sensitivity analysis of differential equation models with applications to dynamics of influenza infection.

PubMed

Lee, Yeonok; Wu, Hulin

2012-01-01

Differential equation models are widely used for the study of natural phenomena in many fields. The study usually involves unknown factors such as initial conditions and/or parameters. It is important to investigate the impact of unknown factors (parameters and initial conditions) on model outputs in order to better understand the system the model represents. Apportioning the uncertainty (variation) of output variables of a model according to the input factors is referred to as sensitivity analysis. In this paper, we focus on the global sensitivity analysis of ordinary differential equation (ODE) models over a time period using the multivariate adaptive regression spline (MARS) as a meta model based on the concept of the variance of conditional expectation (VCE). We suggest to evaluate the VCE analytically using the MARS model structure of univariate tensor-product functions which is more computationally efficient. Our simulation studies show that the MARS model approach performs very well and helps to significantly reduce the computational cost. We present an application example of sensitivity analysis of ODE models for influenza infection to further illustrate the usefulness of the proposed method.

A Tale of Two Masses

ERIC Educational Resources Information Center

Bryan, Kurt

2011-01-01

This article presents an application of standard undergraduate ODE techniques to a modern engineering problem, that of using a tuned mass damper to control the vibration of a skyscraper. This material can be used in any ODE course in which the students have been familiarized with basic spring-mass models, resonance, and linear systems of ODEs.…

Investigating the two-moment characterisation of subcellular biochemical networks.

PubMed

Ullah, Mukhtar; Wolkenhauer, Olaf

2009-10-07

While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insight into the influence of noise. Towards that end, the two-moment approximation (2MA) is a promising addition to the established analytical approaches including the chemical Langevin equation (CLE) and the related linear noise approximation (LNA). The 2MA approach directly tracks the mean and (co)variance which are coupled in general. This coupling is not obvious in CME and CLE and ignored by LNA and conventional ODE models. We extend previous derivations of 2MA by allowing (a) non-elementary reactions and (b) relative concentrations. Often, several elementary reactions are approximated by a single step. Furthermore, practical situations often require the use of relative concentrations. We investigate the applicability of the 2MA approach to the well-established fission yeast cell cycle model. Our analytical model reproduces the clustering of cycle times observed in experiments. This is explained through multiple resettings of M-phase promoting factor (MPF), caused by the coupling between mean and (co)variance, near the G2/M transition.

Using constraints and their value for optimization of large ODE systems

PubMed Central

Domijan, Mirela; Rand, David A.

2015-01-01

We provide analytical tools to facilitate a rigorous assessment of the quality and value of the fit of a complex model to data. We use this to provide approaches to model fitting, parameter estimation, the design of optimization functions and experimental optimization. This is in the context where multiple constraints are used to select or optimize a large model defined by differential equations. We illustrate the approach using models of circadian clocks and the NF-κB signalling system. PMID:25673300

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

PubMed

Ullah, M; Schmidt, H; Cho, K H; Wolkenhauer, O

2006-03-01

The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.

Robust variable selection method for nonparametric differential equation models with application to nonlinear dynamic gene regulatory network analysis.

PubMed

Lu, Tao

2016-01-01

The gene regulation network (GRN) evaluates the interactions between genes and look for models to describe the gene expression behavior. These models have many applications; for instance, by characterizing the gene expression mechanisms that cause certain disorders, it would be possible to target those genes to block the progress of the disease. Many biological processes are driven by nonlinear dynamic GRN. In this article, we propose a nonparametric differential equation (ODE) to model the nonlinear dynamic GRN. Specially, we address following questions simultaneously: (i) extract information from noisy time course gene expression data; (ii) model the nonlinear ODE through a nonparametric smoothing function; (iii) identify the important regulatory gene(s) through a group smoothly clipped absolute deviation (SCAD) approach; (iv) test the robustness of the model against possible shortening of experimental duration. We illustrate the usefulness of the model and associated statistical methods through a simulation and a real application examples.

Solving ay'' + by' + cy = 0 with a Simple Product Rule Approach

ERIC Educational Resources Information Center

Tolle, John

2011-01-01

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

Radical Literary Education: A Classroom Experiment with Wordsworth's "Ode."

ERIC Educational Resources Information Center

Robinson, Jeffrey C.

Using a college course on William Wordsworth's "Ode: Intimations of Immortality from Recollections of Early Childhood" as a case study, this book presents an alternative approach to teaching poetry. Divided into seven sections with 19 chapters, the book describes how students can develop and exercise an historical imagination in the…

Two classes of ODE models with switch-like behavior.

PubMed

Just, Winfried; Korb, Mason; Elbert, Ben; Young, Todd

2013-12-01

In cases where the same real-world system can be modeled both by an ODE system ⅅ and a Boolean system , it is of interest to identify conditions under which the two systems will be consistent, that is, will make qualitatively equivalent predictions. In this note we introduce two broad classes of relatively simple models that provide a convenient framework for studying such questions. In contrast to the widely known class of Glass networks, the right-hand sides of our ODEs are Lipschitz-continuous. We prove that if has certain structures, consistency between ⅅ and is implied by sufficient separation of time scales in one class of our models. Namely, if the trajectories of are "one-stepping" then we prove a strong form of consistency and if has a certain monotonicity property then there is a weaker consistency between ⅅ and . These results appear to point to more general structure properties that favor consistency between ODE and Boolean models.

Modelling and Inverse-Modelling: Experiences with O.D.E. Linear Systems in Engineering Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor

2009-01-01

In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics,…

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

NASA Technical Reports Server (NTRS)

Turpin, Jason B.

2004-01-01

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Optimizing ion channel models using a parallel genetic algorithm on graphical processors.

PubMed

Ben-Shalom, Roy; Aviv, Amit; Razon, Benjamin; Korngreen, Alon

2012-01-01

We have recently shown that we can semi-automatically constrain models of voltage-gated ion channels by combining a stochastic search algorithm with ionic currents measured using multiple voltage-clamp protocols. Although numerically successful, this approach is highly demanding computationally, with optimization on a high performance Linux cluster typically lasting several days. To solve this computational bottleneck we converted our optimization algorithm for work on a graphical processing unit (GPU) using NVIDIA's CUDA. Parallelizing the process on a Fermi graphic computing engine from NVIDIA increased the speed ∼180 times over an application running on an 80 node Linux cluster, considerably reducing simulation times. This application allows users to optimize models for ion channel kinetics on a single, inexpensive, desktop "super computer," greatly reducing the time and cost of building models relevant to neuronal physiology. We also demonstrate that the point of algorithm parallelization is crucial to its performance. We substantially reduced computing time by solving the ODEs (Ordinary Differential Equations) so as to massively reduce memory transfers to and from the GPU. This approach may be applied to speed up other data intensive applications requiring iterative solutions of ODEs. Copyright © 2012 Elsevier B.V. All rights reserved.

Dimension reduction method for SPH equations

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

Tartakovsky, Alexandre M.; Scheibe, Timothy D.

2011-08-26

Smoothed Particle Hydrodynamics model of a complex multiscale processe often results in a system of ODEs with an enormous number of unknowns. Furthermore, a time integration of the SPH equations usually requires time steps that are smaller than the observation time by many orders of magnitude. A direct solution of these ODEs can be extremely expensive. Here we propose a novel dimension reduction method that gives an approximate solution of the SPH ODEs and provides an accurate prediction of the average behavior of the modeled system. The method consists of two main elements. First, effective equationss for evolution of averagemore » variables (e.g. average velocity, concentration and mass of a mineral precipitate) are obtained by averaging the SPH ODEs over the entire computational domain. These effective ODEs contain non-local terms in the form of volume integrals of functions of the SPH variables. Second, a computational closure is used to close the system of the effective equations. The computational closure is achieved via short bursts of the SPH model. The dimension reduction model is used to simulate flow and transport with mixing controlled reactions and mineral precipitation. An SPH model is used model transport at the porescale. Good agreement between direct solutions of the SPH equations and solutions obtained with the dimension reduction method for different boundary conditions confirms the accuracy and computational efficiency of the dimension reduction model. The method significantly accelerates SPH simulations, while providing accurate approximation of the solution and accurate prediction of the average behavior of the system.« less

Alternative Stable States, Coral Reefs, and Smooth Dynamics with a Kick.

PubMed

Ippolito, Stephen; Naudot, Vincent; Noonburg, Erik G

2016-03-01

We consider a computer simulation, which was found to be faithful to time series data for Caribbean coral reefs, and an analytical model to help understand the dynamics of the simulation. The analytical model is a system of ordinary differential equations (ODE), and the authors claim this model demonstrates the existence of alternative stable states. The existence of an alternative stable state should consider a sudden shift in coral and macroalgae populations, while the grazing rate remains constant. The results of such shifts, however, are often confounded by changes in grazing rate. Although the ODE suggest alternative stable states, the ODE need modification to explicitly account for shifts or discrete events such as hurricanes. The goal of this paper will be to study the simulation dynamics through a simplified analytical representation. We proceed by modifying the original analytical model through incorporating discrete changes into the ODE. We then analyze the resulting dynamics and their bifurcations with respect to changes in grazing rate and hurricane frequency. In particular, a "kick" enabling the ODE to consider impulse events is added. Beyond adding a "kick" we employ the grazing function that is suggested by the simulation. The extended model was fit to the simulation data to support its use and predicts the existence cycles depending nonlinearly on grazing rates and hurricane frequency. These cycles may bring new insights into consideration for reef health, restoration and dynamics.

Two classes of ODE models with switch-like behavior

PubMed Central

Just, Winfried; Korb, Mason; Elbert, Ben; Young, Todd

2013-01-01

In cases where the same real-world system can be modeled both by an ODE system ⅅ and a Boolean system 𝔹, it is of interest to identify conditions under which the two systems will be consistent, that is, will make qualitatively equivalent predictions. In this note we introduce two broad classes of relatively simple models that provide a convenient framework for studying such questions. In contrast to the widely known class of Glass networks, the right-hand sides of our ODEs are Lipschitz-continuous. We prove that if 𝔹 has certain structures, consistency between ⅅ and 𝔹 is implied by sufficient separation of time scales in one class of our models. Namely, if the trajectories of 𝔹 are “one-stepping” then we prove a strong form of consistency and if 𝔹 has a certain monotonicity property then there is a weaker consistency between ⅅ and 𝔹. These results appear to point to more general structure properties that favor consistency between ODE and Boolean models. PMID:24244061

Time-Parallel Solutions to Ordinary Differential Equations on GPUs with a New Functional Optimization Approach Related to the Sobolev Gradient Method

DTIC Science & Technology

2012-10-01

black and approximations in cyan and magenta. The second ODE is the pendulum equation, given by: This ODE was also implemented using Crank...The drawback of approaches like the one proposed can be observed with a very simple example. Suppose vector is found by applying 4 linear...public release; distribution unlimited Figure 2. A phase space plot of the Pendulum example. Fine solution (black) contains 32768 time steps

Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

PubMed Central

Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin

2012-01-01

Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online. PMID:23155351

Analytical Insights on the Position, Challenges, and Potential for Promoting OER in ODeL Institutions in Africa

ERIC Educational Resources Information Center

Muganda, Cornelia K.; Samzugi, Athuman S.; Mallinson, Brenda J.

2016-01-01

This paper shares analytical insights on the position, challenges and potential for promoting Open Educational Resources (OER) in African Open Distance and eLearning (ODeL) institutions. The researchers sought to use a participatory research approach as described by Krishnaswamy (2004), in convening a sequence of two workshops at the Open…

The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods.

PubMed

Ross, E W; Taub, I A; Doona, C J; Feeherry, F E; Kustin, K

2005-03-15

Knowledge of the mathematical properties of the quasi-chemical model [Taub, Feeherry, Ross, Kustin, Doona, 2003. A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68 (8), 2530-2537], which is used to characterize and predict microbial growth-death kinetics in foods, is important for its applications in predictive microbiology. The model consists of a system of four ordinary differential equations (ODEs), which govern the temporal dependence of the bacterial life cycle (the lag, exponential growth, stationary, and death phases, respectively). The ODE system derives from a hypothetical four-step reaction scheme that postulates the activity of a critical intermediate as an antagonist to growth (perhaps through a quorum sensing biomechanism). The general behavior of the solutions to the ODEs is illustrated by several examples. In instances when explicit mathematical solutions to these ODEs are not obtainable, mathematical approximations are used to find solutions that are helpful in evaluating growth in the early stages and again near the end of the process. Useful solutions for the ODE system are also obtained in the case where the rate of antagonist formation is small. The examples and the approximate solutions provide guidance in the parameter estimation that must be done when fitting the model to data. The general behavior of the solutions is illustrated by examples, and the MATLAB programs with worked examples are included in the appendices for use by predictive microbiologists for data collected independently.

Outcome Prediction in Mathematical Models of Immune Response to Infection.

PubMed

Mai, Manuel; Wang, Kun; Huber, Greg; Kirby, Michael; Shattuck, Mark D; O'Hern, Corey S

2015-01-01

Clinicians need to predict patient outcomes with high accuracy as early as possible after disease inception. In this manuscript, we show that patient-to-patient variability sets a fundamental limit on outcome prediction accuracy for a general class of mathematical models for the immune response to infection. However, accuracy can be increased at the expense of delayed prognosis. We investigate several systems of ordinary differential equations (ODEs) that model the host immune response to a pathogen load. Advantages of systems of ODEs for investigating the immune response to infection include the ability to collect data on large numbers of 'virtual patients', each with a given set of model parameters, and obtain many time points during the course of the infection. We implement patient-to-patient variability v in the ODE models by randomly selecting the model parameters from distributions with coefficients of variation v that are centered on physiological values. We use logistic regression with one-versus-all classification to predict the discrete steady-state outcomes of the system. We find that the prediction algorithm achieves near 100% accuracy for v = 0, and the accuracy decreases with increasing v for all ODE models studied. The fact that multiple steady-state outcomes can be obtained for a given initial condition, i.e. the basins of attraction overlap in the space of initial conditions, limits the prediction accuracy for v > 0. Increasing the elapsed time of the variables used to train and test the classifier, increases the prediction accuracy, while adding explicit external noise to the ODE models decreases the prediction accuracy. Our results quantify the competition between early prognosis and high prediction accuracy that is frequently encountered by clinicians.

Systems Biology Approach and Mathematical Modeling for Analyzing Phase-Space Switch During Epithelial-Mesenchymal Transition.

PubMed

Simeoni, Chiara; Dinicola, Simona; Cucina, Alessandra; Mascia, Corrado; Bizzarri, Mariano

2018-01-01

In this report, we aim at presenting a viable strategy for the study of Epithelial-Mesenchymal Transition (EMT) and its opposite Mesenchymal-Epithelial Transition (MET) by means of a Systems Biology approach combined with a suitable Mathematical Modeling analysis. Precisely, it is shown how the presence of a metastable state, that is identified at a mesoscopic level of description, is crucial for making possible the appearance of a phase transition mechanism in the framework of fast-slow dynamics for Ordinary Differential Equations (ODEs).

Rational selection of experimental readout and intervention sites for reducing uncertainties in computational model predictions.

PubMed

Flassig, Robert J; Migal, Iryna; der Zalm, Esther van; Rihko-Struckmann, Liisa; Sundmacher, Kai

2015-01-16

Understanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE). Typically, this model class contains many unknown parameters, which are estimated from inadequate and noisy data. Depending on the ODE structure, predictions based on unmeasured states and associated parameters are highly uncertain, even undetermined. For given data, profile likelihood analysis has been proven to be one of the most practically relevant approaches for analyzing the identifiability of an ODE structure, and thus model predictions. In case of highly uncertain or non-identifiable parameters, rational experimental design based on various approaches has shown to significantly reduce parameter uncertainties with minimal amount of effort. In this work we illustrate how to use profile likelihood samples for quantifying the individual contribution of parameter uncertainty to prediction uncertainty. For the uncertainty quantification we introduce the profile likelihood sensitivity (PLS) index. Additionally, for the case of several uncertain parameters, we introduce the PLS entropy to quantify individual contributions to the overall prediction uncertainty. We show how to use these two criteria as an experimental design objective for selecting new, informative readouts in combination with intervention site identification. The characteristics of the proposed multi-criterion objective are illustrated with an in silico example. We further illustrate how an existing practically non-identifiable model for the chlorophyll fluorescence induction in a photosynthetic organism, D. salina, can be rendered identifiable by additional experiments with new readouts. Having data and profile likelihood samples at hand, the here proposed uncertainty quantification based on prediction samples from the profile likelihood provides a simple way for determining individual contributions of parameter uncertainties to uncertainties in model predictions. The uncertainty quantification of specific model predictions allows identifying regions, where model predictions have to be considered with care. Such uncertain regions can be used for a rational experimental design to render initially highly uncertain model predictions into certainty. Finally, our uncertainty quantification directly accounts for parameter interdependencies and parameter sensitivities of the specific prediction.

The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics

NASA Astrophysics Data System (ADS)

Naz, Rehana; Naeem, Imran

2018-03-01

The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.

Bifurcation analysis and dimension reduction of a predator-prey model for the L-H transition

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

Dam, Magnus; Brøns, Morten; Juul Rasmussen, Jens

2013-10-15

The L-H transition denotes a shift to an improved confinement state of a toroidal plasma in a fusion reactor. A model of the L-H transition is required to simulate the time dependence of tokamak discharges that include the L-H transition. A 3-ODE predator-prey type model of the L-H transition is investigated with bifurcation theory of dynamical systems. The analysis shows that the model contains three types of transitions: an oscillating transition, a sharp transition with hysteresis, and a smooth transition. The model is recognized as a slow-fast system. A reduced 2-ODE model consisting of the full model restricted to themore » flow on the critical manifold is found to contain all the same dynamics as the full model. This means that all the dynamics in the system is essentially 2-dimensional, and a minimal model of the L-H transition could be a 2-ODE model.« less

Effects of numerical tolerance levels on an atmospheric chemistry model for mercury

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

Ferris, D.C.; Burns, D.S.; Shuford, J.

1996-12-31

A Box Model was developed to investigate the atmospheric oxidation processes of mercury in the environment. Previous results indicated the most important influences on the atmospheric concentration of HgO(g) are (i) the flux of HgO(g) volatilization, which is related to the surface medium, extent of contamination, and temperature, and (ii) the presence of Cl{sub 2} in the atmosphere. The numerical solver which has been incorporated into the ORganic CHemistry Integrated Dispersion (ORCHID) model uses the Livermore Solver of Ordinary Differential Equations (LSODE). In the solution of the ODE`s, LSODE uses numerical tolerances. The tolerances effect computer run time, the relativemore » accuracy of ODE calculated species concentrations and whether or not LSODE converges to a solution using this system of equations. The effects of varying these tolerances on the solution of the box model and the ORCHID model will be discussed.« less

Finding higher order Darboux polynomials for a family of rational first order ordinary differential equations

NASA Astrophysics Data System (ADS)

Avellar, J.; Claudino, A. L. G. C.; Duarte, L. G. S.; da Mota, L. A. C. P.

2015-10-01

For the Darbouxian methods we are studying here, in order to solve first order rational ordinary differential equations (1ODEs), the most costly (computationally) step is the finding of the needed Darboux polynomials. This can be so grave that it can render the whole approach unpractical. Hereby we introduce a simple heuristics to speed up this process for a class of 1ODEs.

Modeling Dynamic Regulatory Processes in Stroke.

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

McDermott, Jason E.; Jarman, Kenneth D.; Taylor, Ronald C.

2012-10-11

The ability to examine in silico the behavior of biological systems can greatly accelerate the pace of discovery in disease pathologies, such as stroke, where in vivo experimentation is lengthy and costly. In this paper we describe an approach to in silico examination of blood genomic responses to neuroprotective agents and subsequent stroke through the development of dynamic models of the regulatory processes observed in the experimental gene expression data. First, we identified functional gene clusters from these data. Next, we derived ordinary differential equations (ODEs) relating regulators and functional clusters from the data. These ODEs were used to developmore » dynamic models that simulate the expression of regulated functional clusters using system dynamics as the modeling paradigm. The dynamic model has the considerable advantage of only requiring an initial starting state, and does not require measurement of regulatory influences at each time point in order to make accurate predictions. The manipulation of input model parameters, such as changing the magnitude of gene expression, made it possible to assess the behavior of the networks through time under varying conditions. We report that an optimized dynamic model can provide accurate predictions of overall system behavior under several different preconditioning paradigms.« less

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

PubMed Central

Kaltenbacher, Barbara; Hasenauer, Jan

2017-01-01

Mechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small- and medium-scale biological processes. While the same should in principle hold for large- and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions are missing so far. While individual simulations are feasible, the inference of the model parameters from experimental data is computationally too intensive. In this manuscript, we evaluate adjoint sensitivity analysis for parameter estimation in large scale biochemical reaction networks. We present the approach for time-discrete measurement and compare it to state-of-the-art methods used in systems and computational biology. Our comparison reveals a significantly improved computational efficiency and a superior scalability of adjoint sensitivity analysis. The computational complexity is effectively independent of the number of parameters, enabling the analysis of large- and genome-scale models. Our study of a comprehensive kinetic model of ErbB signaling shows that parameter estimation using adjoint sensitivity analysis requires a fraction of the computation time of established methods. The proposed method will facilitate mechanistic modeling of genome-scale cellular processes, as required in the age of omics. PMID:28114351

Deterministic Models of Inhalational Anthrax in New Zealand White Rabbits

PubMed Central

2014-01-01

Computational models describing bacterial kinetics were developed for inhalational anthrax in New Zealand white (NZW) rabbits following inhalation of Ames strain B. anthracis. The data used to parameterize the models included bacterial numbers in the airways, lung tissue, draining lymph nodes, and blood. Initial bacterial numbers were deposited spore dose. The first model was a single exponential ordinary differential equation (ODE) with 3 rate parameters that described mucociliated (physical) clearance, immune clearance (bacterial killing), and bacterial growth. At 36 hours postexposure, the ODE model predicted 1.7×107 bacteria in the rabbit, which agreed well with data from actual experiments (4.0×107 bacteria at 36 hours). Next, building on the single ODE model, a physiological-based biokinetic (PBBK) compartmentalized model was developed in which 1 physiological compartment was the lumen of the airways and the other was the rabbit body (lung tissue, lymph nodes, blood). The 2 compartments were connected with a parameter describing transport of bacteria from the airways into the body. The PBBK model predicted 4.9×107 bacteria in the body at 36 hours, and by 45 hours the model showed all clearance mechanisms were saturated, suggesting the rabbit would quickly succumb to the infection. As with the ODE model, the PBBK model results agreed well with laboratory observations. These data are discussed along with the need for and potential application of the models in risk assessment, drug development, and as a general aid to the experimentalist studying inhalational anthrax. PMID:24527843

Dynamical spike solutions in a nonlocal model of pattern formation

NASA Astrophysics Data System (ADS)

Marciniak-Czochra, Anna; Härting, Steffen; Karch, Grzegorz; Suzuki, Kanako

2018-05-01

Coupling a reaction-diffusion equation with ordinary differential equa- tions (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-type limit of a reaction-diffusion-ODE model, we show that in such cases the instability driven by nonlocal terms (a counterpart of DDI) may lead to formation of unbounded spike patterns.

Accelerating finite-rate chemical kinetics with coprocessors: Comparing vectorization methods on GPUs, MICs, and CPUs

NASA Astrophysics Data System (ADS)

Stone, Christopher P.; Alferman, Andrew T.; Niemeyer, Kyle E.

2018-05-01

Accurate and efficient methods for solving stiff ordinary differential equations (ODEs) are a critical component of turbulent combustion simulations with finite-rate chemistry. The ODEs governing the chemical kinetics at each mesh point are decoupled by operator-splitting allowing each to be solved concurrently. An efficient ODE solver must then take into account the available thread and instruction-level parallelism of the underlying hardware, especially on many-core coprocessors, as well as the numerical efficiency. A stiff Rosenbrock and a nonstiff Runge-Kutta ODE solver are both implemented using the single instruction, multiple thread (SIMT) and single instruction, multiple data (SIMD) paradigms within OpenCL. Both methods solve multiple ODEs concurrently within the same instruction stream. The performance of these parallel implementations was measured on three chemical kinetic models of increasing size across several multicore and many-core platforms. Two separate benchmarks were conducted to clearly determine any performance advantage offered by either method. The first benchmark measured the run-time of evaluating the right-hand-side source terms in parallel and the second benchmark integrated a series of constant-pressure, homogeneous reactors using the Rosenbrock and Runge-Kutta solvers. The right-hand-side evaluations with SIMD parallelism on the host multicore Xeon CPU and many-core Xeon Phi co-processor performed approximately three times faster than the baseline multithreaded C++ code. The SIMT parallel model on the host and Phi was 13%-35% slower than the baseline while the SIMT model on the NVIDIA Kepler GPU provided approximately the same performance as the SIMD model on the Phi. The runtimes for both ODE solvers decreased significantly with the SIMD implementations on the host CPU (2.5-2.7 ×) and Xeon Phi coprocessor (4.7-4.9 ×) compared to the baseline parallel code. The SIMT implementations on the GPU ran 1.5-1.6 times faster than the baseline multithreaded CPU code; however, this was significantly slower than the SIMD versions on the host CPU or the Xeon Phi. The performance difference between the three platforms was attributed to thread divergence caused by the adaptive step-sizes within the ODE integrators. Analysis showed that the wider vector width of the GPU incurs a higher level of divergence than the narrower Sandy Bridge or Xeon Phi. The significant performance improvement provided by the SIMD parallel strategy motivates further research into more ODE solver methods that are both SIMD-friendly and computationally efficient.

Dynamics of a Class of HIV Infection Models with Cure of Infected Cells in Eclipse Stage.

PubMed

Maziane, Mehdi; Lotfi, El Mehdi; Hattaf, Khalid; Yousfi, Noura

2015-12-01

In this paper, we propose two HIV infection models with specific nonlinear incidence rate by including a class of infected cells in the eclipse phase. The first model is described by ordinary differential equations (ODEs) and generalizes a set of previously existing models and their results. The second model extends our ODE model by taking into account the diffusion of virus. Furthermore, the global stability of both models is investigated by constructing suitable Lyapunov functionals. Finally, we check our theoretical results with numerical simulations.

Dynamic models for estimating the effect of HAART on CD4 in observational studies: Application to the Aquitaine Cohort and the Swiss HIV Cohort Study.

PubMed

Prague, Mélanie; Commenges, Daniel; Gran, Jon Michael; Ledergerber, Bruno; Young, Jim; Furrer, Hansjakob; Thiébaut, Rodolphe

2017-03-01

Highly active antiretroviral therapy (HAART) has proved efficient in increasing CD4 counts in many randomized clinical trials. Because randomized trials have some limitations (e.g., short duration, highly selected subjects), it is interesting to assess the effect of treatments using observational studies. This is challenging because treatment is started preferentially in subjects with severe conditions. This general problem had been treated using Marginal Structural Models (MSM) relying on the counterfactual formulation. Another approach to causality is based on dynamical models. We present three discrete-time dynamic models based on linear increments models (LIM): the first one based on one difference equation for CD4 counts, the second with an equilibrium point, and the third based on a system of two difference equations, which allows jointly modeling CD4 counts and viral load. We also consider continuous-time models based on ordinary differential equations with non-linear mixed effects (ODE-NLME). These mechanistic models allow incorporating biological knowledge when available, which leads to increased statistical evidence for detecting treatment effect. Because inference in ODE-NLME is numerically challenging and requires specific methods and softwares, LIM are a valuable intermediary option in terms of consistency, precision, and complexity. We compare the different approaches in simulation and in illustration on the ANRS CO3 Aquitaine Cohort and the Swiss HIV Cohort Study. © 2016, The International Biometric Society.

In silico modeling of axonal reconnection within a discrete fiber tract after spinal cord injury.

PubMed

Woolfe, Franco; Waxman, Stephen G; Hains, Bryan C

2007-02-01

Following spinal cord injury (SCI), descending axons that carry motor commands from the brain to the spinal cord are injured or transected, producing chronic motor dysfunction and paralysis. Reconnection of these axons is a major prerequisite for restoration of function after SCI. Thus far, only modest gains in motor function have been achieved experimentally or in the clinic after SCI, identifying the practical limitations of current treatment approaches. In this paper, we use an ordinary differential equation (ODE) to simulate the relative and synergistic contributions of several experimentally-established biological factors related to inhibition or promotion of axonal repair and restoration of function after SCI. The factors were mathematically modeled by the ODE. The results of our simulation show that in a model system, many factors influenced the achievability of axonal reconnection. Certain factors more strongly affected axonal reconnection in isolation, and some factors interacted in a synergistic fashion to produce further improvements in axonal reconnection. Our data suggest that mathematical modeling may be useful in evaluating the complex interactions of discrete therapeutic factors not possible in experimental preparations, and highlight the benefit of a combinatorial therapeutic approach focused on promoting axonal sprouting, attraction of cut ends, and removal of growth inhibition for achieving axonal reconnection. Predictions of this simulation may be of utility in guiding future experiments aimed at restoring function after SCI.

A numerical investigation of wave-breaking-induced turbulent coherent structure under a solitary wave

NASA Astrophysics Data System (ADS)

Zhou, Zheyu; Sangermano, Jacob; Hsu, Tian-Jian; Ting, Francis C. K.

2014-10-01

To better understand the effect of wave-breaking-induced turbulence on the bed, we report a 3-D large-eddy simulation (LES) study of a breaking solitary wave in spilling condition. Using a turbulence-resolving approach, we study the generation and the fate of wave-breaking-induced turbulent coherent structures, commonly known as obliquely descending eddies (ODEs). Specifically, we focus on how these eddies may impinge onto bed. The numerical model is implemented using an open-source CFD library of solvers, called OpenFOAM, where the incompressible 3-D filtered Navier-Stokes equations for the water and the air phases are solved with a finite volume scheme. The evolution of the water-air interfaces is approximated with a volume of fluid method. Using the dynamic Smagorinsky closure, the numerical model has been validated with wave flume experiments of solitary wave breaking over a 1/50 sloping beach. Simulation results show that during the initial overturning of the breaking wave, 2-D horizontal rollers are generated, accelerated, and further evolve into a couple of 3-D hairpin vortices. Some of these vortices are sufficiently intense to impinge onto the bed. These hairpin vortices possess counter-rotating and downburst features, which are key characteristics of ODEs observed by earlier laboratory studies using Particle Image Velocimetry. Model results also suggest that those ODEs that impinge onto bed can induce strong near-bed turbulence and bottom stress. The intensity and locations of these near-bed turbulent events could not be parameterized by near-surface (or depth integrated) turbulence unless in very shallow depth.

A Tutorial on RxODE: Simulating Differential Equation Pharmacometric Models in R.

PubMed

Wang, W; Hallow, K M; James, D A

2016-01-01

This tutorial presents the application of an R package, RxODE, that facilitates quick, efficient simulations of ordinary differential equation models completely within R. Its application is illustrated through simulation of design decision effects on an adaptive dosing regimen. The package provides an efficient, versatile way to specify dosing scenarios and to perform simulation with variability with minimal custom coding. Models can be directly translated to Rshiny applications to facilitate interactive, real-time evaluation/iteration on simulation scenarios.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Network Reconstruction Using Nonparametric Additive ODE Models

PubMed Central

Henderson, James; Michailidis, George

2014-01-01

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation. PMID:24732037

Transport coefficient computation based on input/output reduced order models

NASA Astrophysics Data System (ADS)

Hurst, Joshua L.

The guiding purpose of this thesis is to address the optimal material design problem when the material description is a molecular dynamics model. The end goal is to obtain a simplified and fast model that captures the property of interest such that it can be used in controller design and optimization. The approach is to examine model reduction analysis and methods to capture a specific property of interest, in this case viscosity, or more generally complex modulus or complex viscosity. This property and other transport coefficients are defined by a input/output relationship and this motivates model reduction techniques that are tailored to preserve input/output behavior. In particular Singular Value Decomposition (SVD) based methods are investigated. First simulation methods are identified that are amenable to systems theory analysis. For viscosity, these models are of the Gosling and Lees-Edwards type. They are high order nonlinear Ordinary Differential Equations (ODEs) that employ Periodic Boundary Conditions. Properties can be calculated from the state trajectories of these ODEs. In this research local linear approximations are rigorously derived and special attention is given to potentials that are evaluated with Periodic Boundary Conditions (PBC). For the Gosling description LTI models are developed from state trajectories but are found to have limited success in capturing the system property, even though it is shown that full order LTI models can be well approximated by reduced order LTI models. For the Lees-Edwards SLLOD type model nonlinear ODEs will be approximated by a Linear Time Varying (LTV) model about some nominal trajectory and both balanced truncation and Proper Orthogonal Decomposition (POD) will be used to assess the plausibility of reduced order models to this system description. An immediate application of the derived LTV models is Quasilinearization or Waveform Relaxation. Quasilinearization is a Newton's method applied to the ODE operator equation. Its a recursive method that solves nonlinear ODE's by solving a LTV systems at each iteration to obtain a new closer solution. LTV models are derived for both Gosling and Lees-Edwards type models. Particular attention is given to SLLOD Lees-Edwards models because they are in a form most amenable to performing Taylor series expansion, and the most commonly used model to examine viscosity. With linear models developed a method is presented to calculate viscosity based on LTI Gosling models but is shown to have some limitations. To address these issues LTV SLLOD models are analyzed with both Balanced Truncation and POD and both show that significant order reduction is possible. By examining the singular values of both techniques it is shown that Balanced Truncation has a potential to offer greater reduction, which should be expected as it is based on the input/output mapping instead of just the state information as in POD. Obtaining reduced order systems that capture the property of interest is challenging. For Balanced Truncation reduced order models for 1-D LJ and FENE systems are obtained and are shown to capture the output of interest fairly well. However numerical challenges currently limit this analysis to small order systems. Suggestions are presented to extend this method to larger systems. In addition reduced 2nd order systems are obtained from POD. Here the challenge is extending the solution beyond the original period used for the projection, in particular identifying the manifold the solution travels along. The remaining challenges are presented and discussed.

Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells.

PubMed

Sundnes, J; Lines, G T; Tveito, A

2001-08-01

The contraction of the heart is preceded and caused by a cellular electro-chemical reaction, causing an electrical field to be generated. Performing realistic computer simulations of this process involves solving a set of partial differential equations, as well as a large number of ordinary differential equations (ODEs) characterizing the reactive behavior of the cardiac tissue. Experiments have shown that the solution of the ODEs contribute significantly to the total work of a simulation, and there is thus a strong need to utilize efficient solution methods for this part of the problem. This paper presents how an efficient implicit Runge-Kutta method may be adapted to solve a complicated cardiac cell model consisting of 31 ODEs, and how this solver may be coupled to a set of PDE solvers to provide complete simulations of the electrical activity.

A partial Hamiltonian approach for current value Hamiltonian systems

NASA Astrophysics Data System (ADS)

Naz, R.; Mahomed, F. M.; Chaudhry, Azam

2014-10-01

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

Transforming Boolean models to continuous models: methodology and application to T-cell receptor signaling

PubMed Central

Wittmann, Dominik M; Krumsiek, Jan; Saez-Rodriguez, Julio; Lauffenburger, Douglas A; Klamt, Steffen; Theis, Fabian J

2009-01-01

Background The understanding of regulatory and signaling networks has long been a core objective in Systems Biology. Knowledge about these networks is mainly of qualitative nature, which allows the construction of Boolean models, where the state of a component is either 'off' or 'on'. While often able to capture the essential behavior of a network, these models can never reproduce detailed time courses of concentration levels. Nowadays however, experiments yield more and more quantitative data. An obvious question therefore is how qualitative models can be used to explain and predict the outcome of these experiments. Results In this contribution we present a canonical way of transforming Boolean into continuous models, where the use of multivariate polynomial interpolation allows transformation of logic operations into a system of ordinary differential equations (ODE). The method is standardized and can readily be applied to large networks. Other, more limited approaches to this task are briefly reviewed and compared. Moreover, we discuss and generalize existing theoretical results on the relation between Boolean and continuous models. As a test case a logical model is transformed into an extensive continuous ODE model describing the activation of T-cells. We discuss how parameters for this model can be determined such that quantitative experimental results are explained and predicted, including time-courses for multiple ligand concentrations and binding affinities of different ligands. This shows that from the continuous model we may obtain biological insights not evident from the discrete one. Conclusion The presented approach will facilitate the interaction between modeling and experiments. Moreover, it provides a straightforward way to apply quantitative analysis methods to qualitatively described systems. PMID:19785753

Errors from approximation of ODE systems with reduced order models

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

Vassilevska, Tanya

2016-12-30

This is a code to calculate the error from approximation of systems of ordinary differential equations (ODEs) by using Proper Orthogonal Decomposition (POD) Reduced Order Models (ROM) methods and to compare and analyze the errors for two POD ROM variants. The first variant is the standard POD ROM, the second variant is a modification of the method using the values of the time derivatives (a.k.a. time-derivative snapshots). The code compares the errors from the two variants under different conditions.

Kinetic modeling of cell metabolism for microbial production.

PubMed

Costa, Rafael S; Hartmann, Andras; Vinga, Susana

2016-02-10

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations. Copyright © 2015 Elsevier B.V. All rights reserved.

Complex discrete dynamics from simple continuous population models.

PubMed

Gamarra, Javier G P; Solé, Ricard V

2002-05-01

Nonoverlapping generations have been classically modelled as difference equations in order to account for the discrete nature of reproductive events. However, other events such as resource consumption or mortality are continuous and take place in the within-generation time. We have realistically assumed a hybrid ODE bidimensional model of resources and consumers with discrete events for reproduction. Numerical and analytical approaches showed that the resulting dynamics resembles a Ricker map, including the doubling route to chaos. Stochastic simulations with a handling-time parameter for indirect competition of juveniles may affect the qualitative behaviour of the model.

Inertial Manifold and Large Deviations Approach to Reduced PDE Dynamics

NASA Astrophysics Data System (ADS)

Cardin, Franco; Favretti, Marco; Lovison, Alberto

2017-09-01

In this paper a certain type of reaction-diffusion equation—similar to the Allen-Cahn equation—is the starting point for setting up a genuine thermodynamic reduction i.e. involving a finite number of parameters or collective variables of the initial system. We firstly operate a finite Lyapunov-Schmidt reduction of the cited reaction-diffusion equation when reformulated as a variational problem. In this way we gain a finite-dimensional ODE description of the initial system which preserves the gradient structure of the original one and that is exact for the static case and only approximate for the dynamic case. Our main concern is how to deal with this approximate reduced description of the initial PDE. To start with, we note that our approximate reduced ODE is similar to the approximate inertial manifold introduced by Temam and coworkers for Navier-Stokes equations. As a second approach, we take into account the uncertainty (loss of information) introduced with the above mentioned approximate reduction by considering the stochastic version of the ODE. We study this reduced stochastic system using classical tools from large deviations, viscosity solutions and weak KAM Hamilton-Jacobi theory. In the last part we suggest a possible use of a result of our approach in the comprehensive treatment non equilibrium thermodynamics given by Macroscopic Fluctuation Theory.

Extended Krylov subspaces approximations of matrix functions. Application to computational electromagnetics

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

Druskin, V.; Lee, Ping; Knizhnerman, L.

There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.

Local structure of equality constrained NLP problems

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

Mari, J.

We show that locally around a feasible point, the behavior of an equality constrained nonlinear program is described by the gradient and the Hessian of the Lagrangian on the tangent subspace. In particular this holds true for reduced gradient approaches. Applying the same ideas to the control of nonlinear ODE:s, one can device first and second order methods that can be applied also to stiff problems. We finally describe an application of these ideas to the optimization of the production of human growth factor by fed-batch fermentation.

Development of Educational Materials to Enhance Students‧ Motivation using the ODE Physics Engine

NASA Astrophysics Data System (ADS)

Demura, Kosei

This paper presents educational materials, a simulator and a textbook, using the Open Dynamics Engine (ODE) . ODE is an open source, fast, robust and industrial quality library for a real-time and interactive simulation of rigid body dynamics. ODE is suitable for developing educational materials. However, there had been no book which introduced how to use ODE to make simulators written in Japanese. Thus I wrote a textbook which gave basic robotics and how to make simulators based on ODE. Students are able to tackle the subject with interest using the textbook and the simulators.

Numerical equilibrium analysis for structured consumer resource models.

PubMed

de Roos, A M; Diekmann, O; Getto, P; Kirkilionis, M A

2010-02-01

In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for "Daphnia consuming algae" models in C-code. The results obtained by way of this implementation are shown in the form of graphs.

Epigenetic game theory and its application in plants. Comment on: ;Epigenetic game theory: How to compute the epigenetic control of maternal-to-zygotic transition; by Qian Wang et al.

NASA Astrophysics Data System (ADS)

Zhang, Yuan-Ming; Zhang, Yinghao; Guo, Mingyue

2017-03-01

Wang's et al. article [1] is the first to integrate game theory (especially evolutionary game theory) with epigenetic modification of zygotic genomes. They described and assessed a modeling framework based on evolutionary game theory to quantify, how sperms and oocytes interact through epigenetic processes, to determine embryo development. They also studied the internal mechanisms for normal embryo development: 1) evolutionary interactions between DNA methylation of the paternal and maternal genomes, and 2) the application of game theory to formulate and quantify how different genes compete or cooperate to regulate embryogenesis through methylation. Although it is not very comprehensive and profound regarding game theory modeling, this article bridges the gap between evolutionary game theory and the epigenetic control of embryo development by powerful ordinary differential equations (ODEs). The epiGame framework includes four aspects: 1) characterizing how epigenetic game theory works by the strategy matrix, in which the pattern and relative magnitude of the methylation effects on embryogenesis, are described by the cooperation and competition mechanisms, 2) quantifying the game that the direction and degree of P-M interactions over embryo development can be explained by the sign and magnitude of interaction parameters in model (2), 3) modeling epigenetic interactions within the morula, especially for two coupled nonlinear ODEs, with explicit functions in model (4), which provide a good fit to the observed data for the two sexes (adjusted R2 = 0.956), and 4) revealing multifactorial interactions in embryogenesis from the coupled ODEs in model (2) to triplet ODEs in model (6). Clearly, this article extends game theory from evolutionary game theory to epigenetic game theory.

Dynamic sensitivity analysis of biological systems

PubMed Central

Wu, Wu Hsiung; Wang, Feng Sheng; Chang, Maw Shang

2008-01-01

Background A mathematical model to understand, predict, control, or even design a real biological system is a central theme in systems biology. A dynamic biological system is always modeled as a nonlinear ordinary differential equation (ODE) system. How to simulate the dynamic behavior and dynamic parameter sensitivities of systems described by ODEs efficiently and accurately is a critical job. In many practical applications, e.g., the fed-batch fermentation systems, the system admissible input (corresponding to independent variables of the system) can be time-dependent. The main difficulty for investigating the dynamic log gains of these systems is the infinite dimension due to the time-dependent input. The classical dynamic sensitivity analysis does not take into account this case for the dynamic log gains. Results We present an algorithm with an adaptive step size control that can be used for computing the solution and dynamic sensitivities of an autonomous ODE system simultaneously. Although our algorithm is one of the decouple direct methods in computing dynamic sensitivities of an ODE system, the step size determined by model equations can be used on the computations of the time profile and dynamic sensitivities with moderate accuracy even when sensitivity equations are more stiff than model equations. To show this algorithm can perform the dynamic sensitivity analysis on very stiff ODE systems with moderate accuracy, it is implemented and applied to two sets of chemical reactions: pyrolysis of ethane and oxidation of formaldehyde. The accuracy of this algorithm is demonstrated by comparing the dynamic parameter sensitivities obtained from this new algorithm and from the direct method with Rosenbrock stiff integrator based on the indirect method. The same dynamic sensitivity analysis was performed on an ethanol fed-batch fermentation system with a time-varying feed rate to evaluate the applicability of the algorithm to realistic models with time-dependent admissible input. Conclusion By combining the accuracy we show with the efficiency of being a decouple direct method, our algorithm is an excellent method for computing dynamic parameter sensitivities in stiff problems. We extend the scope of classical dynamic sensitivity analysis to the investigation of dynamic log gains of models with time-dependent admissible input. PMID:19091016

Predictive Computational Modeling of the Mucosal Immune Responses during Helicobacter pylori Infection

PubMed Central

Carbo, Adria; Bassaganya-Riera, Josep; Pedragosa, Mireia; Viladomiu, Monica; Marathe, Madhav; Eubank, Stephen; Wendelsdorf, Katherine; Bisset, Keith; Hoops, Stefan; Deng, Xinwei; Alam, Maksudul; Kronsteiner, Barbara; Mei, Yongguo; Hontecillas, Raquel

2013-01-01

T helper (Th) cells play a major role in the immune response and pathology at the gastric mucosa during Helicobacter pylori infection. There is a limited mechanistic understanding regarding the contributions of CD4+ T cell subsets to gastritis development during H. pylori colonization. We used two computational approaches: ordinary differential equation (ODE)-based and agent-based modeling (ABM) to study the mechanisms underlying cellular immune responses to H. pylori and how CD4+ T cell subsets influenced initiation, progression and outcome of disease. To calibrate the model, in vivo experimentation was performed by infecting C57BL/6 mice intragastrically with H. pylori and assaying immune cell subsets in the stomach and gastric lymph nodes (GLN) on days 0, 7, 14, 30 and 60 post-infection. Our computational model reproduced the dynamics of effector and regulatory pathways in the gastric lamina propria (LP) in silico. Simulation results show the induction of a Th17 response and a dominant Th1 response, together with a regulatory response characterized by high levels of mucosal Treg) cells. We also investigated the potential role of peroxisome proliferator-activated receptor γ (PPARγ) activation on the modulation of host responses to H. pylori by using loss-of-function approaches. Specifically, in silico results showed a predominance of Th1 and Th17 cells in the stomach of the cell-specific PPARγ knockout system when compared to the wild-type simulation. Spatio-temporal, object-oriented ABM approaches suggested similar dynamics in induction of host responses showing analogous T cell distributions to ODE modeling and facilitated tracking lesion formation. In addition, sensitivity analysis predicted a crucial contribution of Th1 and Th17 effector responses as mediators of histopathological changes in the gastric mucosa during chronic stages of infection, which were experimentally validated in mice. These integrated immunoinformatics approaches characterized the induction of mucosal effector and regulatory pathways controlled by PPARγ during H. pylori infection affecting disease outcomes. PMID:24039925

Dynamics of Social Group Competition: Modeling the Decline of Religious Affiliation

NASA Astrophysics Data System (ADS)

Abrams, Daniel M.; Yaple, Haley A.; Wiener, Richard J.

2011-08-01

When social groups compete for members, the resulting dynamics may be understandable with mathematical models. We demonstrate that a simple ordinary differential equation (ODE) model is a good fit for religious shift by comparing it to a new international data set tracking religious nonaffiliation. We then generalize the model to include the possibility of nontrivial social interaction networks and examine the limiting case of a continuous system. Analytical and numerical predictions of this generalized system, which is robust to polarizing perturbations, match those of the original ODE model and justify its agreement with real-world data. The resulting predictions highlight possible causes of social shift and suggest future lines of research in both physics and sociology.

Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method.

PubMed

Jia, Gengjie; Stephanopoulos, Gregory N; Gunawan, Rudiyanto

2011-07-15

Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.

Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

PubMed Central

Weinberg, Seth H.; Smith, Gregory D.

2012-01-01

Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597

Simulation of Stochastic Processes by Coupled ODE-PDE

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

NASA Astrophysics Data System (ADS)

Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

2010-07-01

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

Interconnections between various analytic approaches applicable to third-order nonlinear differential equations

PubMed Central

Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

2015-01-01

We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ODEs. We establish an important interconnection between the extended Prelle–Singer procedure and λ-symmetries approach applicable to third-order ODEs to bring out the various linkages associated with these different techniques. By establishing this interconnection we demonstrate that given any one of the quantities as a starting point in the family consisting of Jacobi last multipliers, Darboux polynomials, Lie point symmetries, adjoint-symmetries, λ-symmetries, integrating factors and null forms one can derive the rest of the quantities in this family in a straightforward and unambiguous manner. We also illustrate our findings with three specific examples. PMID:27547076

Interconnections between various analytic approaches applicable to third-order nonlinear differential equations.

PubMed

Mohanasubha, R; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M

2015-04-08

We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ODEs. We establish an important interconnection between the extended Prelle-Singer procedure and λ-symmetries approach applicable to third-order ODEs to bring out the various linkages associated with these different techniques. By establishing this interconnection we demonstrate that given any one of the quantities as a starting point in the family consisting of Jacobi last multipliers, Darboux polynomials, Lie point symmetries, adjoint-symmetries, λ-symmetries, integrating factors and null forms one can derive the rest of the quantities in this family in a straightforward and unambiguous manner. We also illustrate our findings with three specific examples.

A bidirectional coupling procedure applied to multiscale respiratory modeling

NASA Astrophysics Data System (ADS)

Kuprat, A. P.; Kabilan, S.; Carson, J. P.; Corley, R. A.; Einstein, D. R.

2013-07-01

In this study, we present a novel multiscale computational framework for efficiently linking multiple lower-dimensional models describing the distal lung mechanics to imaging-based 3D computational fluid dynamics (CFDs) models of the upper pulmonary airways in order to incorporate physiologically appropriate outlet boundary conditions. The framework is an extension of the modified Newton's method with nonlinear Krylov accelerator developed by Carlson and Miller [1], Miller [2] and Scott and Fenves [3]. Our extensions include the retention of subspace information over multiple timesteps, and a special correction at the end of a timestep that allows for corrections to be accepted with verified low residual with as little as a single residual evaluation per timestep on average. In the case of a single residual evaluation per timestep, the method has zero additional computational cost compared to uncoupled or unidirectionally coupled simulations. We expect these enhancements to be generally applicable to other multiscale coupling applications where timestepping occurs. In addition we have developed a "pressure-drop" residual which allows for stable coupling of flows between a 3D incompressible CFD application and another (lower-dimensional) fluid system. We expect this residual to also be useful for coupling non-respiratory incompressible fluid applications, such as multiscale simulations involving blood flow. The lower-dimensional models that are considered in this study are sets of simple ordinary differential equations (ODEs) representing the compliant mechanics of symmetric human pulmonary airway trees. To validate the method, we compare the predictions of hybrid CFD-ODE models against an ODE-only model of pulmonary airflow in an idealized geometry. Subsequently, we couple multiple sets of ODEs describing the distal lung to an imaging-based human lung geometry. Boundary conditions in these models consist of atmospheric pressure at the mouth and intrapleural pressure applied to the multiple sets of ODEs. In both the simplified geometry and in the imaging-based geometry, the performance of the method was comparable to that of monolithic schemes, in most cases requiring only a single CFD evaluation per time step. Thus, this new accelerator allows us to begin combining pulmonary CFD models with lower-dimensional models of pulmonary mechanics with little computational overhead. Moreover, because the CFD and lower-dimensional models are totally separate, this framework affords great flexibility in terms of the type and breadth of the adopted lower-dimensional model, allowing the biomedical researcher to appropriately focus on model design. Research funded by the National Heart and Blood Institute Award 1RO1HL073598.

Bootstrapping Least Squares Estimates in Biochemical Reaction Networks

PubMed Central

Linder, Daniel F.

2015-01-01

The paper proposes new computational methods of computing confidence bounds for the least squares estimates (LSEs) of rate constants in mass-action biochemical reaction network and stochastic epidemic models. Such LSEs are obtained by fitting the set of deterministic ordinary differential equations (ODEs), corresponding to the large volume limit of a reaction network, to network’s partially observed trajectory treated as a continuous-time, pure jump Markov process. In the large volume limit the LSEs are asymptotically Gaussian, but their limiting covariance structure is complicated since it is described by a set of nonlinear ODEs which are often ill-conditioned and numerically unstable. The current paper considers two bootstrap Monte-Carlo procedures, based on the diffusion and linear noise approximations for pure jump processes, which allow one to avoid solving the limiting covariance ODEs. The results are illustrated with both in-silico and real data examples from the LINE 1 gene retrotranscription model and compared with those obtained using other methods. PMID:25898769

A Bidirectional Coupling Procedure Applied to Multiscale Respiratory Modeling☆

PubMed Central

Kuprat, A.P.; Kabilan, S.; Carson, J.P.; Corley, R.A.; Einstein, D.R.

2012-01-01

In this study, we present a novel multiscale computational framework for efficiently linking multiple lower-dimensional models describing the distal lung mechanics to imaging-based 3D computational fluid dynamics (CFD) models of the upper pulmonary airways in order to incorporate physiologically appropriate outlet boundary conditions. The framework is an extension of the Modified Newton’s Method with nonlinear Krylov accelerator developed by Carlson and Miller [1, 2, 3]. Our extensions include the retention of subspace information over multiple timesteps, and a special correction at the end of a timestep that allows for corrections to be accepted with verified low residual with as little as a single residual evaluation per timestep on average. In the case of a single residual evaluation per timestep, the method has zero additional computational cost compared to uncoupled or unidirectionally coupled simulations. We expect these enhancements to be generally applicable to other multiscale coupling applications where timestepping occurs. In addition we have developed a “pressure-drop” residual which allows for stable coupling of flows between a 3D incompressible CFD application and another (lower-dimensional) fluid system. We expect this residual to also be useful for coupling non-respiratory incompressible fluid applications, such as multiscale simulations involving blood flow. The lower-dimensional models that are considered in this study are sets of simple ordinary differential equations (ODEs) representing the compliant mechanics of symmetric human pulmonary airway trees. To validate the method, we compare the predictions of hybrid CFD-ODE models against an ODE-only model of pulmonary airflow in an idealized geometry. Subsequently, we couple multiple sets of ODEs describing the distal lung to an imaging-based human lung geometry. Boundary conditions in these models consist of atmospheric pressure at the mouth and intrapleural pressure applied to the multiple sets of ODEs. In both the simplified geometry and in the imaging-based geometry, the performance of the method was comparable to that of monolithic schemes, in most cases requiring only a single CFD evaluation per time step. Thus, this new accelerator allows us to begin combining pulmonary CFD models with lower-dimensional models of pulmonary mechanics with little computational overhead. Moreover, because the CFD and lower-dimensional models are totally separate, this framework affords great flexibility in terms of the type and breadth of the adopted lower-dimensional model, allowing the biomedical researcher to appropriately focus on model design. Research funded by the National Heart and Blood Institute Award 1RO1HL073598. PMID:24347680

From differential to difference equations for first order ODEs

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.

Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

PubMed

Griffith, Mark; Courtney, Tod; Peccoud, Jean; Sanders, William H

2006-11-15

The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. Software and benchmark models used for this publication can be made available upon request from the authors.

Hybrid Equation/Agent-Based Model of Ischemia-Induced Hyperemia and Pressure Ulcer Formation Predicts Greater Propensity to Ulcerate in Subjects with Spinal Cord Injury

PubMed Central

Solovyev, Alexey; Mi, Qi; Tzen, Yi-Ting; Brienza, David; Vodovotz, Yoram

2013-01-01

Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI). People with SCI also exhibit differential blood flow properties in non-ulcerated skin. We hypothesized that a computer simulation of the pressure ulcer formation process, informed by data regarding skin blood flow and reactive hyperemia in response to pressure, could provide insights into the pathogenesis and effective treatment of post-SCI pressure ulcers. Agent-Based Models (ABM) are useful in settings such as pressure ulcers, in which spatial realism is important. Ordinary Differential Equation-based (ODE) models are useful when modeling physiological phenomena such as reactive hyperemia. Accordingly, we constructed a hybrid model that combines ODEs related to blood flow along with an ABM of skin injury, inflammation, and ulcer formation. The relationship between pressure and the course of ulcer formation, as well as several other important characteristic patterns of pressure ulcer formation, was demonstrated in this model. The ODE portion of this model was calibrated to data related to blood flow following experimental pressure responses in non-injured human subjects or to data from people with SCI. This model predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects, and thus may serve as novel diagnostic platform for post-SCI ulcer formation. PMID:23696726

Uncertainty quantification in Eulerian-Lagrangian models for particle-laden flows

NASA Astrophysics Data System (ADS)

Fountoulakis, Vasileios; Jacobs, Gustaaf; Udaykumar, Hs

2017-11-01

A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based Eulerian-Lagrangian model, which traces individual particles in their Lagrangian frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear Eulerian-Lagrangian systems. This research is supported by AFOSR under Grant FA9550-16-1-0008.

Investigation of the Stability of POD-Galerkin Techniques for Reduced Order Model Development

DTIC Science & Technology

2016-01-09

symmetrizing the higher- order PDE with a preconditioning matrix. Rowley et al. also pointed out that defining a proper inner product can be important when...equations. The ROM is obtained by employing Galerkin’s method to reduce the high-order PDEs to a lower-order ODE system by means of POD eigen-bases...employing Galerkin’s method to reduce the high-order PDEs to a lower-order ODE system by means of POD eigen-bases. Possible solutions of the ROM stability

Exploration of POD-Galerkin Techniques for Developing Reduced Order Models of the Euler Equations

DTIC Science & Technology

2015-07-01

modes [1]. Barone et al [15, 16] proposed to stabilize the reduced system by symmetrizing the higher-order PDE with a preconditioning matrix. Rowley et...advection scalar equation. The ROM is obtained by employing Galerkin’s method to reduce the high-order PDEs to a lower- order ODE system by means of POD...high-order PDEs to a lower-order ODE system by means of POD eigen-bases. For purposes of this study, a linearized version of the Euler equations is

ODES (Online Data Extraction Service) for hydrology

NASA Astrophysics Data System (ADS)

Rosmorduc, Vinca; Birol, Florence; Briol, Frederic; Bronner, Emilie; Dibarboure, Gerald; Guinle, Thierry; Nicolas, Clara; Nino, Fernando; Valladeau, Guillaume

2015-04-01

AVISO+ proposes a new dissemination service, the Online Data Extraction Service (ODES), in order to provide users and applications with a wider range of altimetry-derived data (including high-resolution and experimental data). The platform is designed to distribute both operational products from CNES and partner Agencies (Eumetsat, ESA, NOAA, NASA) but also research-grade data from LEGOS/CTOH and CLS and other contributions from the OSTST research community. An example of use of ODES to extract hydrology experimental expert product (from Pistach processor) for hydrology will be shown. ODES is available at http://odes.altimetry.cnes.fr, download with your Aviso FTP login / password.

ODES (Online Data Extraction Service) for cryosphere studies

NASA Astrophysics Data System (ADS)

Rosmorduc, Vinca; Birol, Florence; Briol, Frederic; Bronner, Emilie; Dibarboure, Gerald; Guinle, Thierry; Nicolas, Clara; Nino, Fernando; Valladeau, Guillaume

2015-04-01

AVISO+ proposes a new dissemination service, the Online Data Extraction Service (ODES), in order to provide users and applications with a wider range of altimetry-derived data (including high-resolution and experimental data). The platform is designed to distribute both operational products from CNES and partner Agencies (Eumetsat, ESA, NOAA, NASA) but also research-grade data from LEGOS/CTOH and CLS and other contributions from the OSTST research community. An example of the use of ODES to extract AltiKa experimental expert products (from PEACHI prototype) over iced areas will be shown. ODES is available at http://odes.altimetry.cnes.fr, download with your Aviso FTP login / password.

Fitting ordinary differential equations to short time course data.

PubMed

Brewer, Daniel; Barenco, Martino; Callard, Robin; Hubank, Michael; Stark, Jaroslav

2008-02-28

Ordinary differential equations (ODEs) are widely used to model many systems in physics, chemistry, engineering and biology. Often one wants to compare such equations with observed time course data, and use this to estimate parameters. Surprisingly, practical algorithms for doing this are relatively poorly developed, particularly in comparison with the sophistication of numerical methods for solving both initial and boundary value problems for differential equations, and for locating and analysing bifurcations. A lack of good numerical fitting methods is particularly problematic in the context of systems biology where only a handful of time points may be available. In this paper, we present a survey of existing algorithms and describe the main approaches. We also introduce and evaluate a new efficient technique for estimating ODEs linear in parameters particularly suited to situations where noise levels are high and the number of data points is low. It employs a spline-based collocation scheme and alternates linear least squares minimization steps with repeated estimates of the noise-free values of the variables. This is reminiscent of expectation-maximization methods widely used for problems with nuisance parameters or missing data.

Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.

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

Robinson, Brandon; Rocha da Costa, Leandro Jose; Poirel, Dominique

Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from themore » fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.« less

A System of ODEs for a Perturbation of a Minimal Mass Soliton

NASA Astrophysics Data System (ADS)

Marzuola, Jeremy L.; Raynor, Sarah; Simpson, Gideon

2010-08-01

We study soliton solutions to the nonlinear Schrödinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We consider a small perturbation of a minimal mass soliton and identify a system of ODEs extending the work of Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565-1607, 2003), which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of Pelinovsky et al. (Phys. Rev. E 53(2):1940-1953, 1996). Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.

Regioisomeric distribution of 9‐ and 13‐hydroperoxy linoleic acid in vegetable oils during storage and heating

PubMed Central

Zaunschirm, Mathias; Lach, Judith; Unterberger, Laura; Kopic, Antonio; Keßler, Claudia; Kienesberger, Julia; Pischetsrieder, Monika; Eggersdorfer, Manfred; Riegger, Christoph; Somoza, Veronika

2017-01-01

Abstract BACKGROUND The oxidative deterioration of vegetable oils is commonly measured by the peroxide value, thereby not considering the contribution of individual lipid hydroperoxide isomers, which might have different bioactive effects. Thus, the formation of 9‐ and 13‐hydroperoxy octadecadienoic acid (9‐HpODE and 13‐ HpODE), was quantified after short‐term heating and conditions representative of long‐term domestic storage in samples of linoleic acid, canola, sunflower and soybean oil, by means of stable isotope dilution analysis–liquid chromatography‐mass spectroscopy. RESULTS Although heating of pure linoleic acid at 180 °C for 30 min led to an almost complete loss of 9‐HpODE and 13‐HpODE, heating of canola, sunflower and soybean oil resulted in the formation of 5.74 ± 3.32, 2.00 ± 1.09, 16.0 ± 2.44 mmol L–1 13‐HpODE and 13.8 ± 8.21, 10.0 ± 6.74 and 45.2 ± 6.23 mmol L–1 9‐HpODE. An almost equimolar distribution of the 9‐ and 13‐HpODE was obtained during household‐representative storage conditions after 56 days, whereas, under heating conditions, an approximately 2.4‐, 2.8‐ and 5.0‐fold (P ≤ 0.001) higher concentration of 9‐HpODE than 13‐HpODE was detected in canola, soybean and sunflower oil, respectively. CONCLUSION A temperature‐dependent distribution of HpODE regioisomers could be shown in vegetable oils, suggesting their application as markers of lipid oxidation in oils used for short‐term heating. © 2017 The Authors. Journal of The Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry. PMID:29095495

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study.

PubMed

MacLean, Adam L; Harrington, Heather A; Stumpf, Michael P H; Byrne, Helen M

2016-01-01

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

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

Du, Qiang, E-mail: jyanghkbu@gmail.com; Yang, Jiang, E-mail: qd2125@columbia.edu

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simplemore » ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.« less

State-transition diagrams for biologists.

PubMed

Bersini, Hugues; Klatzmann, David; Six, Adrien; Thomas-Vaslin, Véronique

2012-01-01

It is clearly in the tradition of biologists to conceptualize the dynamical evolution of biological systems in terms of state-transitions of biological objects. This paper is mainly concerned with (but obviously not limited too) the immunological branch of biology and shows how the adoption of UML (Unified Modeling Language) state-transition diagrams can ease the modeling, the understanding, the coding, the manipulation or the documentation of population-based immune software model generally defined as a set of ordinary differential equations (ODE), describing the evolution in time of populations of various biological objects. Moreover, that same UML adoption naturally entails a far from negligible representational economy since one graphical item of the diagram might have to be repeated in various places of the mathematical model. First, the main graphical elements of the UML state-transition diagram and how they can be mapped onto a corresponding ODE mathematical model are presented. Then, two already published immune models of thymocyte behavior and time evolution in the thymus, the first one originally conceived as an ODE population-based model whereas the second one as an agent-based one, are refactored and expressed in a state-transition form so as to make them much easier to understand and their respective code easier to access, to modify and run. As an illustrative proof, for any immunologist, it should be possible to understand faithfully enough what the two software models are supposed to reproduce and how they execute with no need to plunge into the Java or Fortran lines.

State-Transition Diagrams for Biologists

PubMed Central

Bersini, Hugues; Klatzmann, David; Six, Adrien; Thomas-Vaslin, Véronique

2012-01-01

It is clearly in the tradition of biologists to conceptualize the dynamical evolution of biological systems in terms of state-transitions of biological objects. This paper is mainly concerned with (but obviously not limited too) the immunological branch of biology and shows how the adoption of UML (Unified Modeling Language) state-transition diagrams can ease the modeling, the understanding, the coding, the manipulation or the documentation of population-based immune software model generally defined as a set of ordinary differential equations (ODE), describing the evolution in time of populations of various biological objects. Moreover, that same UML adoption naturally entails a far from negligible representational economy since one graphical item of the diagram might have to be repeated in various places of the mathematical model. First, the main graphical elements of the UML state-transition diagram and how they can be mapped onto a corresponding ODE mathematical model are presented. Then, two already published immune models of thymocyte behavior and time evolution in the thymus, the first one originally conceived as an ODE population-based model whereas the second one as an agent-based one, are refactored and expressed in a state-transition form so as to make them much easier to understand and their respective code easier to access, to modify and run. As an illustrative proof, for any immunologist, it should be possible to understand faithfully enough what the two software models are supposed to reproduce and how they execute with no need to plunge into the Java or Fortran lines. PMID:22844438

Multiresolution and Explicit Methods for Vector Field Analysis and Visualization

NASA Technical Reports Server (NTRS)

1996-01-01

We first report on our current progress in the area of explicit methods for tangent curve computation. The basic idea of this method is to decompose the domain into a collection of triangles (or tetrahedra) and assume linear variation of the vector field over each cell. With this assumption, the equations which define a tangent curve become a system of linear, constant coefficient ODE's which can be solved explicitly. There are five different representation of the solution depending on the eigenvalues of the Jacobian. The analysis of these five cases is somewhat similar to the phase plane analysis often associate with critical point classification within the context of topological methods, but it is not exactly the same. There are some critical differences. Moving from one cell to the next as a tangent curve is tracked, requires the computation of the exit point which is an intersection of the solution of the constant coefficient ODE and the edge of a triangle. There are two possible approaches to this root computation problem. We can express the tangent curve into parametric form and substitute into an implicit form for the edge or we can express the edge in parametric form and substitute in an implicit form of the tangent curve. Normally the solution of a system of ODE's is given in parametric form and so the first approach is the most accessible and straightforward. The second approach requires the 'implicitization' of these parametric curves. The implicitization of parametric curves can often be rather difficult, but in this case we have been successful and have been able to develop algorithms and subsequent computer programs for both approaches. We will give these details along with some comparisons in a forthcoming research paper on this topic.

GPU acceleration of Runge Kutta-Fehlberg and its comparison with Dormand-Prince method

NASA Astrophysics Data System (ADS)

Seen, Wo Mei; Gobithaasan, R. U.; Miura, Kenjiro T.

2014-07-01

There is a significant reduction of processing time and speedup of performance in computer graphics with the emergence of Graphic Processing Units (GPUs). GPUs have been developed to surpass Central Processing Unit (CPU) in terms of performance and processing speed. This evolution has opened up a new area in computing and researches where highly parallel GPU has been used for non-graphical algorithms. Physical or phenomenal simulations and modelling can be accelerated through General Purpose Graphic Processing Units (GPGPU) and Compute Unified Device Architecture (CUDA) implementations. These phenomena can be represented with mathematical models in the form of Ordinary Differential Equations (ODEs) which encompasses the gist of change rate between independent and dependent variables. ODEs are numerically integrated over time in order to simulate these behaviours. The classical Runge-Kutta (RK) scheme is the common method used to numerically solve ODEs. The Runge Kutta Fehlberg (RKF) scheme has been specially developed to provide an estimate of the principal local truncation error at each step, known as embedding estimate technique. This paper delves into the implementation of RKF scheme for GPU devices and compares its result with Dorman Prince method. A pseudo code is developed to show the implementation in detail. Hence, practitioners will be able to understand the data allocation in GPU, formation of RKF kernels and the flow of data to/from GPU-CPU upon RKF kernel evaluation. The pseudo code is then written in C Language and two ODE models are executed to show the achievable speedup as compared to CPU implementation. The accuracy and efficiency of the proposed implementation method is discussed in the final section of this paper.

Influence of climate variability on near-surface ozone depletion events in the Arctic spring

NASA Astrophysics Data System (ADS)

Koo, Ja-Ho; Wang, Yuhang; Jiang, Tianyu; Deng, Yi; Oltmans, Samuel J.; Solberg, Sverre

2014-04-01

Near-surface ozone depletion events (ODEs) generally occur in the Arctic spring, and the frequency shows large interannual variations. We use surface ozone measurements at Barrow, Alert, and Zeppelinfjellet to analyze if their variations are due to climate variability. In years with frequent ODEs at Barrow and Alert, the western Pacific (WP) teleconnection pattern is usually in its negative phase, during which the Pacific jet is strengthened but the storm track originated over the western Pacific is weakened. Both factors tend to reduce the transport of ozone-rich air mass from midlatitudes to the Arctic, creating a favorable environment for the ODEs. The correlation of ODE frequencies at Zeppelinfjellet with WP indices is higher in the 2000s, reflecting stronger influence of the WP pattern in recent decade to cover ODEs in broader Arctic regions. We find that the WP pattern can be used to diagnose ODE changes and subsequent environmental impacts in the Arctic spring.

Modeling eutrophic lakes: From mass balance laws to ordinary differential equations

NASA Astrophysics Data System (ADS)

Marasco, Addolorata; Ferrara, Luciano; Romano, Antonio

Starting from integral balance laws, a model based on nonlinear ordinary differential equations (ODEs) describing the evolution of Phosphorus cycle in a lake is proposed. After showing that the usual homogeneous model is not compatible with the mixture theory, we prove that an ODEs model still holds but for the mean values of the state variables provided that the nonhomogeneous involved fields satisfy suitable conditions. In this model the trophic state of a lake is described by the mean densities of Phosphorus in water and sediments, and phytoplankton biomass. All the quantities appearing in the model can be experimentally evaluated. To propose restoration programs, the evolution of these state variables toward stable steady state conditions is analyzed. Moreover, the local stability analysis is performed with respect to all the model parameters. Some numerical simulations and a real application to lake Varese conclude the paper.

Influence of human behavior on cholera dynamics

PubMed Central

Wang, Xueying; Gao, Daozhou; Wang, Jin

2015-01-01

This paper is devoted to studying the impact of human behavior on cholera infection. We start with a cholera ordinary differential equation (ODE) model that incorporates human behavior via modeling disease prevalence dependent contact rates for direct and indirect transmissions and infectious host shedding. Local and global dynamics of the model are analyzed with respect to the basic reproduction number. We then extend the ODE model to a reaction-convection-diffusion partial differential equation (PDE) model that accounts for the movement of both human hosts and bacteria. Particularly, we investigate the cholera spreading speed by analyzing the traveling wave solutions of the PDE model, and disease threshold dynamics by numerically evaluating the basic reproduction number of the PDE model. Our results show that human behavior can reduce (a) the endemic and epidemic levels, (b) cholera spreading speeds and (c) the risk of infection (characterized by the basic reproduction number). PMID:26119824

Parameter estimation in tree graph metabolic networks.

PubMed

Astola, Laura; Stigter, Hans; Gomez Roldan, Maria Victoria; van Eeuwijk, Fred; Hall, Robert D; Groenenboom, Marian; Molenaar, Jaap J

2016-01-01

We study the glycosylation processes that convert initially toxic substrates to nutritionally valuable metabolites in the flavonoid biosynthesis pathway of tomato (Solanum lycopersicum) seedlings. To estimate the reaction rates we use ordinary differential equations (ODEs) to model the enzyme kinetics. A popular choice is to use a system of linear ODEs with constant kinetic rates or to use Michaelis-Menten kinetics. In reality, the catalytic rates, which are affected among other factors by kinetic constants and enzyme concentrations, are changing in time and with the approaches just mentioned, this phenomenon cannot be described. Another problem is that, in general these kinetic coefficients are not always identifiable. A third problem is that, it is not precisely known which enzymes are catalyzing the observed glycosylation processes. With several hundred potential gene candidates, experimental validation using purified target proteins is expensive and time consuming. We aim at reducing this task via mathematical modeling to allow for the pre-selection of most potential gene candidates. In this article we discuss a fast and relatively simple approach to estimate time varying kinetic rates, with three favorable properties: firstly, it allows for identifiable estimation of time dependent parameters in networks with a tree-like structure. Secondly, it is relatively fast compared to usually applied methods that estimate the model derivatives together with the network parameters. Thirdly, by combining the metabolite concentration data with a corresponding microarray data, it can help in detecting the genes related to the enzymatic processes. By comparing the estimated time dynamics of the catalytic rates with time series gene expression data we may assess potential candidate genes behind enzymatic reactions. As an example, we show how to apply this method to select prominent glycosyltransferase genes in tomato seedlings.

One-dimensional Numerical Model of Transient Discharges in Air of a Spatial Plasma Ignition Device

NASA Astrophysics Data System (ADS)

Saceleanu, Florin N.

This thesis examines the modes of discharge of a plasma ignition device. Oscilloscope data of the discharge voltage and current are analyzed for various pressures in air at ambient temperature. It is determined that the discharge operates in 2 modes: a glow discharge and a postulated streamer discharge. Subsequently, a 1-dimensional fluid simulation of plasma using the finite volume method (FVM) is developed to gain insight into the particle kinetics. Transient results of the simulation agree with theories of electric discharges; however, quasi-steady state results were not reached due to high diffusion time of ions in air. Next, an ordinary differential equation (ODE) is derived to understand the discharge transition. Simulated results were used to estimate the voltage waveform, which describes the ODE's forcing function; additional simulated results were used to estimate the discharge current and the ODE's non-linearity. It is found that the ODE's non-linearity increases exponentially for capacitive discharges. It is postulated that the non-linearity defines the mode transition observed experimentally. The research is motivated by Spatial Plasma Discharge Ignition (SPDI), an innovative ignition system postulated to increase combustion efficiency in automobile engines for up to 9%. The research thus far can only hypothesize SPDI's benefits on combustion, based on the literature review and the modes of discharge.

Identifying interactions in the time and frequency domains in local and global networks - A Granger Causality Approach.

PubMed

Zou, Cunlu; Ladroue, Christophe; Guo, Shuixia; Feng, Jianfeng

2010-06-21

Reverse-engineering approaches such as Bayesian network inference, ordinary differential equations (ODEs) and information theory are widely applied to deriving causal relationships among different elements such as genes, proteins, metabolites, neurons, brain areas and so on, based upon multi-dimensional spatial and temporal data. There are several well-established reverse-engineering approaches to explore causal relationships in a dynamic network, such as ordinary differential equations (ODE), Bayesian networks, information theory and Granger Causality. Here we focused on Granger causality both in the time and frequency domain and in local and global networks, and applied our approach to experimental data (genes and proteins). For a small gene network, Granger causality outperformed all the other three approaches mentioned above. A global protein network of 812 proteins was reconstructed, using a novel approach. The obtained results fitted well with known experimental findings and predicted many experimentally testable results. In addition to interactions in the time domain, interactions in the frequency domain were also recovered. The results on the proteomic data and gene data confirm that Granger causality is a simple and accurate approach to recover the network structure. Our approach is general and can be easily applied to other types of temporal data.

Generalization of the Bernoulli ODE

ERIC Educational Resources Information Center

Azevedo, Douglas; Valentino, Michele C.

2017-01-01

In this note, we propose a generalization of the famous Bernoulli differential equation by introducing a class of nonlinear first-order ordinary differential equations (ODEs). We provide a family of solutions for this introduced class of ODEs and also we present some examples in order to illustrate the applications of our result.

HiDi: an efficient reverse engineering schema for large-scale dynamic regulatory network reconstruction using adaptive differentiation.

PubMed

Deng, Yue; Zenil, Hector; Tegnér, Jesper; Kiani, Narsis A

2017-12-15

The use of differential equations (ODE) is one of the most promising approaches to network inference. The success of ODE-based approaches has, however, been limited, due to the difficulty in estimating parameters and by their lack of scalability. Here, we introduce a novel method and pipeline to reverse engineer gene regulatory networks from gene expression of time series and perturbation data based upon an improvement on the calculation scheme of the derivatives and a pre-filtration step to reduce the number of possible links. The method introduces a linear differential equation model with adaptive numerical differentiation that is scalable to extremely large regulatory networks. We demonstrate the ability of this method to outperform current state-of-the-art methods applied to experimental and synthetic data using test data from the DREAM4 and DREAM5 challenges. Our method displays greater accuracy and scalability. We benchmark the performance of the pipeline with respect to dataset size and levels of noise. We show that the computation time is linear over various network sizes. The Matlab code of the HiDi implementation is available at: www.complexitycalculator.com/HiDiScript.zip. hzenilc@gmail.com or narsis.kiani@ki.se. Supplementary data are available at Bioinformatics online. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Oscillations in epidemic models with spread of awareness.

PubMed

Just, Winfried; Saldaña, Joan; Xin, Ying

2018-03-01

We study ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models have mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes. Our results show that such oscillations are ruled out in Susceptible-Aware-Infectious-Susceptible models with a single compartment of aware hosts, but can occur if we consider two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts.

Target mediated drug disposition with drug–drug interaction, Part II: competitive and uncompetitive cases

PubMed Central

Jusko, William J.; Schropp, Johannes

2017-01-01

We present competitive and uncompetitive drug–drug interaction (DDI) with target mediated drug disposition (TMDD) equations and investigate their pharmacokinetic DDI properties. For application of TMDD models, quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are necessary to reduce the number of parameters. To realize those approximations of DDI TMDD models, we derive an ordinary differential equation (ODE) representation formulated in free concentration and free receptor variables. This ODE formulation can be straightforward implemented in typical PKPD software without solving any non-linear equation system arising from the QE or QSS approximation of the rapid binding assumptions. This manuscript is the second in a series to introduce and investigate DDI TMDD models and to apply the QE or QSS approximation. PMID:28074396

Pattern formation for NO+N H3 on Pt(100): Two-dimensional numerical results

NASA Astrophysics Data System (ADS)

Uecker, Hannes

2005-01-01

The Lombardo-Fink-Imbihl model of the NO+NH3 reaction on a Pt(100) surface consists of seven coupled ordinary differential equations (ODE) and shows stable relaxation oscillations with sharp transitions in the relevant temperature range. Here we study numerically the effect of coupling of these oscillators by surface diffusion in two dimensions. We find different types of patterns, in particular phase clusters and standing waves. In models of related surface reactions such clustered solutions are known to exist only under a global coupling through the gas phase. This global coupling is replaced here by relatively fast diffusion of two variables which are kinetically slaved in the ODE. We also compare our simulations with experimental results and discuss some shortcomings of the model.

Exploring Students' Understanding of Ordinary Differential Equations Using Computer Algebraic System (CAS)

ERIC Educational Resources Information Center

Maat, Siti Mistima; Zakaria, Effandi

2011-01-01

Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…

SBML-PET: a Systems Biology Markup Language-based parameter estimation tool.

PubMed

Zi, Zhike; Klipp, Edda

2006-11-01

The estimation of model parameters from experimental data remains a bottleneck for a major breakthrough in systems biology. We present a Systems Biology Markup Language (SBML) based Parameter Estimation Tool (SBML-PET). The tool is designed to enable parameter estimation for biological models including signaling pathways, gene regulation networks and metabolic pathways. SBML-PET supports import and export of the models in the SBML format. It can estimate the parameters by fitting a variety of experimental data from different experimental conditions. SBML-PET has a unique feature of supporting event definition in the SMBL model. SBML models can also be simulated in SBML-PET. Stochastic Ranking Evolution Strategy (SRES) is incorporated in SBML-PET for parameter estimation jobs. A classic ODE Solver called ODEPACK is used to solve the Ordinary Differential Equation (ODE) system. http://sysbio.molgen.mpg.de/SBML-PET/. The website also contains detailed documentation for SBML-PET.

OFFl Models: Novel Schema for Dynamical Modeling of Biological Systems

PubMed Central

2016-01-01

Flow diagrams are a common tool used to help build and interpret models of dynamical systems, often in biological contexts such as consumer-resource models and similar compartmental models. Typically, their usage is intuitive and informal. Here, we present a formalized version of flow diagrams as a kind of weighted directed graph which follow a strict grammar, which translate into a system of ordinary differential equations (ODEs) by a single unambiguous rule, and which have an equivalent representation as a relational database. (We abbreviate this schema of “ODEs and formalized flow diagrams” as OFFL.) Drawing a diagram within this strict grammar encourages a mental discipline on the part of the modeler in which all dynamical processes of a system are thought of as interactions between dynamical species that draw parcels from one or more source species and deposit them into target species according to a set of transformation rules. From these rules, the net rate of change for each species can be derived. The modeling schema can therefore be understood as both an epistemic and practical heuristic for modeling, serving both as an organizational framework for the model building process and as a mechanism for deriving ODEs. All steps of the schema beyond the initial scientific (intuitive, creative) abstraction of natural observations into model variables are algorithmic and easily carried out by a computer, thus enabling the future development of a dedicated software implementation. Such tools would empower the modeler to consider significantly more complex models than practical limitations might have otherwise proscribed, since the modeling framework itself manages that complexity on the modeler’s behalf. In this report, we describe the chief motivations for OFFL, carefully outline its implementation, and utilize a range of classic examples from ecology and epidemiology to showcase its features. PMID:27270918

Quantum Dynamics of Multi Harmonic Oscillators Described by Time Variant Conic Hamiltonian and their Use in Contemporary Sciences

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

Demiralp, Metin

This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if themore » dynamic of the system is related to a set of ODEs.« less

Boundary control for a constrained two-link rigid-flexible manipulator with prescribed performance

NASA Astrophysics Data System (ADS)

Cao, Fangfei; Liu, Jinkun

2018-05-01

In this paper, we consider a boundary control problem for a constrained two-link rigid-flexible manipulator. The nonlinear system is described by hybrid ordinary differential equation-partial differential equation (ODE-PDE) dynamic model. Based on the coupled ODE-PDE model, boundary control is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. With the help of prescribed performance functions, the tracking error can converge to an arbitrarily small residual set and the convergence rate is no less than a certain pre-specified value. Asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle extended to infinite-dimensional system. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.

Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs

NASA Astrophysics Data System (ADS)

Niemeyer, Kyle E.; Sung, Chih-Jen

2014-01-01

The chemical kinetics ODEs arising from operator-split reactive-flow simulations were solved on GPUs using explicit integration algorithms. Nonstiff chemical kinetics of a hydrogen oxidation mechanism (9 species and 38 irreversible reactions) were computed using the explicit fifth-order Runge-Kutta-Cash-Karp method, and the GPU-accelerated version performed faster than single- and six-core CPU versions by factors of 126 and 25, respectively, for 524,288 ODEs. Moderately stiff kinetics, represented with mechanisms for hydrogen/carbon-monoxide (13 species and 54 irreversible reactions) and methane (53 species and 634 irreversible reactions) oxidation, were computed using the stabilized explicit second-order Runge-Kutta-Chebyshev (RKC) algorithm. The GPU-based RKC implementation demonstrated an increase in performance of nearly 59 and 10 times, for problem sizes consisting of 262,144 ODEs and larger, than the single- and six-core CPU-based RKC algorithms using the hydrogen/carbon-monoxide mechanism. With the methane mechanism, RKC-GPU performed more than 65 and 11 times faster, for problem sizes consisting of 131,072 ODEs and larger, than the single- and six-core RKC-CPU versions, and up to 57 times faster than the six-core CPU-based implicit VODE algorithm on 65,536 ODEs. In the presence of more severe stiffness, such as ethylene oxidation (111 species and 1566 irreversible reactions), RKC-GPU performed more than 17 times faster than RKC-CPU on six cores for 32,768 ODEs and larger, and at best 4.5 times faster than VODE on six CPU cores for 65,536 ODEs. With a larger time step size, RKC-GPU performed at best 2.5 times slower than six-core VODE for 8192 ODEs and larger. Therefore, the need for developing new strategies for integrating stiff chemistry on GPUs was discussed.

Asymptotic integration algorithms for first-order ODEs with application to viscoplasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Yao, Minwu; Walker, Kevin P.

1992-01-01

When constructing an algorithm for the numerical integration of a differential equation, one must first convert the known ordinary differential equation (ODE), which is defined at a point, into an ordinary difference equation (O(delta)E), which is defined over an interval. Asymptotic, generalized, midpoint, and trapezoidal, O(delta)E algorithms are derived for a nonlinear first order ODE written in the form of a linear ODE. The asymptotic forward (typically underdamped) and backward (typically overdamped) integrators bound these midpoint and trapezoidal integrators, which tend to cancel out unwanted numerical damping by averaging, in some sense, the forward and backward integrations. Viscoplasticity presents itself as a system of nonlinear, coupled first-ordered ODE's that are mathematically stiff, and therefore, difficult to numerically integrate. They are an excellent application for the asymptotic integrators. Considering a general viscoplastic structure, it is demonstrated that one can either integrate the viscoplastic stresses or their associated eigenstrains.

A solution to neural field equations by a recurrent neural network method

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2012-09-01

Neural field equations (NFE) are used to model the activity of neurons in the brain, it is introduced from a single neuron 'integrate-and-fire model' starting point. The neural continuum is spatially discretized for numerical studies, and the governing equations are modeled as a system of ordinary differential equations. In this article the recurrent neural network approach is used to solve this system of ODEs. This consists of a technique developed by combining the standard numerical method of finite-differences with the Hopfield neural network. The architecture of the net, energy function, updating equations, and algorithms are developed for the NFE model. A Hopfield Neural Network is then designed to minimize the energy function modeling the NFE. Results obtained from the Hopfield-finite-differences net show excellent performance in terms of accuracy and speed. The parallelism nature of the Hopfield approaches may make them easier to implement on fast parallel computers and give them the speed advantage over the traditional methods.

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

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

Hoang, Tuan L.; Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, CA 94550; Marian, Jaime, E-mail: jmarian@ucla.edu

2015-11-01

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a proceduremore » for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe{sup 3+}, He{sup +} and H{sup +}) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.« less

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

NASA Astrophysics Data System (ADS)

Hoang, Tuan L.; Marian, Jaime; Bulatov, Vasily V.; Hosemann, Peter

2015-11-01

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe3+, He+ and H+) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.

ODE/IM correspondence and the Argyres-Douglas theory

NASA Astrophysics Data System (ADS)

Ito, Katsushi; Shu, Hongfei

2017-08-01

We study the quantum spectral curve of the Argyres-Douglas theories in the Nekrasov-Sahashvili limit of the Omega-background. Using the ODE/IM correspondence we investigate the quantum integrable model corresponding to the quantum spectral curve. We show that the models for the A 2 N -type theories are non-unitary coset models ( A 1)1 × ( A 1) L /( A 1) L+1 at the fractional level L=2/2N+1-2 , which appear in the study of the 4d/2d correspondence of N = 2 superconformal field theories. Based on the WKB analysis, we clarify the relation between the Y-functions and the quantum periods and study the exact Bohr-Sommerfeld quantization condition for the quantum periods. We also discuss the quantum spectral curves for the D and E type theories.

An invariant asymptotic formula for solutions of second-order linear ODE's

NASA Technical Reports Server (NTRS)

Gingold, H.

1988-01-01

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

Studies of Arctic Tropospheric Ozone Depletion Events Through Buoy-Borne Observations and Laboratory Studies

NASA Astrophysics Data System (ADS)

Halfacre, John W.

The photochemically-induced destruction of ground-level Arctic ozone in the Arctic occurs at the onset of spring, in concert with polar sunrise. Solar radiation is believed to stimulate a series of reactions that cause the production and release of molecular halogens from frozen, salty surfaces, though this mechanism is not yet well understood. The subsequent photolysis of molecular halogens produces reactive halogen atoms that remove ozone from the atmosphere in these so-called "Ozone Depletion Events" (ODEs). Given that much of the Arctic region is sunlit, meteorologically stable, and covered by saline ice and snow, it is expected that ODEs could be a phenomenon that occurs across the entire Arctic region. Indeed, an ever-growing body of evidence from coastal sites indicates that Arctic air masses devoid of O3 most often pass over sea ice-covered regions before arriving at an observation site, suggesting ODE chemistry occurs upwind over the frozen Arctic Ocean. However, outside of coastal observations, there exist very few long-term observations from the Arctic Ocean from which quantitative assessments of basic ODE characteristics can be made. This work presents the interpretation of ODEs through unique chemical and meteorological observations from several ice-tethered buoys deployed around the Arctic Ocean. These observations include detection of ozone, bromine monoxide, and measurements of temperature, relative humidity, atmospheric pressure, wind speed, and wind direction. To assess whether the O-Buoys were observing locally based depletion chemistry or the transport of ozone-poor air masses, periods of ozone decay were interpreted based on current understanding of ozone depletion kinetics, which are believed to follow a pseudo-first order rate law. In addition, the spatial extents of ODEs were estimated using air mass trajectory modeling to assess whether they are a localized or synoptic phenomenon. Results indicate that current understanding of the responsible chemical mechanisms are lacking, ODEs are observed primarily due to air mass transport (even in the Arctic Ocean), or some combination of both. Air mass trajectory modeling was also used in tandem with remote sensing observations of sea ice to determine the types of surfaces air masses were exposed to before arriving at O-Buoys. The impact of surface exposure was subsequently compared with local meteorology to assess which variables had the most effect on O 3 variability. For two observation sites, the impact of local meteorology was significantly stronger than air mass history, while a third was inconclusive. Finally, this work tests the viability of the hypothesis that initial production of molecular halogens from frozen saline surfaces results from photolytic production of the hydroxyl radical, and could be enhanced in the presence of O3. This investigation was enabled by a custom frozen-walled flow reactor coupled with chemical ionization spectrometry. It was found that hydroxyl radical could indeed promote the production and release of iodine, bromine, and chlorine, and that this production could be enhanced in the presence of ozone.

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis.

PubMed

Tashkova, Katerina; Korošec, Peter; Silc, Jurij; Todorovski, Ljupčo; Džeroski, Sašo

2011-10-11

We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology.

Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis

PubMed Central

2011-01-01

Background We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods. Results We apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input. Conclusions Overall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology. PMID:21989196

Genome-scale fluxes predicted under the guidance of enzyme abundance using a novel hyper-cube shrink algorithm.

PubMed

Xie, Zhengwei; Zhang, Tianyu; Ouyang, Qi

2018-02-01

One of the long-expected goals of genome-scale metabolic modelling is to evaluate the influence of the perturbed enzymes on flux distribution. Both ordinary differential equation (ODE) models and constraint-based models, like Flux balance analysis (FBA), lack the capacity to perform metabolic control analysis (MCA) for large-scale networks. In this study, we developed a hyper-cube shrink algorithm (HCSA) to incorporate the enzymatic properties into the FBA model by introducing a pseudo reaction V constrained by enzymatic parameters. Our algorithm uses the enzymatic information quantitatively rather than qualitatively. We first demonstrate the concept by applying HCSA to a simple three-node network, whereby we obtained a good correlation between flux and enzyme abundance. We then validate its prediction by comparison with ODE and with a synthetic network producing voilacein and analogues in Saccharomyces cerevisiae. We show that HCSA can mimic the state-state results of ODE. Finally, we show its capability of predicting the flux distribution in genome-scale networks by applying it to sporulation in yeast. We show the ability of HCSA to operate without biomass flux and perform MCA to determine rate-limiting reactions. Algorithm was implemented by Matlab and C ++. The code is available at https://github.com/kekegg/HCSA. xiezhengwei@hsc.pku.edu.cn or qi@pku.edu.cn. Supplementary data are available at Bioinformatics online. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Effects of active links on epidemic transmission over social networks

NASA Astrophysics Data System (ADS)

Zhu, Guanghu; Chen, Guanrong; Fu, Xinchu

2017-02-01

A new epidemic model with two infection periods is developed to account for the human behavior in social network, where newly infected individuals gradually restrict most of future contacts or are quarantined, causing infectivity change from a degree-dependent form to a constant. The corresponding dynamics are formulated by a set of ordinary differential equations (ODEs) via mean-field approximation. The effects of diverse infectivity on the epidemic dynamics ​are examined, with a behavioral interpretation of the basic reproduction number. Results show that such simple adaptive reactions largely determine the impact of network structure on epidemics. Particularly, a theorem proposed by Lajmanovich and Yorke in 1976 is generalized, so that it can be applied for the analysis of the epidemic models with multi-compartments especially network-coupled ODE systems.

On framing potential features of SWCNTs and MWCNTs in mixed convective flow

NASA Astrophysics Data System (ADS)

Hayat, T.; Ullah, Siraj; Khan, M. Ijaz; Alsaedi, A.

2018-03-01

Our target in this research article is to elaborate the characteristics of Darcy-Forchheimer relation in carbon-water nanoliquid flow induced by impermeable stretched cylinder. Energy expression is modeled through viscous dissipation and nonlinear thermal radiation. Application of appropriate transformations yields nonlinear ODEs through nonlinear PDEs. Shooting technique is adopted for the computations of nonlinear ODEs. Importance of influential variables for velocity and thermal fields is elaborated graphically. Moreover rate of heat transfer and drag force are calculated and demonstrated through Tables. Our analysis reports that velocity is higher for ratio of rate constant and buoyancy factor when compared with porosity and volume fraction.

Ordinary differential equations.

PubMed

Lebl, Jiří

2013-01-01

In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.

Two-Term Asymptotic Approximation of a Cardiac Restitution Curve*

PubMed Central

Cain, John W.; Schaeffer, David G.

2007-01-01

If spatial extent is neglected, ionic models of cardiac cells consist of systems of ordinary differential equations (ODEs) which have the property of excitability, i.e., a brief stimulus produces a prolonged evolution (called an action potential in the cardiac context) before the eventual return to equilibrium. Under repeated stimulation, or pacing, cardiac tissue exhibits electrical restitution: the steady-state action potential duration (APD) at a given pacing period B shortens as B is decreased. Independent of ionic models, restitution is often modeled phenomenologically by a one-dimensional mapping of the form APDnext = f(B – APDprevious). Under some circumstances, a restitution function f can be derived as an asymptotic approximation to the behavior of an ionic model. In this paper, extending previous work, we derive the next term in such an asymptotic approximation for a particular ionic model consisting of two ODEs. The two-term approximation exhibits excellent quantitative agreement with the actual restitution curve, whereas the leading-order approximation significantly underestimates actual APD values. PMID:18080006

A 1.26 μW Cytomimetic IC Emulating Complex Nonlinear Mammalian Cell Cycle Dynamics: Synthesis, Simulation and Proof-of-Concept Measured Results.

PubMed

Houssein, Alexandros; Papadimitriou, Konstantinos I; Drakakis, Emmanuel M

2015-08-01

Cytomimetic circuits represent a novel, ultra low-power, continuous-time, continuous-value class of circuits, capable of mapping on silicon cellular and molecular dynamics modelled by means of nonlinear ordinary differential equations (ODEs). Such monolithic circuits are in principle able to emulate on chip, single or multiple cell operations in a highly parallel fashion. Cytomimetic topologies can be synthesized by adopting the Nonlinear Bernoulli Cell Formalism (NBCF), a mathematical framework that exploits the striking similarities between the equations describing weakly-inverted Metal-Oxide Semiconductor (MOS) devices and coupled nonlinear ODEs, typically appearing in models of naturally encountered biochemical systems. The NBCF maps biological state variables onto strictly positive subthreshold MOS circuit currents. This paper presents the synthesis, the simulation and proof-of-concept chip results corresponding to the emulation of a complex cellular network mechanism, the skeleton model for the network of Cyclin-dependent Kinases (CdKs) driving the mammalian cell cycle. This five variable nonlinear biological model, when appropriate model parameter values are assigned, can exhibit multiple oscillatory behaviors, varying from simple periodic oscillations, to complex oscillations such as quasi-periodicity and chaos. The validity of our approach is verified by simulated results with realistic process parameters from the commercially available AMS 0.35 μm technology and by chip measurements. The fabricated chip occupies an area of 2.27 mm2 and consumes a power of 1.26 μW from a power supply of 3 V. The presented cytomimetic topology follows closely the behavior of its biological counterpart, exhibiting similar time-dependent solutions of the Cdk complexes, the transcription factors and the proteins.

The Local Brewery: A Project for Use in Differential Equations Courses

ERIC Educational Resources Information Center

Starling, James K.; Povich, Timothy J.; Findlay, Michael

2016-01-01

We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

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

Luchtenburg, Dirk M., E-mail: dluchten@cooper.edu; Brunton, Steven L.; Rowley, Clarence W.

2014-10-01

We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The compositionmore » of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.« less

A Textbook for a First Course in Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zingg, D. W.; Pulliam, T. H.; Nixon, David (Technical Monitor)

1999-01-01

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Estimating division and death rates from CFSE data

NASA Astrophysics Data System (ADS)

de Boer, Rob J.; Perelson, Alan S.

2005-12-01

The division tracking dye, carboxyfluorescin diacetate succinimidyl ester (CFSE) is currently the most informative labeling technique for characterizing the division history of cells in the immune system. Gett and Hodgkin (Nat. Immunol. 1 (2000) 239-244) have proposed to normalize CFSE data by the 2-fold expansion that is associated with each division, and have argued that the mean of the normalized data increases linearly with time, t, with a slope reflecting the division rate p. We develop a number of mathematical models for the clonal expansion of quiescent cells after stimulation and show, within the context of these models, under which conditions this approach is valid. We compare three means of the distribution of cells over the CFSE profile at time t: the mean, [mu](t), the mean of the normalized distribution, [mu]2(t), and the mean of the normalized distribution excluding nondivided cells, .In the simplest models, which deal with homogeneous populations of cells with constant division and death rates, the normalized frequency distribution of the cells over the respective division numbers is a Poisson distribution with mean [mu]2(t)=pt, where p is the division rate. The fact that in the data these distributions seem Gaussian is therefore insufficient to establish that the times at which cells are recruited into the first division have a Gaussian variation because the Poisson distribution approaches the Gaussian distribution for large pt. Excluding nondivided cells complicates the data analysis because , and only approaches a slope p after an initial transient.In models where the first division of the quiescent cells takes longer than later divisions, all three means have an initial transient before they approach an asymptotic regime, which is the expected [mu](t)=2pt and . Such a transient markedly complicates the data analysis. After the same initial transients, the normalized cell numbers tend to decrease at a rate e-dt, where d is the death rate.Nonlinear parameter fitting of CFSE data obtained from Gett and Hodgkin to ordinary differential equation (ODE) models with first-order terms for cell proliferation and death gave poor fits to the data. The Smith-Martin model with an explicit time delay for the deterministic phase of the cell cycle performed much better. Nevertheless, the insights gained from analysis of the ODEs proved useful as we showed by generating virtual CFSE data with a simulation model, where cell cycle times were drawn from various distributions, and then computing the various mean division numbers.

Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems

NASA Astrophysics Data System (ADS)

Cavaglieri, Daniele; Bewley, Thomas

2015-04-01

Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.

The State-of-the-Art Parabolic Equation Approximation as Applied to Underwater Acoustic Propagation with Discussions on Intensive Computations: An Invited Paper Presented at the Meeting of the Acoustical Society of America (108th) Held in Minneapolis, Minnesota on 8-12 October 1984

DTIC Science & Technology

1984-10-12

MCYwWWm M& de4 l 8.id iW d by N1wk "wt Finite Difference Reference Wavenumber Interface Split-Step Ordinary Difference Equation Wide Angle Parabolic...Problems D. Lee and S. Praiser J. Comp. & Math. with Appls., 7(2), pp. 195-202 (1981) Finite - Difference Solution to the Parabolic Wave Equation D. Lee, G...was incorporated into the ODE and finite difference models. At that time, we did not have a better implementation of the ODE solution, but we

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Designing ROW Methods

NASA Technical Reports Server (NTRS)

Freed, Alan D.

1996-01-01

There are many aspects to consider when designing a Rosenbrock-Wanner-Wolfbrandt (ROW) method for the numerical integration of ordinary differential equations (ODE's) solving initial value problems (IVP's). The process can be simplified by constructing ROW methods around good Runge-Kutta (RK) methods. The formulation of a new, simple, embedded, third-order, ROW method demonstrates this design approach.

Identification of gene regulation models from single-cell data

NASA Astrophysics Data System (ADS)

Weber, Lisa; Raymond, William; Munsky, Brian

2018-09-01

In quantitative analyses of biological processes, one may use many different scales of models (e.g. spatial or non-spatial, deterministic or stochastic, time-varying or at steady-state) or many different approaches to match models to experimental data (e.g. model fitting or parameter uncertainty/sloppiness quantification with different experiment designs). These different analyses can lead to surprisingly different results, even when applied to the same data and the same model. We use a simplified gene regulation model to illustrate many of these concerns, especially for ODE analyses of deterministic processes, chemical master equation and finite state projection analyses of heterogeneous processes, and stochastic simulations. For each analysis, we employ MATLAB and PYTHON software to consider a time-dependent input signal (e.g. a kinase nuclear translocation) and several model hypotheses, along with simulated single-cell data. We illustrate different approaches (e.g. deterministic and stochastic) to identify the mechanisms and parameters of the same model from the same simulated data. For each approach, we explore how uncertainty in parameter space varies with respect to the chosen analysis approach or specific experiment design. We conclude with a discussion of how our simulated results relate to the integration of experimental and computational investigations to explore signal-activated gene expression models in yeast (Neuert et al 2013 Science 339 584–7) and human cells (Senecal et al 2014 Cell Rep. 8 75–83)5.

Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of Neurospora crassa

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

Cannon, William; Zucker, Jeremy; Baxter, Douglas

We report the application of a recently proposed approach for modeling biological systems using a maximum entropy production rate principle in lieu of having in vivo rate constants. The method is applied in four steps: (1) a new ODE-based optimization approach based on Marcelin’s 1910 mass action equation is used to obtain the maximum entropy distribution, (2) the predicted metabolite concentrations are compared to those generally expected from experiment using a loss function from which post-translational regulation of enzymes is inferred, (3) the system is re-optimized with the inferred regulation from which rate constants are determined from the metabolite concentrationsmore » and reaction fluxes, and finally (4) a full ODE-based, mass action simulation with rate parameters and allosteric regulation is obtained. From the last step, the power characteristics and resistance of each reaction can be determined. The method is applied to the central metabolism of Neurospora crassa and the flow of material through the three competing pathways of upper glycolysis, the non-oxidative pentose phosphate pathway, and the oxidative pentose phosphate pathway are evaluated as a function of the NADP/NADPH ratio. It is predicted that regulation of phosphofructokinase (PFK) and flow through the pentose phosphate pathway are essential for preventing an extreme level of fructose 1, 6-bisphophate accumulation. Such an extreme level of fructose 1,6-bisphophate would otherwise result in a glassy cytoplasm with limited diffusion, dramatically decreasing the entropy and energy production rate and, consequently, biological competitiveness.« less

Sectional methods for aggregation problems: application to volcanic eruptions

NASA Astrophysics Data System (ADS)

Rossi, E.

2016-12-01

Particle aggregation is a general problem that is common to several scientific disciplines such as planetary formation, food industry and aerosol sciences. So far the ordinary approach to this class of problems relies on the solution of the Smoluchowski Coagulation Equations (SCE), a set of Ordinary Differential Equations (ODEs) derived from the Population Balance Equations (PBE), which basically describe the change in time of an initial grain-size distribution due to the interaction of "single" particles. The frequency of particles collisions and their sticking efficiencies depend on the specific problem under analysis, but the mathematical framework and the possible solutions to the ODEs seem to be somehow discipline-independent and very general. In this work we will focus on the problem of volcanic ash aggregation, since it represents an extreme case of complexity that can be relevant also to other disciplines. In fact volcanic ash aggregates observed during the fallouts are characterized by relevant porosities and they do not fit with simplified descriptions based on monomer-like structures or fractal geometries. In this work we propose a bidimensional approach to the PBEs which uses additive (mass) and non-additive (volume) internal descriptors in order to better characterize the evolution of volcanic ash aggregation. In particular we used sectional methods (fixed-pivot) to discretize the internal parameters space. This algorithm has been applied to a one dimensional volcanic plume model in order to investigate how the Total Grain Size Distribution (TGSD) changes throughout the erupted column in real scenarios (i.e. Eyjafjallajokull 2010, Sakurajima 2013 and Mt. Saint Helens 1980).

Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems.

PubMed

Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai

2014-10-20

We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.

Quality factors and local adaption (with applications in Eulerian hydrodynamics)

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

Crowley, W.P.

1992-06-17

Adapting the mesh to suit the solution is a technique commonly used for solving both ode`s and pde`s. For Lagrangian hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For Eulerian hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to Eulerian hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh elements. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less

Optimal control on hybrid ode systems with application to a tick disease model.

PubMed

Ding, Wandi

2007-10-01

We are considering an optimal control problem for a type of hybrid system involving ordinary differential equations and a discrete time feature. One state variable has dynamics in only one season of the year and has a jump condition to obtain the initial condition for that corresponding season in the next year. The other state variable has continuous dynamics. Given a general objective functional, existence, necessary conditions and uniqueness for an optimal control are established. We apply our approach to a tick-transmitted disease model with age structure in which the tick dynamics changes seasonally while hosts have continuous dynamics. The goal is to maximize disease-free ticks and minimize infected ticks through an optimal control strategy of treatment with acaricide. Numerical examples are given to illustrate the results.

Three-dimensional flow of Prandtl fluid with Cattaneo-Christov double diffusion

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2018-06-01

This research paper intends to investigate the 3D flow of Prandtl liquid in the existence of improved heat conduction and mass diffusion models. Flow is created by considering linearly bidirectional stretchable sheet. Thermal and concentration diffusions are considered by employing Cattaneo-Christov double diffusion models. Boundary layer approach has been used to simplify the governing PDEs. Suitable nondimensional similarity variables correspond to strong nonlinear ODEs. Optimal homotopy analysis method (OHAM) is employed for solutions development. The role of various pertinent variables on temperature and concentration are analyzed through graphs. The physical quantities such as surface drag coefficients and heat and mass transfer rates at the wall are also plotted and discussed. Our results indicate that the temperature and concentration are decreasing functions of thermal and concentration relaxation parameters respectively.

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

PubMed

Ibrahim, Bashar

2018-05-21

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

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

Differential Equations Models to Study Quorum Sensing.

PubMed

Pérez-Velázquez, Judith; Hense, Burkhard A

2018-01-01

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

The line roughness improvement with plasma coating and cure treatment for 193nm lithography and beyond

NASA Astrophysics Data System (ADS)

Zheng, Erhu; Huang, Yi; Zhang, Haiyang

2017-03-01

As CMOS technology reaches 14nm node and beyond, one of the key challenges of the extension of 193nm immersion lithography is how to control the line edge and width roughness (LER/LWR). For Self-aligned Multiple Patterning (SaMP), LER becomes larger while LWR becomes smaller as the process proceeds[1]. It means plasma etch process becomes more and more dominant for LER reduction. In this work, we mainly focus on the core etch solution including an extra plasma coating process introduced before the bottom anti reflective coating (BARC) open step, and an extra plasma cure process applied right after BARC-open step. Firstly, we leveraged the optimal design experiment (ODE) to investigate the impact of plasma coating step on LER and identified the optimal condition. ODE is an appropriate method for the screening experiments of non-linear parameters in dynamic process models, especially for high-cost-intensive industry [2]. Finally, we obtained the proper plasma coating treatment condition that has been proven to achieve 32% LER improvement compared with standard process. Furthermore, the plasma cure scheme has been also optimized with ODE method to cover the LWR degradation induced by plasma coating treatment.

ODEion--a software module for structural identification of ordinary differential equations.

PubMed

Gennemark, Peter; Wedelin, Dag

2014-02-01

In the systems biology field, algorithms for structural identification of ordinary differential equations (ODEs) have mainly focused on fixed model spaces like S-systems and/or on methods that require sufficiently good data so that derivatives can be accurately estimated. There is therefore a lack of methods and software that can handle more general models and realistic data. We present ODEion, a software module for structural identification of ODEs. Main characteristic features of the software are: • The model space is defined by arbitrary user-defined functions that can be nonlinear in both variables and parameters, such as for example chemical rate reactions. • ODEion implements computationally efficient algorithms that have been shown to efficiently handle sparse and noisy data. It can run a range of realistic problems that previously required a supercomputer. • ODEion is easy to use and provides SBML output. We describe the mathematical problem, the ODEion system itself, and provide several examples of how the system can be used. Available at: http://www.odeidentification.org.

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

NASA Technical Reports Server (NTRS)

Lucia, David J.; Beran, Philip S.; Silva, Walter A.

2003-01-01

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

A numerical investigation of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet via rational Chebyshev functions

NASA Astrophysics Data System (ADS)

Parand, Kourosh; Mahdi Moayeri, Mohammad; Latifi, Sobhan; Delkhosh, Mehdi

2017-07-01

In this paper, a spectral method based on the four kinds of rational Chebyshev functions is proposed to approximate the solution of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet. First, by using the quasilinearization method (QLM), the model which is a nonlinear ordinary differential equation is converted to a sequence of linear ordinary differential equations (ODEs). By applying the proposed method on the ODEs in each iteration, the equations are converted to a system of linear algebraic equations. The results indicate the high accuracy and convergence of our method. Moreover, the effects of the Eyring-Powell fluid material parameters are discussed.

A toolbox for discrete modelling of cell signalling dynamics.

PubMed

Paterson, Yasmin Z; Shorthouse, David; Pleijzier, Markus W; Piterman, Nir; Bendtsen, Claus; Hall, Benjamin A; Fisher, Jasmin

2018-06-18

In an age where the volume of data regarding biological systems exceeds our ability to analyse it, many researchers are looking towards systems biology and computational modelling to help unravel the complexities of gene and protein regulatory networks. In particular, the use of discrete modelling allows generation of signalling networks in the absence of full quantitative descriptions of systems, which are necessary for ordinary differential equation (ODE) models. In order to make such techniques more accessible to mainstream researchers, tools such as the BioModelAnalyzer (BMA) have been developed to provide a user-friendly graphical interface for discrete modelling of biological systems. Here we use the BMA to build a library of discrete target functions of known canonical molecular interactions, translated from ordinary differential equations (ODEs). We then show that these BMA target functions can be used to reconstruct complex networks, which can correctly predict many known genetic perturbations. This new library supports the accessibility ethos behind the creation of BMA, providing a toolbox for the construction of complex cell signalling models without the need for extensive experience in computer programming or mathematical modelling, and allows for construction and simulation of complex biological systems with only small amounts of quantitative data.

Age- and bite-structured models for vector-borne diseases.

PubMed

Rock, K S; Wood, D A; Keeling, M J

2015-09-01

The biology and behaviour of biting insects is a vitally important aspect in the spread of vector-borne diseases. This paper aims to determine, through the use of mathematical models, what effect incorporating vector senescence and realistic feeding patterns has on disease. A novel model is developed to enable the effects of age- and bite-structure to be examined in detail. This original PDE framework extends previous age-structured models into a further dimension to give a new insight into the role of vector biting and its interaction with vector mortality and spread of disease. Through the PDE model, the roles of the vector death and bite rates are examined in a way which is impossible under the traditional ODE formulation. It is demonstrated that incorporating more realistic functions for vector biting and mortality in a model may give rise to different dynamics than those seen under a more simple ODE formulation. The numerical results indicate that the efficacy of control methods that increase vector mortality may not be as great as predicted under a standard host-vector model, whereas other controls including treatment of humans may be more effective than previously thought. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

Application of Petri net based analysis techniques to signal transduction pathways.

PubMed

Sackmann, Andrea; Heiner, Monika; Koch, Ina

2006-11-02

Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules.

Application of Petri net based analysis techniques to signal transduction pathways

PubMed Central

Sackmann, Andrea; Heiner, Monika; Koch, Ina

2006-01-01

Background Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. Methods We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. Results We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. Conclusion The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules. PMID:17081284

On the Tracy-Widomβ Distribution for β=6

NASA Astrophysics Data System (ADS)

Grava, Tamara; Its, Alexander; Kapaev, Andrei; Mezzadri, Francesco

2016-11-01

We study the Tracy-Widom distribution function for Dyson's β-ensemble with β = 6. The starting point of our analysis is the recent work of I. Rumanov where he produces a Lax-pair representation for the Bloemendal-Virág equation. The latter is a linear PDE which describes the Tracy-Widom functions corresponding to general values of β. Using his Lax pair, Rumanov derives an explicit formula for the Tracy-Widom β=6 function in terms of the second Painlevé transcendent and the solution of an auxiliary ODE. Rumanov also shows that this formula allows him to derive formally the asymptotic expansion of the Tracy-Widom function. Our goal is to make Rumanov's approach and hence the asymptotic analysis it provides rigorous. In this paper, the first one in a sequel, we show that Rumanov's Lax-pair can be interpreted as a certain gauge transformation of the standard Lax pair for the second Painlevé equation. This gauge transformation though contains functional parameters which are defined via some auxiliary nonlinear ODE which is equivalent to the auxiliary ODE of Rumanov's formula. The gauge-interpretation of Rumanov's Lax-pair allows us to highlight the steps of the original Rumanov's method which needs rigorous justifications in order to make the method complete. We provide a rigorous justification of one of these steps. Namely, we prove that the Painlevé function involved in Rumanov's formula is indeed, as it has been suggested by Rumanov, the Hastings-McLeod solution of the second Painlevé equation. The key issue which we also discuss and which is still open is the question of integrability of the auxiliary ODE in Rumanov's formula. We note that this question is crucial for the rigorous asymptotic analysis of the Tracy-Widom function. We also notice that our work is a partial answer to one of the problems related to the β-ensembles formulated by Percy Deift during the June 2015 Montreal Conference on integrable systems.

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

EXPONENTIAL TIME DIFFERENCING FOR HODGKIN–HUXLEY-LIKE ODES

PubMed Central

Börgers, Christoph; Nectow, Alexander R.

2013-01-01

Several authors have proposed the use of exponential time differencing (ETD) for Hodgkin–Huxley-like partial and ordinary differential equations (PDEs and ODEs). For Hodgkin–Huxley-like PDEs, ETD is attractive because it can deal effectively with the stiffness issues that diffusion gives rise to. However, large neuronal networks are often simulated assuming “space-clamped” neurons, i.e., using the Hodgkin–Huxley ODEs, in which there are no diffusion terms. Our goal is to clarify whether ETD is a good idea even in that case. We present a numerical comparison of first- and second-order ETD with standard explicit time-stepping schemes (Euler’s method, the midpoint method, and the classical fourth-order Runge–Kutta method). We find that in the standard schemes, the stable computation of the very rapid rising phase of the action potential often forces time steps of a small fraction of a millisecond. This can result in an expensive calculation yielding greater overall accuracy than needed. Although it is tempting at first to try to address this issue with adaptive or fully implicit time-stepping, we argue that neither is effective here. The main advantage of ETD for Hodgkin–Huxley-like systems of ODEs is that it allows underresolution of the rising phase of the action potential without causing instability, using time steps on the order of one millisecond. When high quantitative accuracy is not necessary and perhaps, because of modeling inaccuracies, not even useful, ETD allows much faster simulations than standard explicit time-stepping schemes. The second-order ETD scheme is found to be substantially more accurate than the first-order one even for large values of Δt. PMID:24058276

Investigation of ODE integrators using interactive graphics. [Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Brown, R. L.

1978-01-01

Two FORTRAN programs using an interactive graphic terminal to generate accuracy and stability plots for given multistep ordinary differential equation (ODE) integrators are described. The first treats the fixed stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution, as well as the linear stability region. The second generates an analog to the stability region for classes of non-linear ODE's as well as accuracy plots. Both systems can compute method coefficients from a simple specification of the method. Example plots are given.

Massive juvenile nasopharyngeal angiofibroma: ode to the open surgical approach.

PubMed

Meher, Ravi; Arora, Nikhil; Bhargava, Eishaan Kamta; Juneja, Ruchika

2017-08-01

The management of juvenile nasopharyngeal angiofibroma has undergone a significant evolution, with more surgeons moving towards the minimal invasive endoscopic approaches. Although considered the standard of care by most, an endoscopic approach may not be sufficient for extensive tumours, as exemplified by the current case of a young man presenting with the largest juvenile nasopharyngeal angiofibroma described in English literature until the present that was eventually excised via an anterior external approach. © BMJ Publishing Group Ltd (unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

Optimum survival strategies against zombie infestations - a population dynamics approach

NASA Astrophysics Data System (ADS)

Mota, Bruno

2014-03-01

We model a zombie infestation by three coupled ODEs that jointly describe the time evolution of three populations: regular humans, zombies, and survivors (humans that have survived at least one zombie encounter). This can be generalized to take into account more levels of expertise and/or skill degradation. We compute the fixed points, and stability thereof, that correspond to one of three possible outcomes: human extinction, zombie extermination or, if one allows for a human non-zero birth-rate, co-habitation. We obtain analytically the optimum strategy for humans in terms of the model's parameters (essentially, whether to flee and hide, or fight). Zombies notwithstanding, this can also be seen as a toy model for infections of immune system cells, such as CD4+ T cells in AIDS, and macrophages in tuberculosis, whereby cells are both the target of infection, and mediate the acquired immunity response against the same infection. I thank FAPERJ for financial support.

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

Optimal Control via Self-Generated Stochasticity

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.

LASSIE: simulating large-scale models of biochemical systems on GPUs.

PubMed

Tangherloni, Andrea; Nobile, Marco S; Besozzi, Daniela; Mauri, Giancarlo; Cazzaniga, Paolo

2017-05-10

Mathematical modeling and in silico analysis are widely acknowledged as complementary tools to biological laboratory methods, to achieve a thorough understanding of emergent behaviors of cellular processes in both physiological and perturbed conditions. Though, the simulation of large-scale models-consisting in hundreds or thousands of reactions and molecular species-can rapidly overtake the capabilities of Central Processing Units (CPUs). The purpose of this work is to exploit alternative high-performance computing solutions, such as Graphics Processing Units (GPUs), to allow the investigation of these models at reduced computational costs. LASSIE is a "black-box" GPU-accelerated deterministic simulator, specifically designed for large-scale models and not requiring any expertise in mathematical modeling, simulation algorithms or GPU programming. Given a reaction-based model of a cellular process, LASSIE automatically generates the corresponding system of Ordinary Differential Equations (ODEs), assuming mass-action kinetics. The numerical solution of the ODEs is obtained by automatically switching between the Runge-Kutta-Fehlberg method in the absence of stiffness, and the Backward Differentiation Formulae of first order in presence of stiffness. The computational performance of LASSIE are assessed using a set of randomly generated synthetic reaction-based models of increasing size, ranging from 64 to 8192 reactions and species, and compared to a CPU-implementation of the LSODA numerical integration algorithm. LASSIE adopts a novel fine-grained parallelization strategy to distribute on the GPU cores all the calculations required to solve the system of ODEs. By virtue of this implementation, LASSIE achieves up to 92× speed-up with respect to LSODA, therefore reducing the running time from approximately 1 month down to 8 h to simulate models consisting in, for instance, four thousands of reactions and species. Notably, thanks to its smaller memory footprint, LASSIE is able to perform fast simulations of even larger models, whereby the tested CPU-implementation of LSODA failed to reach termination. LASSIE is therefore expected to make an important breakthrough in Systems Biology applications, for the execution of faster and in-depth computational analyses of large-scale models of complex biological systems.

Extending the Constant Coefficient Solution Technique to Variable Coefficient Ordinary Differential Equations

ERIC Educational Resources Information Center

Mohammed, Ahmed; Zeleke, Aklilu

2015-01-01

We introduce a class of second-order ordinary differential equations (ODEs) with variable coefficients whose closed-form solutions can be obtained by the same method used to solve ODEs with constant coefficients. General solutions for the homogeneous case are discussed.

Multistationarity in mass action networks with applications to ERK activation.

PubMed

Conradi, Carsten; Flockerzi, Dietrich

2012-07-01

Ordinary Differential Equations (ODEs) are an important tool in many areas of Quantitative Biology. For many ODE systems multistationarity (i.e. the existence of at least two positive steady states) is a desired feature. In general establishing multistationarity is a difficult task as realistic biological models are large in terms of states and (unknown) parameters and in most cases poorly parameterized (because of noisy measurement data of few components, a very small number of data points and only a limited number of repetitions). For mass action networks establishing multistationarity hence is equivalent to establishing the existence of at least two positive solutions of a large polynomial system with unknown coefficients. For mass action networks with certain structural properties, expressed in terms of the stoichiometric matrix and the reaction rate-exponent matrix, we present necessary and sufficient conditions for multistationarity that take the form of linear inequality systems. Solutions of these inequality systems define pairs of steady states and parameter values. We also present a sufficient condition to identify networks where the aforementioned conditions hold. To show the applicability of our results we analyse an ODE system that is defined by the mass action network describing the extracellular signal-regulated kinase (ERK) cascade (i.e. ERK-activation).

Role of seasonality on predator-prey-subsidy population dynamics.

PubMed

Levy, Dorian; Harrington, Heather A; Van Gorder, Robert A

2016-05-07

The role of seasonality on predator-prey interactions in the presence of a resource subsidy is examined using a system of non-autonomous ordinary differential equations (ODEs). The problem is motivated by the Arctic, inhabited by the ecological system of arctic foxes (predator), lemmings (prey), and seal carrion (subsidy). We construct two nonlinear, nonautonomous systems of ODEs named the Primary Model, and the n-Patch Model. The Primary Model considers spatial factors implicitly, and the n-Patch Model considers space explicitly as a "Stepping Stone" system. We establish the boundedness of the dynamics, as well as the necessity of sufficiently nutritional food for the survival of the predator. We investigate the importance of including the resource subsidy explicitly in the model, and the importance of accounting for predator mortality during migration. We find a variety of non-equilibrium dynamics for both systems, obtaining both limit cycles and chaotic oscillations. We were then able to discuss relevant implications for biologically interesting predator-prey systems including subsidy under seasonal effects. Notably, we can observe the extinction or persistence of a species when the corresponding autonomous system might predict the opposite. Copyright © 2016 Elsevier Ltd. All rights reserved.

On twisting type [N] ⊗ [N] Ricci flat complex spacetimes with two homothetic symmetries

NASA Astrophysics Data System (ADS)

Chudecki, Adam; Przanowski, Maciej

2018-04-01

In this article, H H spaces of type [N] ⊗ [N] with twisting congruence of null geodesics defined by the 4-fold undotted and dotted Penrose spinors are investigated. It is assumed that these spaces admit two homothetic symmetries. The general form of the homothetic vector fields is found. New coordinates are introduced, which enable us to reduce the H H system of partial differential equations to one ordinary differential equation (ODE) on one holomorphic function. In a special case, this is a second-order ODE and its general solution is explicitly given. In the generic case, one gets rather involved fifth-order ODE.

Bromine release from blowing snow and its impact on tropospheric chemistry

NASA Astrophysics Data System (ADS)

Griffiths, Paul; Yang, Xin; Abraham, N. Luke; Archibald, Alexander; Pyle, John

2016-04-01

In the last two decades, significant depletion of boundary layer ozone (ozone depletion events, ODEs) has been observed in both Arctic and Antarctic spring. ODEs are attributed to catalytic destruction by bromine radicals (Br plus BrO), especially during bromine explosion events (BEs), when high concentrations of BrO periodically occur. The source of bromine and the mechanism that sustains the high BrO levels are still the subject of study. Recent work by Pratt et al. (2013) posits Br2 production within saline snow and sea ice which leads to sudden ODEs. Previously, Yang et al. (2008) suggested snow could provide a source of (depleted) sea-salt aerosol if wicked from the surface of ice. They suggest that rapid depletion of bromide from the aerosol will constitute a source of photochemical Bry. Given the large sea ice extent in polar regions, this may constitute a significant source of sea salt and bromine in the polar lower atmosphere. While bromine release from blowing snow is perhaps less likely to trigger sudden ODEs, it may make a contribution to regional scale processes affecting ozone levels. Currently, the model parameterisations of Yang et al. assumes that rapid release of bromine occurs from fresh snow on sea ice during periods of strong wind. The parameterisation depends on an assumed sea-salt aerosol distribution generated via sublimation of the snow above the boundary layer, as well as taking into account the salinity of the snow. In this work, we draw on recent measurements by scientists from the British Antarctic Survey during a cruise aboard the Polarstern in the southern oceans. This has provided an extensive set of measurements of the chemical and physical characteristics of blowing snow over sea ice, and of the aerosol associated with it. Based on the observations, we have developed an improved parameterisation of the release of bromine from blowing snow. The paper presents results from the simulation performed using the United Kingdom Chemistry and Aerosols (UKCA) model, run as a component of the UK Met Office Unified Model, employing the updated parameterisation of Yang et al. We assess the performance of the parameterisation in simulating tropospheric BrO, a review of relevant parameters, as well as a quantitative assessment of the release of sea salt aerosol and its contribution to halogen chemistry in the polar and global atmosphere.

A non-Fourier approach towards the analysis of heat transfer enhancement with water based nanofluids through a channel

NASA Astrophysics Data System (ADS)

Dil, Taimoor; Khan, M. Sabeel

2018-05-01

In this article, a non-Fourier approach to model the heat transfer phenomenon in nanofluids having application to automotive industry is studied. In this respect, a recently proposed hyperbolic heat flux equation is embedded into the heat energy equation and thereby incorporating the effect of thermal relaxation time. Nanofluids are formed by considering copper oxide (CuO), Titanium dioxide (TiO2) and Aluminum oxide (Al2O3) nano-solid particles in the base fluid. The flow governing system of PDEs along with boundary conditions is transformed into its respective coupled system of nonlinear ODEs using suitable similarity functions. Runge-Kutta-Fehlberg (RK-5) numerical scheme embedded with shooting method is implemented and used to solve the obtained boundary value problem. Numerical simulations are performed and tabulated to analyze the influence of solid volume fraction on local coefficient of skin-friction and Nusselt number. A comparison is made between the results by Fourier and present heat flux model. We conclude that the presented new approach is more general and thus allows predicting the influence of thermal relaxation time on the heat transfer characteristics. Moreover, consideration of present model over the Fourier model helps to predict the actual temporal behavior of solution.

FAST SIMULATION OF SOLID TUMORS THERMAL ABLATION TREATMENTS WITH A 3D REACTION DIFFUSION MODEL *

PubMed Central

BERTACCINI, DANIELE; CALVETTI, DANIELA

2007-01-01

An efficient computational method for near real-time simulation of thermal ablation of tumors via radio frequencies is proposed. Model simulations of the temperature field in a 3D portion of tissue containing the tumoral mass for different patterns of source heating can be used to design the ablation procedure. The availability of a very efficient computational scheme makes it possible update the predicted outcome of the procedure in real time. In the algorithms proposed here a discretization in space of the governing equations is followed by an adaptive time integration based on implicit multistep formulas. A modification of the ode15s MATLAB function which uses Krylov space iterative methods for the solution of for the linear systems arising at each integration step makes it possible to perform the simulations on standard desktop for much finer grids than using the built-in ode15s. The proposed algorithm can be applied to a wide class of nonlinear parabolic differential equations. PMID:17173888

Data Association Algorithms for Tracking Satellites

DTIC Science & Technology

2013-03-27

validation of the new tools. The description provided here includes the mathematical back ground and description of the models implemented, as well as a...simulation development. This work includes the addition of higher-fidelity models in CU-TurboProp and validation of the new tools. The description...ode45(), used in Ananke, and (3) provide the necessary inputs to the bidirectional reflectance distribution function ( BRDF ) model provided by Pacific

On the Importance of the Dynamics of Discretizations

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, H. C.; Rai, ManMohan (Technical Monitor)

1995-01-01

It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.

LIDAR measurements of Arctic boundary layer ozone depletion events over the frozen Arctic Ocean

NASA Astrophysics Data System (ADS)

Seabrook, J. A.; Whiteway, J.; Staebler, R. M.; Bottenheim, J. W.; Komguem, L.; Gray, L. H.; Barber, D.; Asplin, M.

2011-09-01

A differential absorption light detection and ranging instrument (Differential Absorption LIDAR or DIAL) was installed on-board the Canadian Coast Guard Ship Amundsen and operated during the winter and spring of 2008. During this period the vessel was stationed in the Amundsen Gulf (71°N, 121-124°W), approximately 10-40 km off the south coast of Banks Island. The LIDAR was operated to obtain a continuous record of the vertical profile of ozone concentration in the lower atmosphere over the sea ice during the polar sunrise. The observations included several ozone depletion events (ODE's) within the atmospheric boundary layer. The strongest ODEs consisted of air with ozone mixing ratio less than 10 ppbv up to heights varying from 200 m to 600 m, and the increase to the background mixing ratio of about 35-40 ppbv occurred within about 200 m in the overlying air. All of the observed ODEs were connected to the ice surface. Back trajectory calculations indicated that the ODEs only occurred in air that had spent an extended period of time below a height of 500 m above the sea ice. Also, all the ODEs occurred in air with temperature below -25°C. Air not depleted in ozone was found to be associated with warmer air originating from above the surface layer.

Organ donation after euthanasia, morally acceptable under strict procedural safeguards.

PubMed

van Dijk, Gert; van Bruchem-Visser, Rozemarijn; de Beaufort, Inez

2018-05-23

In this paper, we will present a case of organ donation after active euthanasia (ODE) in The Netherlands from a patient who had his life ended at his explicit and voluntary request. The form of ODE we describe here concerns patients who are not unconscious and on life support, but who are conscious and want to have their life ended because of their hopeless and unbearable suffering, for instance due to a terminal illness such as Amyotrophic Lateral Sclerosis (ALS) or Multiple Sclerosis (MS). This form of ODE is of course only possible in jurisdictions where euthanasia is allowed. In these jurisdictions, organ donation after euthanasia is an option that may be considered. We believe ODE is worthwhile to pursue, as it can strengthen patient autonomy, can give meaning to the inevitable death of the patient, and be an extra source of much needed donor organs. To ensure voluntariness of both euthanasia and organ donation and avoid conflict of interest by physicians, ODE does need strict procedural safeguards however. The most important safeguard is a strict separation between the two procedures. The paper discusses several ethical issues such as who should broach the subject of organ donation and who should perform the euthanasia, and how a conflict of interest can be avoided. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

LASSIM-A network inference toolbox for genome-wide mechanistic modeling.

PubMed

Magnusson, Rasmus; Mariotti, Guido Pio; Köpsén, Mattias; Lövfors, William; Gawel, Danuta R; Jörnsten, Rebecka; Linde, Jörg; Nordling, Torbjörn E M; Nyman, Elin; Schulze, Sylvie; Nestor, Colm E; Zhang, Huan; Cedersund, Gunnar; Benson, Mikael; Tjärnberg, Andreas; Gustafsson, Mika

2017-06-01

Recent technological advancements have made time-resolved, quantitative, multi-omics data available for many model systems, which could be integrated for systems pharmacokinetic use. Here, we present large-scale simulation modeling (LASSIM), which is a novel mathematical tool for performing large-scale inference using mechanistically defined ordinary differential equations (ODE) for gene regulatory networks (GRNs). LASSIM integrates structural knowledge about regulatory interactions and non-linear equations with multiple steady state and dynamic response expression datasets. The rationale behind LASSIM is that biological GRNs can be simplified using a limited subset of core genes that are assumed to regulate all other gene transcription events in the network. The LASSIM method is implemented as a general-purpose toolbox using the PyGMO Python package to make the most of multicore computers and high performance clusters, and is available at https://gitlab.com/Gustafsson-lab/lassim. As a method, LASSIM works in two steps, where it first infers a non-linear ODE system of the pre-specified core gene expression. Second, LASSIM in parallel optimizes the parameters that model the regulation of peripheral genes by core system genes. We showed the usefulness of this method by applying LASSIM to infer a large-scale non-linear model of naïve Th2 cell differentiation, made possible by integrating Th2 specific bindings, time-series together with six public and six novel siRNA-mediated knock-down experiments. ChIP-seq showed significant overlap for all tested transcription factors. Next, we performed novel time-series measurements of total T-cells during differentiation towards Th2 and verified that our LASSIM model could monitor those data significantly better than comparable models that used the same Th2 bindings. In summary, the LASSIM toolbox opens the door to a new type of model-based data analysis that combines the strengths of reliable mechanistic models with truly systems-level data. We demonstrate the power of this approach by inferring a mechanistically motivated, genome-wide model of the Th2 transcription regulatory system, which plays an important role in several immune related diseases.

76 FR 1660 - Culturally Significant Objects Imported for Exhibition Determinations: “Reconfiguring an African...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-01-11

... DEPARTMENT OF STATE [Public Notice 7290] Culturally Significant Objects Imported for Exhibition Determinations: ``Reconfiguring an African Icon: Odes to the Mask by Modern and Contemporary Artists From Three... ``Reconfiguring an African Icon: Odes to the Mask by Modern and Contemporary Artists from Three Continents...

Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

ERIC Educational Resources Information Center

Kull, Trent C.

2011-01-01

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

Understanding the Damped SHM without ODEs

ERIC Educational Resources Information Center

Ng, Chiu-king

2016-01-01

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

A Look at Damped Harmonic Oscillators through the Phase Plane

ERIC Educational Resources Information Center

Daneshbod, Yousef; Latulippe, Joe

2011-01-01

Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…

Diagnostic and Therapeutic Cancer Care Equipment

DTIC Science & Technology

2009-07-01

Content of Premarket Submissions for Software Contained in Medical Devices” available at http://www.fda.gov/ cdrh /ode/guidance/337.pdf and “Guidance for...Off-the-Shelf Software Use in Medical Devices” available at http://www.fda.gov/ cdrh /ode/guidance/585.pdf. 5. It is unclear what the “Nellcor Puritan

A boundary PDE feedback control approach for the stabilization of mortgage price dynamics

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Sarno, D.

2017-11-01

Several transactions taking place in financial markets are dependent on the pricing of mortgages (loans for the purchase of residences, land or farms). In this article, a method for stabilization of mortgage price dynamics is developed. It is considered that mortgage prices follow a PDE model which is equivalent to a multi-asset Black-Scholes PDE. Actually it is a diffusion process evolving in a 2D assets space, where the first asset is the house price and the second asset is the interest rate. By applying semi-discretization and a finite differences scheme this multi-asset PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For the local subsystems, into which the mortgage PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the mortgage price PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem's dynamics and can eliminate the subsystem's tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the multi-factor mortgage price PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the mortgage price PDE system so as to assure that all its state variables will converge to the desirable setpoints. By showing the feasibility of such a control method it is also proven that through selected modification of the PDE boundary conditions the price of the mortgage can be made to converge and stabilize at specific reference values.

Stabilization of the Rayleigh-Taylor instability in quantum magnetized plasmas

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

Wang, L. F.; Ye, W. H.; He, X. T.

2012-07-15

In this research, stabilization of the Rayleigh-Taylor instability (RTI) due to density gradients, magnetic fields, and quantum effects, in an ideal incompressible plasma, is studied analytically and numerically. A second-order ordinary differential equation (ODE) for the RTI including quantum corrections, with a continuous density profile, in a uniform external magnetic field, is obtained. Analytic expressions of the linear growth rate of the RTI, considering modifications of density gradients, magnetic fields, and quantum effects, are presented. Numerical approaches are performed to solve the second-order ODE. The analytical model proposed here agrees with the numerical calculation. It is found that the densitymore » gradients, the magnetic fields, and the quantum effects, respectively, have a stabilizing effect on the RTI (reduce the linear growth of the RTI). The RTI can be completely quenched by the magnetic field stabilization and/or the quantum effect stabilization in proper circumstances leading to a cutoff wavelength. The quantum effect stabilization plays a central role in systems with large Atwood number and small normalized density gradient scale length. The presence of external transverse magnetic fields beside the quantum effects will bring about more stability on the RTI. The stabilization of the linear growth of the RTI, for parameters closely related to inertial confinement fusion and white dwarfs, is discussed. Results could potentially be valuable for the RTI treatment to analyze the mixing in supernovas and other RTI-driven objects.« less

First integrals of the axisymmetric shape equation of lipid membranes

NASA Astrophysics Data System (ADS)

Zhang, Yi-Heng; McDargh, Zachary; Tu, Zhan-Chun

2018-03-01

The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor. Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).

Human Performance Task Batteries and Models: An Abilities-Based Directory

DTIC Science & Technology

1986-12-01

8217. BATTERY/TASKLS^ f^ODELYS^ none located to date Sanders Stamina The ability to withstand considerable physical exertion without becoming winded or...Tha Frnfi Pmsg I Jerison, H.J. & Arginteau, J. (1958). Time judgment, acoustic noise and judgement drift (Technical Report No. 57-474). Dayton, OH

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

An Ode to PSII

ERIC Educational Resources Information Center

Firooznia, Fardad

2009-01-01

Many instructors of biology have noted the usefulness of hands-on exercises that require building and using a model or role-playing in helping students to visualize and understand abstract concepts better. In the author's introductory courses, he has resorted to role-playing and biological "plays" to help students visualize more abstract subjects…

An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles

DTIC Science & Technology

2012-06-01

Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre -Gauss-Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...low order polynomials patched together in such away so that the resulting trajectory has several continuous derivatives at all points. In [7], Murray...claims that splines are ideal for optimal control problems because each segment of the spline’s piecewise polynomials approximate the trajectory

Ion Kinetics in Silane Plasmas

DTIC Science & Technology

1988-04-20

field and orthogonal to the excite plates. The image current is amplified, digitized, and Fourier analyzed to yield a spectrum of 0 cyclotron...Laboratory (AFWAL/P0OC). 17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number) FIELD GROUP SUB-GROUP 20 U9 09 03...d.c., microwave, or capacatively coupled, radiofrequency electric fields . Alternatively, hollow cath- ode or electron beam approaches may be employed

Efficient Nonlinear Low-Order Models for Atmospheric and Climate Dynamics

NASA Astrophysics Data System (ADS)

Grady, Kevin A.

The governing equations of atmospheric and climate dynamics present enormous mathematical challenges when studied analytically. Following the pioneering work of Kolmogorov, Lorenz, and Obukhov, a popular approach to handle these difficult partial differential equations (PDEs) is to approximate them with finite systems of ordinary differential equations (ODEs), called low-order models (LOMs). One such LOM is the celebrated Lorenz (1963) model of just three ODEs, but attempts to extend it to larger, more realistic models of atmospheric dynamics have sometimes led to LOMs exhibiting unphysical behavior, such as a lack of energy conservation in the dissipationless limit. These behaviors can be avoided by constructing LOMs using 3-mode nonlinear dynamical systems known in mechanics as Volterra gyrostats, the simplest one being equivalent to the Lorenz model. Gyrostatic LOMs guarantee energy conservation, suggesting they may offer a general framework for deriving efficient LOMs for atmospheric and climate dynamics. This study explores the use of gyrostatic LOMs in three important related problems of atmospheric dynamics. The first is 2D Rayleigh-Benard convection (RBC), where an algorithm for studying gyrostatic LOMs was developed. Before now this had to be done manually, limiting the LOMs that could be studied as well as their size. This algorithm permits the study of LOMs larger than previously possible as well as their conservation properties. It was used here to demonstrate that all physically sound LOMs for this problem from recent publications have a gyrostatic form. The second problem is the interplay of buoyancy and shear in the formation of rolls versus cells in mesoscale shallow convection (MSC). A gyrostatic LOM for 3D RBC with the ability to parameterize buoyancy and shear was developed using an adopted version of the algorithm for 2D RBC. This model was run for hundreds of different combinations of buoyancy and shear, with the results generally matching those of other observational and modeling studies. The third problem is convection driven by internal heating, where the algorithm developed for 2D RBC was applied to derive several gyrostatic LOMs. In general these LOMs were shown to match reasonably well with the actual physics of this problem.

Chaste: A test-driven approach to software development for biological modelling

NASA Astrophysics Data System (ADS)

Pitt-Francis, Joe; Pathmanathan, Pras; Bernabeu, Miguel O.; Bordas, Rafel; Cooper, Jonathan; Fletcher, Alexander G.; Mirams, Gary R.; Murray, Philip; Osborne, James M.; Walter, Alex; Chapman, S. Jon; Garny, Alan; van Leeuwen, Ingeborg M. M.; Maini, Philip K.; Rodríguez, Blanca; Waters, Sarah L.; Whiteley, Jonathan P.; Byrne, Helen M.; Gavaghan, David J.

2009-12-01

Chaste ('Cancer, heart and soft-tissue environment') is a software library and a set of test suites for computational simulations in the domain of biology. Current functionality has arisen from modelling in the fields of cancer, cardiac physiology and soft-tissue mechanics. It is released under the LGPL 2.1 licence. Chaste has been developed using agile programming methods. The project began in 2005 when it was reasoned that the modelling of a variety of physiological phenomena required both a generic mathematical modelling framework, and a generic computational/simulation framework. The Chaste project evolved from the Integrative Biology (IB) e-Science Project, an inter-institutional project aimed at developing a suitable IT infrastructure to support physiome-level computational modelling, with a primary focus on cardiac and cancer modelling. Program summaryProgram title: Chaste Catalogue identifier: AEFD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: LGPL 2.1 No. of lines in distributed program, including test data, etc.: 5 407 321 No. of bytes in distributed program, including test data, etc.: 42 004 554 Distribution format: tar.gz Programming language: C++ Operating system: Unix Has the code been vectorised or parallelized?: Yes. Parallelized using MPI. RAM:<90 Megabytes for two of the scenarios described in Section 6 of the manuscript (Monodomain re-entry on a slab or Cylindrical crypt simulation). Up to 16 Gigabytes (distributed across processors) for full resolution bidomain cardiac simulation. Classification: 3. External routines: Boost, CodeSynthesis XSD, CxxTest, HDF5, METIS, MPI, PETSc, Triangle, Xerces Nature of problem: Chaste may be used for solving coupled ODE and PDE systems arising from modelling biological systems. Use of Chaste in two application areas are described in this paper: cardiac electrophysiology and intestinal crypt dynamics. Solution method: Coupled multi-physics with PDE, ODE and discrete mechanics simulation. Running time: The largest cardiac simulation described in the manuscript takes about 6 hours to run on a single 3 GHz core. See results section (Section 6) of the manuscript for discussion on parallel scaling.

Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Beşliu, C.; Jipa, Al.; Felea, D.; Grossu, I. V.

2008-05-01

This work presents a new software package for the study of chaotic flows and maps. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well known examples are implemented, with the capability of the users inserting their own ODE. Program summaryProgram title: Chaos Catalogue identifier: AEAP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 885 No. of bytes in distributed program, including test data, etc.: 5925 Distribution format: tar.gz Programming language: Scilab 3.1.1 Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 100 Megabytes Classification: 6.2 Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincaré sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Restrictions: The package routines are normally able to handle ODE systems of high orders (up to order twelve and possibly higher), depending on the nature of the problem. Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE and Lyapunov exponents calculation.

Delivery of Open, Distance, and E-Learning in Kenya

ERIC Educational Resources Information Center

Nyerere, Jackline Anyona; Gravenir, Frederick Q.; Mse, Godfrey S.

2012-01-01

The increased demand and need for continuous learning have led to the introduction of open, distance, and e-learning (ODeL) in Kenya. Provision of this mode of education has, however, been faced with various challenges, among them infrastructural ones. This study was a survey conducted in two public universities offering major components of ODeL,…

From Inception to Reflection: Ohio's K-4 Content-Enriched Mandarin Chinese Curriculum

ERIC Educational Resources Information Center

Robinson, Deborah W.

2009-01-01

In 2006 the Ohio Department of Education (ODE) submitted and received a three-year Foreign Language Assistance Program grant from the U.S. Department of Education to write and pilot a K-4 content-enriched Mandarin curriculum and to build online professional development modules to support the curriculum. Once funded, ODE formed an advisory…

OER on the Asian Mega Universities: Developments, Motives, Openness, and Sustainability

ERIC Educational Resources Information Center

Farisi, Mohammad Imam

2013-01-01

The OER movement originated and integrated into ODE developments. Mega Universities (MUs) are among the most important of ODE providers worldwide should be to be the primary organizations for providing access to OER. So far, however, in-depth studies on OER developments in the Asian MUs were very limited. This study focuses on the developments,…

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion

NASA Astrophysics Data System (ADS)

Zhang, Yunong; Chen, Ke; Ma, Weimu; Li, Xiao-Dong

This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.

Interactions Between the Cross-Shore Structure of Small Pelagic Fish Population, Offshore Industrial Fisheries and Near Shore Artisanal Fisheries: A Mathematical Approach.

PubMed

Mchich, Rachid; Brochier, Timothée; Auger, Pierre; Brehmer, Patrice

2016-12-01

This work presents a mathematical model describing the interactions between the cross-shore structure of small pelagic fish population an their exploitation by coastal and offshore fisheries. The complete model is a system of seven ODE's governing three stocks of small pelagic fish population moving and growing between three zones. Two types of fishing fleets are inter-acting with the fish population, industrial boats, constrained to offshore area, and artisanal boats, operating from the shore. Two time scales were considered and we use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model, which is a four dimension one. The analysis of the aggregated model is performed. We discuss the possible equilibriums and their meaning in terms of fishery management. An interesting equilibrium state can be obtained for which we can expect coexistence and a stable equilibrium state between fish stocks and fishing efforts. Some identification parameters are also given in the discussion part of the model.

On the Rate of Relaxation for the Landau Kinetic Equation and Related Models

NASA Astrophysics Data System (ADS)

Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong

2017-08-01

We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Mathematical and Numerical Studies of Nonstandard Difference Equation Models of Differential Equations

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

Mickens, Ronald E.

2008-12-22

This research examined the following items/issues: the NSFD methodology, technical achievements and applications, dissemination efforts and research related professional activities. Also a list of unresolved issues were identified that could form the basis for future research in the area of constructing and analyzing NSFD schemes for both ODE's and PDE's.

Thermally Radiative Rotating Magneto-Nanofluid Flow over an Exponential Sheet with Heat Generation and Viscous Dissipation: A Comparative Study

NASA Astrophysics Data System (ADS)

Sagheer, M.; Bilal, M.; Hussain, S.; Ahmed, R. N.

2018-03-01

This article examines a mathematical model to analyze the rotating flow of three-dimensional water based nanofluid over a convectively heated exponentially stretching sheet in the presence of transverse magnetic field with additional effects of thermal radiation, Joule heating and viscous dissipation. Silver (Ag), copper (Cu), copper oxide (CuO), aluminum oxide (Al 2 O 3 ) and titanium dioxide (TiO 2 ) have been taken under consideration as the nanoparticles and water (H 2 O) as the base fluid. Using suitable similarity transformations, the governing partial differential equations (PDEs) of the modeled problem are transformed to the ordinary differential equations (ODEs). These ODEs are then solved numerically by applying the shooting method. For the particular situation, the results are compared with the available literature. The effects of different nanoparticles on the temperature distribution are also discussed graphically and numerically. It is witnessed that the skin friction coefficient is maximum for silver based nanofluid. Also, the velocity profile is found to diminish for the increasing values of the magnetic parameter.

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH 3 on Pt(1 0 0) coupled by diffusion

NASA Astrophysics Data System (ADS)

Uecker, Hannes

2004-04-01

The Lombardo-Imbihl-Fink (LFI) ODE model of the NO+NH 3 reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH 3 and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH 3 and H.

Model Selection in Systems Biology Depends on Experimental Design

PubMed Central

Silk, Daniel; Kirk, Paul D. W.; Barnes, Chris P.; Toni, Tina; Stumpf, Michael P. H.

2014-01-01

Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a model's predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis. PMID:24922483

Model selection in systems biology depends on experimental design.

PubMed

Silk, Daniel; Kirk, Paul D W; Barnes, Chris P; Toni, Tina; Stumpf, Michael P H

2014-06-01

Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a model's predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis.

Solving Second-Order Ordinary Differential Equations without Using Complex Numbers

ERIC Educational Resources Information Center

Kougias, Ioannis E.

2009-01-01

Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…

Self-Efficacy and New Technology Adoption and Use among Trainee Mid-Wives in Ijebu-Ode, Nigeria

ERIC Educational Resources Information Center

Awodoyin, Anuoluwa; Adetoro, Niran; Osisanwo, Temitope

2017-01-01

Technology has impacted positively on health care delivery and particularly medical personnel have had to embrace emerging technologies in order to provide safe, competent and quality health care. The study investigated self-efficacy for new technology adoption and use by trainee midwives at the school of midwifery, Ijebu-Ode. The study is a…

Constructive Development of the Solutions of Linear Equations in Introductory Ordinary Differential Equations

ERIC Educational Resources Information Center

Mallet, D. G.; McCue, S. W.

2009-01-01

The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…

Comparison of stationary and oscillatory dynamics described by differential equations and Boolean maps in transcriptional regulatory circuits

NASA Astrophysics Data System (ADS)

Ye, Weiming; Li, Pengfei; Huang, Xuhui; Xia, Qinzhi; Mi, Yuanyuan; Chen, Runsheng; Hu, Gang

2010-10-01

Exploring the principle and relationship of gene transcriptional regulations (TR) has been becoming a generally researched issue. So far, two major mathematical methods, ordinary differential equation (ODE) method and Boolean map (BM) method have been widely used for these purposes. It is commonly believed that simplified BMs are reasonable approximations of more realistic ODEs, and both methods may reveal qualitatively the same essential features though the dynamical details of both systems may show some differences. In this Letter we exhaustively enumerated all the 3-gene networks and many autonomous randomly constructed TR networks with more genes by using both the ODE and BM methods. In comparison we found that both methods provide practically identical results in most of cases of steady solutions. However, to our great surprise, most of network structures showing periodic cycles with the BM method possess only stationary states in ODE descriptions. These observations strongly suggest that many periodic oscillations and other complicated oscillatory states revealed by the BM rule may be related to the computational errors of variable and time discretizations and rarely have correspondence in realistic biology transcriptional regulatory circuits.

On the rates of decay to equilibrium in degenerate and defective Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Arnold, Anton; Einav, Amit; Wöhrer, Tobias

2018-06-01

We establish sharp long time asymptotic behaviour for a family of entropies to defective Fokker-Planck equations and show that, much like defective finite dimensional ODEs, their decay rate is an exponential multiplied by a polynomial in time. The novelty of our study lies in the amalgamation of spectral theory and a quantitative non-symmetric hypercontractivity result, as opposed to the usual approach of the entropy method.

Predicting geomagnetic reversals via data assimilation: a feasibility study

NASA Astrophysics Data System (ADS)

Morzfeld, Matthias; Fournier, Alexandre; Hulot, Gauthier

2014-05-01

The system of three ordinary differential equations (ODE) presented by Gissinger in [1] was shown to exhibit chaotic reversals whose statistics compared well with those from the paleomagnetic record. We explore the geophysical relevance of this low-dimensional model via data assimilation, i.e. we update the solution of the ODE with information from data of the dipole variable. The data set we use is 'SINT' (Valet et al. [2]), and it provides the signed virtual axial dipole moment over the past 2 millions years. We can obtain an accurate reconstruction of these dipole data using implicit sampling (a fully nonlinear Monte Carlo sampling strategy) and assimilating 5 kyr of data per sweep. We confirm our calibration of the model using the PADM2M dipole data set of Ziegler et al. [3]. The Monte Carlo sampling strategy provides us with quantitative information about the uncertainty of our estimates, and -in principal- we can use this information for making (robust) predictions under uncertainty. We perform synthetic data experiments to explore the predictive capability of the ODE model updated by data assimilation. For each experiment, we produce 2 Myr of synthetic data (with error levels similar to the ones found in the SINT data), calibrate the model to this record, and then check if this calibrated model can reliably predict a reversal within the next 5 kyr. By performing a large number of such experiments, we can estimate the statistics that describe how reliably our calibrated model can predict a reversal of the geomagnetic field. It is found that the 1 kyr-ahead predictions of reversals produced by the model appear to be accurate and reliable. These encouraging results prompted us to also test predictions of the five reversals of the SINT (and PADM2M) data set, using a similarly calibrated model. Results will be presented and discussed. References Gissinger, C., 2012, A new deterministic model for chaotic reversals, European Physical Journal B, 85:137 Valet, J.P., Maynadier,L and Guyodo, Y., 2005, Geomagnetic field strength and reversal rate over the past 2 Million years, Nature, 435, 802-805. Ziegler, L.B., Constable, C.G., Johnson, C.L. and Tauxe, L., 2011, PADM2M: a penalized maximum likelihood moidel of the 0-2 Ma paleomagnetic axial dipole moment, Geophysical Journal International, 184, 1069-1089.

Stochastic nonlinear mixed effects: a metformin case study.

PubMed

Matzuka, Brett; Chittenden, Jason; Monteleone, Jonathan; Tran, Hien

2016-02-01

In nonlinear mixed effect (NLME) modeling, the intra-individual variability is a collection of errors due to assay sensitivity, dosing, sampling, as well as model misspecification. Utilizing stochastic differential equations (SDE) within the NLME framework allows the decoupling of the measurement errors from the model misspecification. This leads the SDE approach to be a novel tool for model refinement. Using Metformin clinical pharmacokinetic (PK) data, the process of model development through the use of SDEs in population PK modeling was done to study the dynamics of absorption rate. A base model was constructed and then refined by using the system noise terms of the SDEs to track model parameters and model misspecification. This provides the unique advantage of making no underlying assumptions about the structural model for the absorption process while quantifying insufficiencies in the current model. This article focuses on implementing the extended Kalman filter and unscented Kalman filter in an NLME framework for parameter estimation and model development, comparing the methodologies, and illustrating their challenges and utility. The Kalman filter algorithms were successfully implemented in NLME models using MATLAB with run time differences between the ODE and SDE methods comparable to the differences found by Kakhi for their stochastic deconvolution.

Dynamical Systems in Circuit Designer's Eyes

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

Odyniec, M.

Examples of nonlinear circuit design are given. Focus of the design process is on theory and engineering methods (as opposed to numerical analysis). Modeling is related to measurements It is seen that the phase plane is still very useful with proper models Harmonic balance/describing function offers powerful insight (via the combination of simulation with circuit and ODE theory). Measurement and simulation capabilities increased, especially harmonics measurements (since sinusoids are easy to generate)

Stable architectures for deep neural networks

NASA Astrophysics Data System (ADS)

Haber, Eldad; Ruthotto, Lars

2018-01-01

Deep neural networks have become invaluable tools for supervised machine learning, e.g. classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in data, deep architectures are known to be challenging to design and train such that they generalize well to new data. Critical issues with deep architectures are numerical instabilities in derivative-based learning algorithms commonly called exploding or vanishing gradients. In this paper, we propose new forward propagation techniques inspired by systems of ordinary differential equations (ODE) that overcome this challenge and lead to well-posed learning problems for arbitrarily deep networks. The backbone of our approach is our interpretation of deep learning as a parameter estimation problem of nonlinear dynamical systems. Given this formulation, we analyze stability and well-posedness of deep learning and use this new understanding to develop new network architectures. We relate the exploding and vanishing gradient phenomenon to the stability of the discrete ODE and present several strategies for stabilizing deep learning for very deep networks. While our new architectures restrict the solution space, several numerical experiments show their competitiveness with state-of-the-art networks.

EMGD-FE: an open source graphical user interface for estimating isometric muscle forces in the lower limb using an EMG-driven model

PubMed Central

2014-01-01

Background This paper describes the “EMG Driven Force Estimator (EMGD-FE)”, a Matlab® graphical user interface (GUI) application that estimates skeletal muscle forces from electromyography (EMG) signals. Muscle forces are obtained by numerically integrating a system of ordinary differential equations (ODEs) that simulates Hill-type muscle dynamics and that utilises EMG signals as input. In the current version, the GUI can estimate the forces of lower limb muscles executing isometric contractions. Muscles from other parts of the body can be tested as well, although no default values for model parameters are provided. To achieve accurate evaluations, EMG collection is performed simultaneously with torque measurement from a dynamometer. The computer application guides the user, step-by-step, to pre-process the raw EMG signals, create inputs for the muscle model, numerically integrate the ODEs and analyse the results. Results An example of the application’s functions is presented using the quadriceps femoris muscle. Individual muscle force estimations for the four components as well the knee isometric torque are shown. Conclusions The proposed GUI can estimate individual muscle forces from EMG signals of skeletal muscles. The estimation accuracy depends on several factors, including signal collection and modelling hypothesis issues. PMID:24708668

EMGD-FE: an open source graphical user interface for estimating isometric muscle forces in the lower limb using an EMG-driven model.

PubMed

Menegaldo, Luciano Luporini; de Oliveira, Liliam Fernandes; Minato, Kin K

2014-04-04

This paper describes the "EMG Driven Force Estimator (EMGD-FE)", a Matlab® graphical user interface (GUI) application that estimates skeletal muscle forces from electromyography (EMG) signals. Muscle forces are obtained by numerically integrating a system of ordinary differential equations (ODEs) that simulates Hill-type muscle dynamics and that utilises EMG signals as input. In the current version, the GUI can estimate the forces of lower limb muscles executing isometric contractions. Muscles from other parts of the body can be tested as well, although no default values for model parameters are provided. To achieve accurate evaluations, EMG collection is performed simultaneously with torque measurement from a dynamometer. The computer application guides the user, step-by-step, to pre-process the raw EMG signals, create inputs for the muscle model, numerically integrate the ODEs and analyse the results. An example of the application's functions is presented using the quadriceps femoris muscle. Individual muscle force estimations for the four components as well the knee isometric torque are shown. The proposed GUI can estimate individual muscle forces from EMG signals of skeletal muscles. The estimation accuracy depends on several factors, including signal collection and modelling hypothesis issues.

Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics.

Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics; Appendices; Index.

Accounting for Space—Quantification of Cell-To-Cell Transmission Kinetics Using Virus Dynamics Models.

PubMed

Kumberger, Peter; Durso-Cain, Karina; Uprichard, Susan L; Dahari, Harel; Graw, Frederik

2018-04-17

Mathematical models based on ordinary differential equations (ODE) that describe the population dynamics of viruses and infected cells have been an essential tool to characterize and quantify viral infection dynamics. Although an important aspect of viral infection is the dynamics of viral spread, which includes transmission by cell-free virions and direct cell-to-cell transmission, models used so far ignored cell-to-cell transmission completely, or accounted for this process by simple mass-action kinetics between infected and uninfected cells. In this study, we show that the simple mass-action approach falls short when describing viral spread in a spatially-defined environment. Using simulated data, we present a model extension that allows correct quantification of cell-to-cell transmission dynamics within a monolayer of cells. By considering the decreasing proportion of cells that can contribute to cell-to-cell spread with progressing infection, our extension accounts for the transmission dynamics on a single cell level while still remaining applicable to standard population-based experimental measurements. While the ability to infer the proportion of cells infected by either of the transmission modes depends on the viral diffusion rate, the improved estimates obtained using our novel approach emphasize the need to correctly account for spatial aspects when analyzing viral spread.

Global Asymptotic Behavior of Iterative Implicit Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1994-01-01

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

Rule-based modeling with Virtual Cell

PubMed Central

Schaff, James C.; Vasilescu, Dan; Moraru, Ion I.; Loew, Leslie M.; Blinov, Michael L.

2016-01-01

Summary: Rule-based modeling is invaluable when the number of possible species and reactions in a model become too large to allow convenient manual specification. The popular rule-based software tools BioNetGen and NFSim provide powerful modeling and simulation capabilities at the cost of learning a complex scripting language which is used to specify these models. Here, we introduce a modeling tool that combines new graphical rule-based model specification with existing simulation engines in a seamless way within the familiar Virtual Cell (VCell) modeling environment. A mathematical model can be built integrating explicit reaction networks with reaction rules. In addition to offering a large choice of ODE and stochastic solvers, a model can be simulated using a network free approach through the NFSim simulation engine. Availability and implementation: Available as VCell (versions 6.0 and later) at the Virtual Cell web site (http://vcell.org/). The application installs and runs on all major platforms and does not require registration for use on the user’s computer. Tutorials are available at the Virtual Cell website and Help is provided within the software. Source code is available at Sourceforge. Contact: vcell_support@uchc.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27497444

Thermal diffusion of Boussinesq solitons.

PubMed

Arévalo, Edward; Mertens, Franz G

2007-10-01

We consider the problem of the soliton dynamics in the presence of an external noisy force for the Boussinesq type equations. A set of ordinary differential equations (ODEs) of the relevant coordinates of the system is derived. We show that for the improved Boussinesq (IBq) equation the set of ODEs has limiting cases leading to a set of ODEs which can be directly derived either from the ill-posed Boussinesq equation or from the Korteweg-de Vries (KdV) equation. The case of a soliton propagating in the presence of damping and thermal noise is considered for the IBq equation. A good agreement between theory and simulations is observed showing the strong robustness of these excitations. The results obtained here generalize previous results obtained in the frame of the KdV equation for lattice solitons in the monatomic chain of atoms.

Analysis of Vibratory Driven Pile.

DTIC Science & Technology

1987-10-01

DF ) . Deiier. CO.I Smioak. F)ctl er. ( (C (odite IS. Port IlierICeme. (A; (odeC 155. Port I Iienemeri. (A..: COdIC 156. P’oll F Ficiciiic. (NA...23C;~.i~ ode F)LNA OF19424(1.\\ N i’i nu, toil. F C: ocO’’lK \\;~i~oi .(d ( CGARF R&D(’ Fijbrir\\. (irotoit CI( (I INWI, IANI COdIC S.31F, Norfolk.V

An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

NASA Astrophysics Data System (ADS)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

2005-12-01

We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs.

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

Matrix Pseudospectral Method for (Visco)Elastic Tides Modeling of Planetary Bodies

NASA Astrophysics Data System (ADS)

Zabranova, Eliska; Hanyk, Ladidslav; Matyska, Ctirad

2010-05-01

We deal with the equations and boundary conditions describing deformation and gravitational potential of prestressed spherically symmetric elastic bodies by decomposing governing equations into a series of boundary value problems (BVP) for ordinary differential equations (ODE) of the second order. In contrast to traditional Runge-Kutta integration techniques, highly accurate pseudospectral schemes are employed to directly discretize the BVP on Chebyshev grids and a set of linear algebraic equations with an almost block diagonal matrix is derived. As a consequence of keeping the governing ODEs of the second order instead of the usual first-order equations, the resulting algebraic system is half-sized but derivatives of the model parameters are required. Moreover, they can be easily evaluated for models, where structural parametres are piecewise polynomially dependent. Both accuracy and efficiency of the method are tested by evaluating the tidal Love numbers for the Earth's model PREM. Finally, we also derive complex Love numbers for models with the Maxwell viscoelastic rheology, where viscosity is a depth-dependent function. The method is applied to evaluation of the tidal Love numbers for models of Mars and Venus. The Love numbers of the two Martian models - the former optimized to cosmochemical data and the latter to the moment of inertia (Sohl and Spohn, 1997) - are h2=0.172 (0.212) and k2=0.093 (0.113). For Venus, the value of k2=0.295 (Konopliv and Yoder, 1996), obtained from the gravity-field analysis, is consistent with the results for our model with the liquid-core radius of 3110 km (Zábranová et al., 2009). Together with rapid evaluation of free oscillation periods by an analogous method, this combined matrix approach could by employed as an efficient numerical tool in structural studies of planetary bodies. REFERENCES Konopliv, A. S. and Yoder, C. F., 1996. Venusian k2 tidal Love number from Magellan and PVO tracking data, Geophys. Res. Lett., 23, 1857-1860. Sohl, F., and Spohn, T., 1997. The interior structure of Mars: Implications from SNC meteorites, J. Geophys. Res., 102, 1613-1635. Zabranova, E., Hanyk L. and Matyska, C.: Matrix Pseudospectral Method for Elastic Tides Modeling. In: Holota P. (Ed.): Mission and Passion: Science. A volume dedicated to Milan Bursa on the occasion of his 80th birthday. Published by the Czech National Committee of Geodesy and Geophysics. Prague, 2009, pp. 243-260.

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

PubMed

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Formulation and Implementation of Nonlinear Integral Equations to Model Neural Dynamics Within the Vertebrate Retina.

PubMed

Eshraghian, Jason K; Baek, Seungbum; Kim, Jun-Ho; Iannella, Nicolangelo; Cho, Kyoungrok; Goo, Yong Sook; Iu, Herbert H C; Kang, Sung-Mo; Eshraghian, Kamran

2018-02-13

Existing computational models of the retina often compromise between the biophysical accuracy and a hardware-adaptable methodology of implementation. When compared to the current modes of vision restoration, algorithmic models often contain a greater correlation between stimuli and the affected neural network, but lack physical hardware practicality. Thus, if the present processing methods are adapted to complement very-large-scale circuit design techniques, it is anticipated that it will engender a more feasible approach to the physical construction of the artificial retina. The computational model presented in this research serves to provide a fast and accurate predictive model of the retina, a deeper understanding of neural responses to visual stimulation, and an architecture that can realistically be transformed into a hardware device. Traditionally, implicit (or semi-implicit) ordinary differential equations (OES) have been used for optimal speed and accuracy. We present a novel approach that requires the effective integration of different dynamical time scales within a unified framework of neural responses, where the rod, cone, amacrine, bipolar, and ganglion cells correspond to the implemented pathways. Furthermore, we show that adopting numerical integration can both accelerate retinal pathway simulations by more than 50% when compared with traditional ODE solvers in some cases, and prove to be a more realizable solution for the hardware implementation of predictive retinal models.

Model identification using stochastic differential equation grey-box models in diabetes.

PubMed

Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard; Møller, Jonas Bech; Nørgaard, Kirsten; Jørgensen, John Bagterp; Madsen, Henrik

2013-03-01

The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors are uncorrelated and provides the possibility to pinpoint model deficiencies. An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the "peak time of meal absorption" parameter showed that the absorption rate varied according to meal type. This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development. © 2013 Diabetes Technology Society.

Algorithm for Stabilizing a POD-Based Dynamical System

NASA Technical Reports Server (NTRS)

Kalb, Virginia L.

2010-01-01

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

A consistent modelling methodology for secondary settling tanks in wastewater treatment.

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

Stability with large step sizes for multistep discretizations of stiff ordinary differential equations

NASA Technical Reports Server (NTRS)

Majda, George

1986-01-01

One-leg and multistep discretizations of variable-coefficient linear systems of ODEs having both slow and fast time scales are investigated analytically. The stability properties of these discretizations are obtained independent of ODE stiffness and compared. The results of numerical computations are presented in tables, and it is shown that for large step sizes the stability of one-leg methods is better than that of the corresponding linear multistep methods.

A Second Chance to Dream: Initiating ODeL in Secondary School Re-Entry Programs for Young Adult Secondary School Dropouts the Case of Mumias District, Western Kenya

ERIC Educational Resources Information Center

Musita, Richard; Ogange, Betty O.; Lugendo, Dorine

2018-01-01

The Kenyan education system has very limited re-entry options for learners who drop out before attaining secondary school certificate. It is very difficult to access training and or secure a job that requires at least secondary school education. This study examined the prospects of initiating Open and Distance e-Learning(ODeL) in re-entry…

Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity

NASA Astrophysics Data System (ADS)

Bartuccelli, Michele; Deane, Jonathan; Gentile, Guido

2017-08-01

We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is C^1 in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation for devising a fast algorithm for its solution comes from the desire to estimate probability of capture in various solutions, via Monte Carlo simulation: the integration times are very long, since we are interested in phenomena occurring on timescales of the order of 10^6-10^7 years. The proposed algorithm is based on the high-order Euler method which was described in Bartuccelli et al. (Celest Mech Dyn Astron 121(3):233-260, 2015), and it requires computer algebra to set up the code for its implementation. The payoff is an overall increase in speed by a factor of about 7.5 compared to standard numerical methods. Means for accelerating the purely numerical computation are also discussed.

Near-resonant excitation and propagation of eccentric density waves by external forcing. [in accretion disks

NASA Technical Reports Server (NTRS)

Ostriker, Eve C.; Shu, Frank H.; Adams, Fred C.

1992-01-01

An overview is presented of the astronomical evidence that relatively massive, distended, gaseous disks form as a natural by-product of the process of star formation, and also the numerical evidence that SLING-amplified eccentric modes in the outer parts of such disks can drive one-armed spiral density waves in the inner parts by near-resonant excitation and propagation. An ordinary differential equation (ODE) of the second order that approximately governs the nonlocalized forcing of waves in a disk satisfying Lindblad resonance almost everywhere is derived. When transformed and appended with an extra model term, this ODE implies, for free waves, the usual asymptotic results of the WKBJ dispersion relationship and the propagation Goldreich-Tremaine (1978) formula for the resonant torque exerted on a localized Lindblad resonance. An analytical solution is given for the rate of energy and angular momentum transfer by nonlocalized near-resonant forcing in the case when the disk has power-law dependences on the radius of the surface density and temperature.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

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

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

A reverse engineering algorithm for neural networks, applied to the subthalamopallidal network of basal ganglia.

PubMed

Floares, Alexandru George

2008-01-01

Modeling neural networks with ordinary differential equations systems is a sensible approach, but also very difficult. This paper describes a new algorithm based on linear genetic programming which can be used to reverse engineer neural networks. The RODES algorithm automatically discovers the structure of the network, including neural connections, their signs and strengths, estimates its parameters, and can even be used to identify the biophysical mechanisms involved. The algorithm is tested on simulated time series data, generated using a realistic model of the subthalamopallidal network of basal ganglia. The resulting ODE system is highly accurate, and results are obtained in a matter of minutes. This is because the problem of reverse engineering a system of coupled differential equations is reduced to one of reverse engineering individual algebraic equations. The algorithm allows the incorporation of common domain knowledge to restrict the solution space. To our knowledge, this is the first time a realistic reverse engineering algorithm based on linear genetic programming has been applied to neural networks.

Global Hopf bifurcation analysis on a BAM neural network with delays

NASA Astrophysics Data System (ADS)

Sun, Chengjun; Han, Maoan; Pang, Xiaoming

2007-01-01

A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large.

Entropy generation analysis for film boiling: A simple model of quenching

NASA Astrophysics Data System (ADS)

Lotfi, Ali; Lakzian, Esmail

2016-04-01

In this paper, quenching in high-temperature materials processing is modeled as a superheated isothermal flat plate. In these phenomena, a liquid flows over the highly superheated surfaces for cooling. So the surface and the liquid are separated by the vapor layer that is formed because of the liquid which is in contact with the superheated surface. This is named forced film boiling. As an objective, the distribution of the entropy generation in the laminar forced film boiling is obtained by similarity solution for the first time in the quenching processes. The PDE governing differential equations of the laminar film boiling including continuity, momentum, and energy are reduced to ODE ones, and a dimensionless equation for entropy generation inside the liquid boundary and vapor layer is obtained. Then the ODEs are solved by applying the 4th-order Runge-Kutta method with a shooting procedure. Moreover, the Bejan number is used as a design criterion parameter for a qualitative study about the rate of cooling and the effects of plate speed are studied in the quenching processes. It is observed that for high speed of the plate the rate of cooling (heat transfer) is more.

Parallel high-precision orbit propagation using the modified Picard-Chebyshev method

NASA Astrophysics Data System (ADS)

Koblick, Darin C.

2012-03-01

The modified Picard-Chebyshev method, when run in parallel, is thought to be more accurate and faster than the most efficient sequential numerical integration techniques when applied to orbit propagation problems. Previous experiments have shown that the modified Picard-Chebyshev method can have up to a one order magnitude speedup over the 12th order Runge-Kutta-Nystrom method. For this study, the evaluation of the accuracy and computational time of the modified Picard-Chebyshev method, using the Java Astrodynamics Toolkit high-precision force model, is conducted to assess its runtime performance. Simulation results of the modified Picard-Chebyshev method, implemented in MATLAB and the MATLAB Parallel Computing Toolbox, are compared against the most efficient first and second order Ordinary Differential Equation (ODE) solvers. A total of six processors were used to assess the runtime performance of the modified Picard-Chebyshev method. It was found that for all orbit propagation test cases, where the gravity model was simulated to be of higher degree and order (above 225 to increase computational overhead), the modified Picard-Chebyshev method was faster, by as much as a factor of two, than the other ODE solvers which were tested.

Tidal disruption of viscous bodies

NASA Technical Reports Server (NTRS)

Sridhar, S.; Tremaine, S.

1992-01-01

Tidal disruptions are investigated in viscous-fluid planetesimals whose radius is small relative to the distance of closest (parabolic-orbit) approach to a planet. The planetesimal surface is in these conditions always ellipsoidal, facilitating treatment by coupled ODEs which are solvable with high accuracy. While the disrupted planetesimals evolve into needlelike ellipsoids, their density does not decrease. The validity of viscous fluid treatment holds for solid (ice or rock) planetesimals in cases where tidal stresses are greater than material strength, but integrity is maintained by self-gravity.

The dynamics of acute inflammation

NASA Astrophysics Data System (ADS)

Kumar, Rukmini

The acute inflammatory response is the non-specific and immediate reaction of the body to pathogenic organisms, tissue trauma and unregulated cell growth. An imbalance in this response could lead to a condition commonly known as "shock" or "sepsis". This thesis is an attempt to elucidate the dynamics of acute inflammatory response to infection and contribute to its systemic understanding through mathematical modeling and analysis. The models of immunity discussed use Ordinary Differential Equations (ODEs) to model the variation of concentration in time of the various interacting species. Chapter 2 discusses three such models of increasing complexity. Sections 2.1 and 2.2 discuss smaller models that capture the core features of inflammation and offer general predictions concerning the design of the system. Phase-space and bifurcation analyses have been used to examine the behavior at various parameter regimes. Section 2.3 discusses a global physiological model that includes several equations modeling the concentration (or numbers) of cells, cytokines and other mediators. The conclusions drawn from the reduced and detailed models about the qualitative effects of the parameters are very similar and these similarities have also been discussed. In Chapter 3, the specific applications of the biologically detailed model are discussed in greater detail. These include a simulation of anthrax infection and an in silico simulation of a clinical trial. Such simulations are very useful to biologists and could prove to be invaluable tools in drug design. Finally, Chapter 4 discusses the general problem of extinction of populations modeled as continuous variables in ODES is discussed. The average time to extinction and threshold are estimated based on analyzing the equivalent stochastic processes.

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors.

PubMed

Walcott, Sam

2014-10-01

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

A neuro approach to solve fuzzy Riccati differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Kumaresan, N.; Kamali, M. Z. M.; Ratnavelu, Kurunathan

2015-10-01

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

A neuro approach to solve fuzzy Riccati differential equations

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

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com; Telekom Malaysia, R&D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor; Kumaresan, N., E-mail: drnk2008@gmail.com

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

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

Chater, Mario, E-mail: chaterm@mit.edu; Ni, Angxiu, E-mail: niangxiu@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu

This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs.

Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

NASA Astrophysics Data System (ADS)

Tang, Wensheng; Sun, Yajuan; Cai, Wenjun

2017-02-01

In this article, we present a unified framework of discontinuous Galerkin (DG) discretizations for Hamiltonian ODEs and PDEs. We show that with appropriate numerical fluxes the numerical algorithms deduced from DG discretizations can be combined with the symplectic methods in time to derive the multi-symplectic PRK schemes. The resulting numerical discretizations are applied to the linear and nonlinear Schrödinger equations. Some conservative properties of the numerical schemes are investigated and confirmed in the numerical experiments.

Possible role of electric forces in bromine activation during polar boundary layer ozone depletion and aerosol formation events

NASA Astrophysics Data System (ADS)

Tkachenko, Ekaterina

2017-11-01

This work presents a hypothesis about the mechanism of bromine activation during polar boundary layer ozone depletion events (ODEs) as well as the mechanism of aerosol formation from the frost flowers. The author suggests that ODEs may be initiated by the electric-field gradients created at the sharp tips of ice formations as a result of the combined effect of various environmental conditions. According to the author's estimates, these electric-field gradients may be sufficient for the onset of point or corona discharges followed by generation of high local concentrations of the reactive oxygen species and initiation of free-radical and redox reactions. This process may be responsible for the formation of seed bromine which then undergoes further amplification by HOBr-driven bromine explosion. The proposed hypothesis may explain a variety of environmental conditions and substrates as well as poor reproducibility of ODE initiation observed by researchers in the field. According to the author's estimates, high wind can generate sufficient conditions for overcoming the Rayleigh limit and thus can initiate ;spraying; of charged aerosol nanoparticles. These charged aerosol nanoparticles can provoke formation of free radicals, turning the ODE on. One can also envision a possible emission of halogen ion as a result of the ;electrospray; process analogous to that of electrospray ionization mass-spectrometry.

Aerosol simulation including chemical and nuclear reactions

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

Marwil, E.S.; Lemmon, E.C.

1985-01-01

The numerical simulation of aerosol transport, including the effects of chemical and nuclear reactions presents a challenging dynamic accounting problem. Particles of different sizes agglomerate and settle out due to various mechanisms, such as diffusion, diffusiophoresis, thermophoresis, gravitational settling, turbulent acceleration, and centrifugal acceleration. Particles also change size, due to the condensation and evaporation of materials on the particle. Heterogeneous chemical reactions occur at the interface between a particle and the suspending medium, or a surface and the gas in the aerosol. Homogeneous chemical reactions occur within the aersol suspending medium, within a particle, and on a surface. These reactionsmore » may include a phase change. Nuclear reactions occur in all locations. These spontaneous transmutations from one element form to another occur at greatly varying rates and may result in phase or chemical changes which complicate the accounting process. This paper presents an approach for inclusion of these effects on the transport of aerosols. The accounting system is very complex and results in a large set of stiff ordinary differential equations (ODEs). The techniques for numerical solution of these ODEs require special attention to achieve their solution in an efficient and affordable manner. 4 refs.« less

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

Predicting the impact of combined therapies on myeloma cell growth using a hybrid multi-scale agent-based model.

PubMed

Ji, Zhiwei; Su, Jing; Wu, Dan; Peng, Huiming; Zhao, Weiling; Nlong Zhao, Brian; Zhou, Xiaobo

2017-01-31

Multiple myeloma is a malignant still incurable plasma cell disorder. This is due to refractory disease relapse, immune impairment, and development of multi-drug resistance. The growth of malignant plasma cells is dependent on the bone marrow (BM) microenvironment and evasion of the host's anti-tumor immune response. Hence, we hypothesized that targeting tumor-stromal cell interaction and endogenous immune system in BM will potentially improve the response of multiple myeloma (MM). Therefore, we proposed a computational simulation of the myeloma development in the complicated microenvironment which includes immune cell components and bone marrow stromal cells and predicted the effects of combined treatment with multi-drugs on myeloma cell growth. We constructed a hybrid multi-scale agent-based model (HABM) that combines an ODE system and Agent-based model (ABM). The ODEs was used for modeling the dynamic changes of intracellular signal transductions and ABM for modeling the cell-cell interactions between stromal cells, tumor, and immune components in the BM. This model simulated myeloma growth in the bone marrow microenvironment and revealed the important role of immune system in this process. The predicted outcomes were consistent with the experimental observations from previous studies. Moreover, we applied this model to predict the treatment effects of three key therapeutic drugs used for MM, and found that the combination of these three drugs potentially suppress the growth of myeloma cells and reactivate the immune response. In summary, the proposed model may serve as a novel computational platform for simulating the formation of MM and evaluating the treatment response of MM to multiple drugs.

Communication scheme using a hyperchaotic semiconductor laser model: Chaos shift key revisited

NASA Astrophysics Data System (ADS)

Fataf, N. A. A.; Palit, Sanjay Kumar; Mukherjee, Sayan; Said, M. R. M.; Son, Doan Hoai; Banerjee, Santo

2017-11-01

Based on the Maxwell-Bloch equations, we considered a five-dimensional ODE system, describing the dynamics of a semiconductor laser. The system has rich dynamics with multi-periodic, chaotic and hyperchaotic states. In this analysis, we have investigated the hyperchaotic nature of the aforesaid model and proposed a communication scheme, the generalized form of chaos shift keys, where the coupled systems do not need to be in the synchronized state. The results are implemented with the hyperchaotic laser model followed by a comprehensive security analysis.

Materials for Adaptive Structural Acoustic Control. Volume 2

DTIC Science & Technology

1994-04-11

Cross. Effects of Electrodes and Elecu’oding Methods on Fatigue Behavior in Ferroelectric Materials. Ferroelectrics: Proceedings of IMF8, Gaithersburg...describe the linear piezoelectric behavior of ferroelectric ceramics. We have generalized this model to describe the nonlinear effects resulting from...report some of the nonlinear effects under resonant conditions for a PZT-501A ceramic. Figure 8 shows the complex admittance circles at different

Multi-scale dynamical behavior of spatially distributed systems: a deterministic point of view

NASA Astrophysics Data System (ADS)

Mangiarotti, S.; Le Jean, F.; Drapeau, L.; Huc, M.

2015-12-01

Physical and biophysical systems are spatially distributed systems. Their behavior can be observed or modelled spatially at various resolutions. In this work, a deterministic point of view is adopted to analyze multi-scale behavior taking a set of ordinary differential equation (ODE) as elementary part of the system.To perform analyses, scenes of study are thus generated based on ensembles of identical elementary ODE systems. Without any loss of generality, their dynamics is chosen chaotic in order to ensure sensitivity to initial conditions, that is, one fundamental property of atmosphere under instable conditions [1]. The Rössler system [2] is used for this purpose for both its topological and algebraic simplicity [3,4].Two cases are thus considered: the chaotic oscillators composing the scene of study are taken either independent, or in phase synchronization. Scale behaviors are analyzed considering the scene of study as aggregations (basically obtained by spatially averaging the signal) or as associations (obtained by concatenating the time series). The global modeling technique is used to perform the numerical analyses [5].One important result of this work is that, under phase synchronization, a scene of aggregated dynamics can be approximated by the elementary system composing the scene, but modifying its parameterization [6]. This is shown based on numerical analyses. It is then demonstrated analytically and generalized to a larger class of ODE systems. Preliminary applications to cereal crops observed from satellite are also presented.[1] Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130-141 (1963).[2] Rössler, An equation for continuous chaos, Phys. Lett. A, 57, 397-398 (1976).[3] Gouesbet & Letellier, Global vector-field reconstruction by using a multivariate polynomial L2 approximation on nets, Phys. Rev. E 49, 4955-4972 (1994).[4] Letellier, Roulin & Rössler, Inequivalent topologies of chaos in simple equations, Chaos, Solitons & Fractals, 28, 337-360 (2006).[5] Mangiarotti, Coudret, Drapeau, & Jarlan, Polynomial search and global modeling, Phys. Rev. E 86(4), 046205 (2012).[6] Mangiarotti, Modélisation globale et Caractérisation Topologique de dynamiques environnementales. Habilitation à Diriger des Recherches, Univ. Toulouse 3 (2014).

A new ODE tumor growth modeling based on tumor population dynamics

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

Oroji, Amin; Omar, Mohd bin; Yarahmadian, Shantia

2015-10-22

In this paper a new mathematical model for the population of tumor growth treated by radiation is proposed. The cells dynamics population in each state and the dynamics of whole tumor population are studied. Furthermore, a new definition of tumor lifespan is presented. Finally, the effects of two main parameters, treatment parameter (q), and repair mechanism parameter (r) on tumor lifespan are probed, and it is showed that the change in treatment parameter (q) highly affects the tumor lifespan.

Robust Consumption-Investment Problem on Infinite Horizon

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

Zawisza, Dariusz, E-mail: dariusz.zawisza@im.uj.edu.pl

In our paper we consider an infinite horizon consumption-investment problem under a model misspecification in a general stochastic factor model. We formulate the problem as a stochastic game and finally characterize the saddle point and the value function of that game using an ODE of semilinear type, for which we provide a proof of an existence and uniqueness theorem for its solution. Such equation is interested on its own right, since it generalizes many other equations arising in various infinite horizon optimization problems.

Numerical solution of second order ODE directly by two point block backward differentiation formula

NASA Astrophysics Data System (ADS)

Zainuddin, Nooraini; Ibrahim, Zarina Bibi; Othman, Khairil Iskandar; Suleiman, Mohamed; Jamaludin, Noraini

2015-12-01

Direct Two Point Block Backward Differentiation Formula, (BBDF2) for solving second order ordinary differential equations (ODEs) will be presented throughout this paper. The method is derived by differentiating the interpolating polynomial using three back values. In BBDF2, two approximate solutions are produced simultaneously at each step of integration. The method derived is implemented by using fixed step size and the numerical results that follow demonstrate the advantage of the direct method as compared to the reduction method.

LSENS - GENERAL CHEMICAL KINETICS AND SENSITIVITY ANALYSIS CODE

NASA Technical Reports Server (NTRS)

Bittker, D. A.

1994-01-01

LSENS has been developed for solving complex, homogeneous, gas-phase, chemical kinetics problems. The motivation for the development of this program is the continuing interest in developing detailed chemical reaction mechanisms for complex reactions such as the combustion of fuels and pollutant formation and destruction. A reaction mechanism is the set of all elementary chemical reactions that are required to describe the process of interest. Mathematical descriptions of chemical kinetics problems constitute sets of coupled, nonlinear, first-order ordinary differential equations (ODEs). The number of ODEs can be very large because of the numerous chemical species involved in the reaction mechanism. Further complicating the situation are the many simultaneous reactions needed to describe the chemical kinetics of practical fuels. For example, the mechanism describing the oxidation of the simplest hydrocarbon fuel, methane, involves over 25 species participating in nearly 100 elementary reaction steps. Validating a chemical reaction mechanism requires repetitive solutions of the governing ODEs for a variety of reaction conditions. Analytical solutions to the systems of ODEs describing chemistry are not possible, except for the simplest cases, which are of little or no practical value. Consequently, there is a need for fast and reliable numerical solution techniques for chemical kinetics problems. In addition to solving the ODEs describing chemical kinetics, it is often necessary to know what effects variations in either initial condition values or chemical reaction mechanism parameters have on the solution. Such a need arises in the development of reaction mechanisms from experimental data. The rate coefficients are often not known with great precision and in general, the experimental data are not sufficiently detailed to accurately estimate the rate coefficient parameters. The development of a reaction mechanism is facilitated by a systematic sensitivity analysis which provides the relationships between the predictions of a kinetics model and the input parameters of the problem. LSENS provides for efficient and accurate chemical kinetics computations and includes sensitivity analysis for a variety of problems, including nonisothermal conditions. LSENS replaces the previous NASA general chemical kinetics codes GCKP and GCKP84. LSENS is designed for flexibility, convenience and computational efficiency. A variety of chemical reaction models can be considered. The models include static system, steady one-dimensional inviscid flow, reaction behind an incident shock wave including boundary layer correction, and the perfectly stirred (highly backmixed) reactor. In addition, computations of equilibrium properties can be performed for the following assigned states, enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. For static problems LSENS computes sensitivity coefficients with respect to the initial values of the dependent variables and/or the three rates coefficient parameters of each chemical reaction. To integrate the ODEs describing chemical kinetics problems, LSENS uses the packaged code LSODE, the Livermore Solver for Ordinary Differential Equations, because it has been shown to be the most efficient and accurate code for solving such problems. The sensitivity analysis computations use the decoupled direct method, as implemented by Dunker and modified by Radhakrishnan. This method has shown greater efficiency and stability with equal or better accuracy than other methods of sensitivity analysis. LSENS is written in FORTRAN 77 with the exception of the NAMELIST extensions used for input. While this makes the code fairly machine independent, execution times on IBM PC compatibles would be unacceptable to most users. LSENS has been successfully implemented on a Sun4 running SunOS and a DEC VAX running VMS. With minor modifications, it should also be easily implemented on other platforms with FORTRAN compilers which support NAMELIST input. LSENS required 4Mb of RAM under SunOS 4.1.1 and 3.4Mb of RAM under VMS 5.5.1. The standard distribution medium for LSENS is a .25 inch streaming magnetic tape cartridge (QIC-24) in UNIX tar format. It is also available on a 1600 BPI 9-track magnetic tape or a TK50 tape cartridge in DEC VAX BACKUP format. Alternate distribution media and formats are available upon request. LSENS was developed in 1992.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Least squares polynomial chaos expansion: A review of sampling strategies

NASA Astrophysics Data System (ADS)

Hadigol, Mohammad; Doostan, Alireza

2018-04-01

As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments (ODE), Gaussian quadratures, as well as more recent techniques, such as coherence-optimal and randomized quadratures are discussed. We also propose a hybrid sampling method, dubbed alphabetic-coherence-optimal, that employs the so-called alphabetic optimality criteria used in the context of ODE in conjunction with coherence-optimal samples. A comparison between the empirical performance of the selected sampling methods applied to three numerical examples, including high-order PCE's, high-dimensional problems, and low oversampling ratios, is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand. We observed that the alphabetic-coherence-optimal technique outperforms other sampling methods, specially when high-order ODE are employed and/or the oversampling ratio is low.

Runge-Kutta Methods for Linear Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Zingg, David W.; Chisholm, Todd T.

1997-01-01

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.

2017-11-01

This paper presents a discrete adjoint version of the recently developed non-intrusive least squares shadowing (NILSS) algorithm, which circumvents the instability that conventional adjoint methods encounter for chaotic systems. The NILSS approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers. Adjoint NILSS is demonstrated on a small chaotic ODE, a one-dimensional scalar PDE, and a direct numerical simulation (DNS) of the minimal flow unit, a turbulent channel flow on a small spatial domain. This is the first application of an adjoint shadowing-based algorithm to a three-dimensional turbulent flow.

Accelerating Calculations of Reaction Dissipative Particle Dynamics in LAMMPS

DTIC Science & Technology

2017-05-17

order reaction mechanism, the best acceleration was 6.1 times. For a larger, more chemically detailed mechanism, the best acceleration exceeded 60 times...simulations at previously inaccessible scales. A principle feature of DPD-RX is its ability to model chemical reactions within each CG particle. The...change in composition due to chemical reactions is described by a system of ordinary differential equations (ODEs) that are evaluated at each DPD time

Variable Speed Hydrodynamic Model of an Auv Utilizing Cross Tunnel Thrusters

DTIC Science & Technology

2017-09-01

Institute NED North East Down NPS Naval Postgraduate School ODE Ordinary Differential Equation PUC Positional Uncertainty REMUS Remote Environmental Measuring ...in its depths. Rising autonomous systems such as the Remote Environmental Measuring Unit (REMUS) 100 vehicle represents not only a feat of...presented account for reduced control surface efficiency at low speeds and build an accurate representation of a REMUS AUV’s behavior while operating at

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

NASA Technical Reports Server (NTRS)

Pratt, D. T.; Radhakrishnan, K.

1986-01-01

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Flow and heat transfer of nanofluid over a stretching sheet with non-linear velocity in the presence of thermal radiation and chemical reaction

NASA Astrophysics Data System (ADS)

Madaki, A. G.; Roslan, R.; Kandasamy, R.; Chowdhury, M. S. H.

2017-04-01

In this paper, the effects of Brownian motion, thermophoresis, chemical reaction, heat generation, magnetohydrodynamic and thermal radiation has been included in the model of nanofluid flow and heat transfer over a moving surface with variable thickness. The similarity transformation is used to transform the governing boundary layer equations into ordinary differential equations (ODE). Both optimal homotopy asymptotic method (OHAM) and Runge-Kutta fourth order method with shooting technique are employed to solve the resulting ODEs. For different values of the pertinent parameters on the velocity, temperature and concentration profiles have been studied and details are given in tables and graphs respectively. A comparison with the previous study is made, where an excellent agreement is achieved. The results demonstrate that the radiation parameter N increases, with the increase in both the temperature and the thermal boundary layer thickness respectively. While the nanoparticles concentration profiles increase with the influence of generative chemical reaction γ < 0, while it decreases with destructive chemical reaction γ > 0.

Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Imad; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

An analysis is performed to explore the effects of homogenous-heterogeneous reactions on two-dimensional flow of Prandtl fluid over a stretching sheet. In present analysis, we used the developed model of homogeneous-heterogeneous reactions in boundary layer flow. The mathematical configuration of presented flow phenomenon yields the nonlinear partial differential equations. Using scaling transformations, the governing partial differential equations (momentum equation and homogenous-heterogeneous reactions equations) are transformed into non-linear ordinary differential equations (ODE's). Then, resulting non-linear ODE's are solved by computational scheme known as shooting method. The quantitative and qualitative manners of concerned physical quantities (velocity, concentration and drag force coefficient) are examined under prescribed physical constrained through figures and tables. It is observed that velocity profile enhances verses fluid parameters α and β while Hartmann number reduced it. The homogeneous and heterogeneous reactions parameters have reverse effects on concentration profile. Concentration profile shows retarding behavior for large values of Schmidt number. Skin fraction coefficient enhances with increment in Hartmann number H and fluid parameter α .

Self-similar solutions to isothermal shock problems

NASA Astrophysics Data System (ADS)

Deschner, Stephan C.; Illenseer, Tobias F.; Duschl, Wolfgang J.

We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary differential equations. We test the numerical solutions against the analytical expressions to verify the correctness of all numerical algorithms. We use similarity methods to derive a system of ordinary differential equations (ODE) yielding exact solutions for power law density distributions as initial conditions. Further, the system of ODEs accounts for implosion problems (IP) as well as explosion problems (EP) by changing the initial or boundary conditions, respectively. Taking genuinely isothermal approximations into account leads to additional insights of EPs in contrast to earlier models. We neglect a constant initial energy contribution but introduce a parameter to adjust the initial mass distribution of the system. Moreover, we show that due to this parameter a constant initial density is not allowed for isothermal EPs. Reasonable restrictions for this parameter are given. Both, the (genuinely) isothermal implosion as well as the explosion problem are solved for the first time.

Metabolic modeling of synthesis gas fermentation in bubble column reactors.

PubMed

Chen, Jin; Gomez, Jose A; Höffner, Kai; Barton, Paul I; Henson, Michael A

2015-01-01

A promising route to renewable liquid fuels and chemicals is the fermentation of synthesis gas (syngas) streams to synthesize desired products such as ethanol and 2,3-butanediol. While commercial development of syngas fermentation technology is underway, an unmet need is the development of integrated metabolic and transport models for industrially relevant syngas bubble column reactors. We developed and evaluated a spatiotemporal metabolic model for bubble column reactors with the syngas fermenting bacterium Clostridium ljungdahlii as the microbial catalyst. Our modeling approach involved combining a genome-scale reconstruction of C. ljungdahlii metabolism with multiphase transport equations that govern convective and dispersive processes within the spatially varying column. The reactor model was spatially discretized to yield a large set of ordinary differential equations (ODEs) in time with embedded linear programs (LPs) and solved using the MATLAB based code DFBAlab. Simulations were performed to analyze the effects of important process and cellular parameters on key measures of reactor performance including ethanol titer, ethanol-to-acetate ratio, and CO and H2 conversions. Our computational study demonstrated that mathematical modeling provides a complementary tool to experimentation for understanding, predicting, and optimizing syngas fermentation reactors. These model predictions could guide future cellular and process engineering efforts aimed at alleviating bottlenecks to biochemical production in syngas bubble column reactors.

Nonconvergence to Saddle Boundary Points under Perturbed Reinforcement Learning

DTIC Science & Technology

2012-12-07

of the ODE (12). Note that for some games not all stationary points of the ODE (12) are Nash equilibria. For example, if you consider the Typewriter ...B A 4, 4 2, 2 B 2, 2 3, 3 Table 1: The Typewriter Game. On the other hand, any stationary point in the interior of the probability simplex will... Typewriter Game of Table 1. We observe that it is possible for the process to converge to a pure strategy profile which is not a Nash equilibrium when Ri(α

"Ode Ori": a culture-bound disorder with prominent somatic features in Yoruba Nigerian patients.

PubMed

Makanjuola, R O

1987-03-01

Thirty patients diagnosed by Nigerian Yoruba traditional healers as suffering from a condition termed "Ode Ori" are described. The chief complaints were of a crawling sensation in the head and body, noises in the ears, palpitations and various other somatic complaints. Anxiety and depressive symptoms were prominent in all the patients and indeed the most common DSM-III diagnoses were of depressive and anxiety disorders. The significance of the disorder and its features is discussed in the context of the socio-cultural background of the patients.

Modelling the evaporation of a tear film over a contact lens.

PubMed

Talbott, Kevin; Xu, Amber; Anderson, Daniel M; Seshaiyer, Padmanabhan

2015-06-01

A contact lens (CL) separates the tear film into a pre-lens tear film (PrLTF), the fluid layer between the CL and the outside environment, and a post-lens tear film (PoLTF), the fluid layer between the CL and the cornea. We examine a model for evaporation of a PrLTF on a modern permeable CL allowing fluid transfer between the PrLTF and the PoLTF. Evaporation depletes the PrLTF, and continued evaporation causes depletion of the PoLTF via fluid loss through the CL. Governing equations include Navier-Stokes, heat and Darcy's equations for the fluid flow and heat transfer in the PrLTF and porous layer. The PoLTF is modelled by a fixed pressure condition on the posterior surface of the CL. The original model is simplified using lubrication theory for the PrLTF and CL applied to a sagittal plane through the eye. We obtain a partial differential equation (PDE) for the PrLTF thickness that is first-order in time and fourth-order in space. This model incorporates evaporation, conjoining pressure effects in the PrLTF, capillarity and heat transfer. For a planar film, we find that this PDE can be reduced to an ordinary differential equation (ODE) that can be solved analytically or numerically. This reduced model allows for interpretation of the various system parameters and captures most of the basic physics contained in the model. Comparisons of ODE and PDE models, including estimates for the loss of fluid through the lens due to evaporation, are given. © The Authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Peridigm summary report : lessons learned in development with agile components.

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

Salinger, Andrew Gerhard; Mitchell, John Anthony; Littlewood, David John

2011-09-01

This report details efforts to deploy Agile Components for rapid development of a peridynamics code, Peridigm. The goal of Agile Components is to enable the efficient development of production-quality software by providing a well-defined, unifying interface to a powerful set of component-based software. Specifically, Agile Components facilitate interoperability among packages within the Trilinos Project, including data management, time integration, uncertainty quantification, and optimization. Development of the Peridigm code served as a testbed for Agile Components and resulted in a number of recommendations for future development. Agile Components successfully enabled rapid integration of Trilinos packages into Peridigm. A cost of thismore » approach, however, was a set of restrictions on Peridigm's architecture which impacted the ability to track history-dependent material data, dynamically modify the model discretization, and interject user-defined routines into the time integration algorithm. These restrictions resulted in modifications to the Agile Components approach, as implemented in Peridigm, and in a set of recommendations for future Agile Components development. Specific recommendations include improved handling of material states, a more flexible flow control model, and improved documentation. A demonstration mini-application, SimpleODE, was developed at the onset of this project and is offered as a potential supplement to Agile Components documentation.« less

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

A control theoretical approach to crowd management. Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Borzí, Alfio; Caponigro, Marco

2016-09-01

The formulation of mathematical models for crowd dynamics is one current challenge in many fields of applied sciences. It involves the modelization of the complex behavior of a large number of individuals. In particular, the difficulty lays in describing emerging collective behaviors by means of a relatively small number of local interaction rules between individuals in a crowd. Clearly, the individual's free will involved in decision making processes and in the management of the social interactions cannot be described by a finite number of deterministic rules. On the other hand, in large crowds, this individual indeterminacy can be considered as a local fluctuation averaged to zero by the size of the crowd. While at the microscopic scale, using a system of coupled ODEs, the free will should be included in the mathematical description (e.g. with a stochastic term), the mesoscopic and macroscopic scales, modeled by PDEs, represent a powerful modelling tool that allows to neglect this feature and provide a reliable description. In this sense, the work by Bellomo, Clarke, Gibelli, Townsend, and Vreugdenhil [2] represents a mathematical-epistemological contribution towards the design of a reliable model of human behavior.

Two phase modeling of nanofluid flow in existence of melting heat transfer by means of HAM

NASA Astrophysics Data System (ADS)

Sheikholeslami, M.; Jafaryar, M.; Bateni, K.; Ganji, D. D.

2018-02-01

In this article, Buongiorno Model is applied for investigation of nanofluid flow over a stretching plate in existence of magnetic field. Radiation and Melting heat transfer are taken into account. Homotopy analysis method (HAM) is selected to solve ODEs which are obtained from similarity transformation. Roles of Brownian motion, thermophoretic parameter, Hartmann number, porosity parameter, Melting parameter and Eckert number are presented graphically. Results indicate that nanofluid velocity and concentration enhance with rise of melting parameter. Nusselt number reduces with increase of porosity and melting parameters.

Particle Impact Erosion. Volume 4. User’s Manual Erosion Prediction Procedure for Rocket Nozzle Expansion Region

DTIC Science & Technology

1983-05-01

empirical erosion model, with use of the debris-layer model optional. 1.1 INTERFACE WITH ISPP ISPP is a collection of computer codes designed to calculate...expansion with the ODK code, 4. A two-dimensional, two-phase nozzle expansion with the TD2P code, 5. A turbulent boundary layer solution along the...INPUT THERMODYNAMIC DATA FOR TEMPERATURESBELOW 300°K OIF NEEDED) NO A• 11 READ SSP NAMELIST (ODE. BAL. ODK . TD2P. TEL. NOZZLE GEOMETRY) PROfLM 2

Regarding on the prototype solutions for the nonlinear fractional-order biological population model

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

Baskonus, Haci Mehmet, E-mail: hmbaskonus@gmail.com; Bulut, Hasan

2016-06-08

In this study, we have submitted to literature a method newly extended which is called as Improved Bernoulli sub-equation function method based on the Bernoulli Sub-ODE method. The proposed analytical scheme has been expressed with steps. We have obtained some new analytical solutions to the nonlinear fractional-order biological population model by using this technique. Two and three dimensional surfaces of analytical solutions have been drawn by wolfram Mathematica 9. Finally, a conclusion has been submitted by mentioning important acquisitions founded in this study.

A New Modified Histogram Matching Normalization for Time Series Microarray Analysis.

PubMed

Astola, Laura; Molenaar, Jaap

2014-07-01

Microarray data is often utilized in inferring regulatory networks. Quantile normalization (QN) is a popular method to reduce array-to-array variation. We show that in the context of time series measurements QN may not be the best choice for this task, especially not if the inference is based on continuous time ODE model. We propose an alternative normalization method that is better suited for network inference from time series data.

New trends in Taylor series based applications

NASA Astrophysics Data System (ADS)

Kocina, Filip; Šátek, Václav; Veigend, Petr; Nečasová, Gabriela; Valenta, Václav; Kunovský, Jiří

2016-06-01

The paper deals with the solution of large system of linear ODEs when minimal comunication among parallel processors is required. The Modern Taylor Series Method (MTSM) is used. The MTSM allows using a higher order during the computation that means a larger integration step size while keeping desired accuracy. As an example of complex systems we can take the Telegraph Equation Model. Symbolic and numeric solutions are compared when harmonic input signal is used.

Prediction of geomagnetic reversals using low-dimensional dynamical models and advanced data assimilation: a feasibility study

NASA Astrophysics Data System (ADS)

Fournier, A.; Morzfeld, M.; Hulot, G.

2013-12-01

For a suitable choice of parameters, the system of three ordinary differential equations (ODE) presented by Gissinger [1] was shown to exhibit chaotic reversals whose statistics compared well with those from the paleomagnetic record. In order to further assess the geophysical relevance of this low-dimensional model, we resort to data assimilation methods to calibrate it using reconstructions of the fluctuation of the virtual axial dipole moment spanning the past 2 millions years. Moreover, we test to which extent a properly calibrated model could possibly be used to predict a reversal of the geomagnetic field. We calibrate the ODE model to the geomagnetic field over the past 2 Ma using the SINT data set of Valet et al. [2]. To this end, we consider four data assimilation algorithms: the ensemble Kalman filter (EnKF), a variational method and two Monte Carlo (MC) schemes, prior importance sampling and implicit sampling. We observe that EnKF performs poorly and that prior importance sampling is inefficient. We obtain the most accurate reconstructions of the geomagnetic data using implicit sampling with five data points per assimilation sweep (of duration 5 kyr). The variational scheme performs equally well, but it does not provide us with quantitative information about the uncertainty of the estimates, which makes this method difficult to use for robust prediction under uncertainty. A calibration of the model using the PADM2M data set of Ziegler et al. [3] confirms these findings. We study the predictive capability of the ODE model using statistics computed from synthetic data experiments. For each experiment, we produce 2 Myr of synthetic data (with error levels similar to the ones found in real data), then calibrate the model to this record and then check if this calibrated model can correctly and reliably predict a reversal within the next 10 kyr (say). By performing 100 such experiments, we can assess how reliably our calibrated model can predict a (non-) reversal. It is found that the 5 kyr ahead predictions of reversals produced by the model appear to be accurate and reliable.These encouraging results prompted us to also test predictions of the five reversals of the SINT (and PADM2M) data set, using a similarly calibrated model. Results will be presented and discussed. [1] Gissinger, C., 2012, A new deterministic model for chaotic reversals, European Physical Journal B, 85:137 [2] Valet, J.-P., Meynadier, L. and Guyodo, Y., 2005, Geomagnetic field strength and reversal rate over the past 2 Million years, Nature, 435, 802-805. [3] Ziegler, L. B., Constable, C. G., Johnson, C. L. and Tauxe, L., 2011, PADM2M: a penalized maximum likelihood model of the 0-2 Ma paleomagnetic axial dipole moment, Geophysical Journal International, 184, 1069-1089.

On a sparse pressure-flow rate condensation of rigid circulation models

PubMed Central

Schiavazzi, D. E.; Hsia, T. Y.; Marsden, A. L.

2015-01-01

Cardiovascular simulation has shown potential value in clinical decision-making, providing a framework to assess changes in hemodynamics produced by physiological and surgical alterations. State-of-the-art predictions are provided by deterministic multiscale numerical approaches coupling 3D finite element Navier Stokes simulations to lumped parameter circulation models governed by ODEs. Development of next-generation stochastic multiscale models whose parameters can be learned from available clinical data under uncertainty constitutes a research challenge made more difficult by the high computational cost typically associated with the solution of these models. We present a methodology for constructing reduced representations that condense the behavior of 3D anatomical models using outlet pressure-flow polynomial surrogates, based on multiscale model solutions spanning several heart cycles. Relevance vector machine regression is compared with maximum likelihood estimation, showing that sparse pressure/flow rate approximations offer superior performance in producing working surrogate models to be included in lumped circulation networks. Sensitivities of outlets flow rates are also quantified through a Sobol’ decomposition of their total variance encoded in the orthogonal polynomial expansion. Finally, we show that augmented lumped parameter models including the proposed surrogates accurately reproduce the response of multiscale models they were derived from. In particular, results are presented for models of the coronary circulation with closed loop boundary conditions and the abdominal aorta with open loop boundary conditions. PMID:26671219

mRNA translation and protein synthesis: an analysis of different modelling methodologies and a new PBN based approach

PubMed Central

2014-01-01

Background mRNA translation involves simultaneous movement of multiple ribosomes on the mRNA and is also subject to regulatory mechanisms at different stages. Translation can be described by various codon-based models, including ODE, TASEP, and Petri net models. Although such models have been extensively used, the overlap and differences between these models and the implications of the assumptions of each model has not been systematically elucidated. The selection of the most appropriate modelling framework, and the most appropriate way to develop coarse-grained/fine-grained models in different contexts is not clear. Results We systematically analyze and compare how different modelling methodologies can be used to describe translation. We define various statistically equivalent codon-based simulation algorithms and analyze the importance of the update rule in determining the steady state, an aspect often neglected. Then a novel probabilistic Boolean network (PBN) model is proposed for modelling translation, which enjoys an exact numerical solution. This solution matches those of numerical simulation from other methods and acts as a complementary tool to analytical approximations and simulations. The advantages and limitations of various codon-based models are compared, and illustrated by examples with real biological complexities such as slow codons, premature termination and feedback regulation. Our studies reveal that while different models gives broadly similiar trends in many cases, important differences also arise and can be clearly seen, in the dependence of the translation rate on different parameters. Furthermore, the update rule affects the steady state solution. Conclusions The codon-based models are based on different levels of abstraction. Our analysis suggests that a multiple model approach to understanding translation allows one to ascertain which aspects of the conclusions are robust with respect to the choice of modelling methodology, and when (and why) important differences may arise. This approach also allows for an optimal use of analysis tools, which is especially important when additional complexities or regulatory mechanisms are included. This approach can provide a robust platform for dissecting translation, and results in an improved predictive framework for applications in systems and synthetic biology. PMID:24576337

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

NASA Astrophysics Data System (ADS)

Validi, AbdoulAhad

2014-03-01

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

Systematic parameter estimation in data-rich environments for cell signalling dynamics

PubMed Central

Nim, Tri Hieu; Luo, Le; Clément, Marie-Véronique; White, Jacob K.; Tucker-Kellogg, Lisa

2013-01-01

Motivation: Computational models of biological signalling networks, based on ordinary differential equations (ODEs), have generated many insights into cellular dynamics, but the model-building process typically requires estimating rate parameters based on experimentally observed concentrations. New proteomic methods can measure concentrations for all molecular species in a pathway; this creates a new opportunity to decompose the optimization of rate parameters. Results: In contrast with conventional parameter estimation methods that minimize the disagreement between simulated and observed concentrations, the SPEDRE method fits spline curves through observed concentration points, estimates derivatives and then matches the derivatives to the production and consumption of each species. This reformulation of the problem permits an extreme decomposition of the high-dimensional optimization into a product of low-dimensional factors, each factor enforcing the equality of one ODE at one time slice. Coarsely discretized solutions to the factors can be computed systematically. Then the discrete solutions are combined using loopy belief propagation, and refined using local optimization. SPEDRE has unique asymptotic behaviour with runtime polynomial in the number of molecules and timepoints, but exponential in the degree of the biochemical network. SPEDRE performance is comparatively evaluated on a novel model of Akt activation dynamics including redox-mediated inactivation of PTEN (phosphatase and tensin homologue). Availability and implementation: Web service, software and supplementary information are available at www.LtkLab.org/SPEDRE Supplementary information: Supplementary data are available at Bioinformatics online. Contact: LisaTK@nus.edu.sg PMID:23426255

Non-autonomous Hénon--Heiles systems

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.

1998-07-01

Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent generalizations of the well-known integrable Hénon-Heiles systems. The (time-dependent) Hamiltonians are given by logarithmic derivatives of the tau-functions (inherited from the original PDEs). The ODEs for the similarity solutions also have inherited Bäcklund transformations, which may be used to generate sequences of rational solutions as well as other special solutions related to the first Painlevé transcendent.

Modeling of Nonlinear Dynamics and Synchronized Oscillations of Microbial Populations, Carbon and Oxygen Concentrations, Induced by Root Exudation in the Rhizosphere

NASA Astrophysics Data System (ADS)

Molz, F. J.; Faybishenko, B.; Jenkins, E. W.

2012-12-01

Mass and energy fluxes within the soil-plant-atmosphere continuum are highly coupled and inherently nonlinear. The main focus of this presentation is to demonstrate the results of numerical modeling of a system of 4 coupled, nonlinear ordinary differential equations (ODEs), which are used to describe the long-term, rhizosphere processes of soil microbial dynamics, including the competition between nitrogen-fixing bacteria and those unable to fix nitrogen, along with substrate concentration (nutrient supply) and oxygen concentration. Modeling results demonstrate the synchronized patterns of temporal oscillations of competing microbial populations, which are affected by carbon and oxygen concentrations. The temporal dynamics and amplitude of the root exudation process serve as a driving force for microbial and geochemical phenomena, and lead to the development of the Gompetzian dynamics, synchronized oscillations, and phase-space attractors of microbial populations and carbon and oxygen concentrations. The nonlinear dynamic analysis of time series concentrations from the solution of the ODEs was used to identify several types of phase-space attractors, which appear to be dependent on the parameters of the exudation function and Monod kinetic parameters. This phase space analysis was conducted by means of assessing the global and local embedding dimensions, correlation time, capacity and correlation dimensions, and Lyapunov exponents of the calculated model variables defining the phase space. Such results can be used for planning experimental and theoretical studies of biogeochemical processes in the fields of plant nutrition, phyto- and bio-remediation, and other ecological areas.

Heroin epidemics, treatment and ODE modelling.

PubMed

White, Emma; Comiskey, Catherine

2007-07-01

The UN [United Nations Office on Drugs and Crime (UNODC): World Drug Report, 2005, vol. 1: Analysis. UNODC, 2005.], EU [European Monitoring Centre for Drugs and Drug Addiction (EMCDDA): Annual Report, 2005.http://annualreport.emcdda.eu.int/en/home-en.html.] and WHO [World Health Organisation (WHO): Biregional Strategy for Harm Reduction, 2005-2009. HIV and Injecting Drug Use. WHO, 2005.] have consistently highlighted in recent years the ongoing and persistent nature of opiate and particularly heroin use on a global scale. While this is a global phenomenon, authors have emphasised the significant impact such an epidemic has on individual lives and on society. National prevalence studies have indicated the scale of the problem, but the drug-using career, typically consisting of initiation, habitual use, a treatment-relapse cycle and eventual recovery, is not well understood. This paper presents one of the first ODE models of opiate addiction, based on the principles of mathematical epidemiology. The aim of this model is to identify parameters of interest for further study, with a view to informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness. An epidemic threshold value, R(0), is proposed for the drug-using career. Sensitivity analysis is performed on R(0) and it is then used to examine the stability of the system. A condition under which a backward bifurcation may exist is found, as are conditions that permit the existence of one or more endemic equilibria. A key result arising from this model is that prevention is indeed better than cure.

Determination of equilibrium electron temperature and times using an electron swarm model with BOLSIG+ calculated collision frequencies and rate coefficients

DOE PAGES

Pusateri, Elise N.; Morris, Heidi E.; Nelson, Eric M.; ...

2015-08-04

Electromagnetic pulse (EMP) events produce low-energy conduction electrons from Compton electron or photoelectron ionizations with air. It is important to understand how conduction electrons interact with air in order to accurately predict EMP evolution and propagation. An electron swarm model can be used to monitor the time evolution of conduction electrons in an environment characterized by electric field and pressure. Here a swarm model is developed that is based on the coupled ordinary differential equations (ODEs) described by Higgins et al. (1973), hereinafter HLO. The ODEs characterize the swarm electric field, electron temperature, electron number density, and drift velocity. Importantmore » swarm parameters, the momentum transfer collision frequency, energy transfer collision frequency, and ionization rate, are calculated and compared to the previously reported fitted functions given in HLO. These swarm parameters are found using BOLSIG+, a two term Boltzmann solver developed by Hagelaar and Pitchford (2005), which utilizes updated cross sections from the LXcat website created by Pancheshnyi et al. (2012). We validate the swarm model by comparing to experimental effective ionization coefficient data in Dutton (1975) and drift velocity data in Ruiz-Vargas et al. (2010). In addition, we report on electron equilibrium temperatures and times for a uniform electric field of 1 StatV/cm for atmospheric heights from 0 to 40 km. We show that the equilibrium temperature and time are sensitive to the modifications in the collision frequencies and ionization rate based on the updated electron interaction cross sections.« less

A New Modified Histogram Matching Normalization for Time Series Microarray Analysis

PubMed Central

Astola, Laura; Molenaar, Jaap

2014-01-01

Microarray data is often utilized in inferring regulatory networks. Quantile normalization (QN) is a popular method to reduce array-to-array variation. We show that in the context of time series measurements QN may not be the best choice for this task, especially not if the inference is based on continuous time ODE model. We propose an alternative normalization method that is better suited for network inference from time series data. PMID:27600344

The stress state near Spanish Peaks, colorado determined from a dike pattern

USGS Publications Warehouse

Muller, O.H.; Pollard, D.D.

1977-01-01

The radial pattern of syenite and syenodiorite dikes of the Spanish Peaks region is analysed using theories of elasticity and dike emplacement. The three basic components of Ode??'s model for the dike pattern (a pressurized, circular hole; a rigid, planar boundary; and uniform regional stresses) are adopted, but modified to free the regional stresses from the constraint of being orthogonal to the rigid boundary. Dike areal density, the White Peaks intrusion, the strike of the upturned Mesozoic strata, and the contact between these strata and the intensely folded and faulted Paleozoic rocks are used to brient the rigid boundary along a north-south line. The line of dike terminations locates the rigid boundary about 8 km west of West Peak. The location of a circular plug, Goemmer Butte, is chosen as a point of isotropic stress. A map correlating the location of isotropic stress points with regional stress parameters is derived from the theory and used to determine a regional stress orientation (N82E) and a normalized stress magnitude. The stress trajectory map constructed using these parameters mimics the dike pattern exceptionally well. The model indicates that the regional principal stress difference was less than 0.05 times the driving pressure in the West Peak intrusion. The regional stress difference probably did not exced 5 MN/m2. ?? 1977 Birkha??user Verlag.

Computational study of a magnetic design to improve the diagnosis of malaria: 2D model

NASA Astrophysics Data System (ADS)

Vyas, Siddharth; Genis, Vladimir; Friedman, Gary

2017-02-01

This paper investigates the feasibility of a cost effective high gradient magnetic separation based device for the detection and identification of malaria parasites in a blood sample. The design utilizes magnetic properties of hemozoin present in malaria-infected red blood cells (mRBCs) in order to separate and concentrate them inside a microfluidic channel slide for easier examination under the microscope. The design consists of a rectangular microfluidic channel with multiple magnetic wires positioned on top of and underneath it along the length of the channel at a small angle with respect to the channel axis. Strong magnetic field gradients, produced by the wires, exert sufficient magnetic forces on the mRBCs in order to separate and concentrate them in a specific region small enough to fit within the microscope field of view at magnifications typically required to identify the malaria parasite type. The feasibility of the device is studied using a model where the trajectories of the mRBCs inside the channel are determined using first-order ordinary differential equations (ODEs) solved numerically using a multistep ODE solver available within MATLAB. The mRBCs trajectories reveal that it is possible to separate and concentrate the mRBCs in less than 5 min, even in cases of very low parasitemia (1-10 parasites/μL of blood) using blood sample volumes of around 3 μL employed today.

Redox-responsive solid lipid microparticles composed of octadecyl acrylate and allyl disulfide.

PubMed

Kim, Tae Hoon; Kim, Jin-Chul

2018-04-01

Redox-responsive solid lipid microparticles were prepared by an emulsification photo-polymerization method. Octadecyl acrylate (ODA) and a cross-linker (i.e. allyl disulfide (ADS) and octadiene (ODE)) were dissolved in dichloromethane, it was emulsified in poly(vinyl alcohol) solution, and the resulting O/W emulsion was irradiated with UV light. On the scanning electron microscope micrographs, the microparticles were sphere-like and they were not markedly different from the oil droplets in size. Using the atomic compositions analyzed by energy dispersive X-ray spectroscopy, the ODA to cross-linker molar ratio of ODA/ADS microparticles and ODA/ODE ones were calculated to be 1:0.13 and 1:0.15, respectively. In the FT-IR spectra of the microparticles, the signal of the vinyl group was hardly detected, implying that the monomer and the cross-linkers participated in the photo-polymerization. In differential scanning calorimetry study, ODA/ADS microparticles and ODA/ODE ones exhibited their endothermic peaks around 42.9 and 41.3 °C, respectively, possibly due to the melting of polymeric ODA. Dithiothreitol (DTT, a reducing agent) concentration had little effect on the release degree of dye loaded in ODA/ODE microparticles. Whereas, DTT concentration had a significant effect on the release degree of dye loaded in ODA/ADS microparticles. The release degree at 26 °C was weakly affected by DTT concentration. When the temperature was 37 °C, DTT concentration had a strong effect on the release degree. The disulfide cross-linker (i.e. ADS) can be broken to thiol compounds by the reducing agent, resulting in an increase in the release degree.

SU-E-T-751: Three-Component Kinetic Model of Tumor Growth and Radiation Response for Stereotactic Radiosurgery

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

Watanabe, Y; Dahlman, E; Leder, K

Purpose: To develop and study a kinetic model of tumor growth and its response to stereotactic radiosurgery (SRS) by assuming that the cells in irradiated tumor volume were made of three types. Methods: A set of ordinary differential equations (ODEs) were derived for three types of cells and a tumor growth rate. It is assumed that the cells were composed of actively proliferating cells, lethally damaged-dividing cells, and non-dividing cells. We modeled the tumor volume growth with a time-dependent growth rate to simulate the saturation of growth. After SRS, the proliferating cells were permanently damaged and converted to the lethallymore » damaged cells. The amount of damaged cells were estimated by the LQ-model. The damaged cells gradually stopped dividing/proliferating and died with a constant rate. The dead cells were cleared from their original location with a constant rate. The total tumor volume was the sum of the three components. The ODEs were numerically solved with appropriate initial conditions for a given dosage. The proposed model was used to model an animal experiment, for which the temporal change of a rhabdomyosarcoma tumor volume grown in a rat was measured with time resolution sufficient to test the model. Results: To fit the model to the experimental data, the following characteristics were needed with the model parameters. The α-value in the LQ-model was smaller than the commonly used value; furthermore, it decreased with increasing dose. At the same time, the tumor growth rate after SRS had to increase. Conclusions: The new 3-component model of tumor could simulate the experimental data very well. The current study suggested that the radiation sensitivity and the growth rate of the proliferating tumor cells may change after irradiation and it depended on the dosage used for SRS. These preliminary observations must be confirmed by future animal experiments.« less

Fully Nonlinear Modeling and Analysis of Precision Membranes

NASA Technical Reports Server (NTRS)

Pai, P. Frank; Young, Leyland G.

2003-01-01

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib

PubMed Central

Sobotta, Svantje; Raue, Andreas; Huang, Xiaoyun; Vanlier, Joep; Jünger, Anja; Bohl, Sebastian; Albrecht, Ute; Hahnel, Maximilian J.; Wolf, Stephanie; Mueller, Nikola S.; D'Alessandro, Lorenza A.; Mueller-Bohl, Stephanie; Boehm, Martin E.; Lucarelli, Philippe; Bonefas, Sandra; Damm, Georg; Seehofer, Daniel; Lehmann, Wolf D.; Rose-John, Stefan; van der Hoeven, Frank; Gretz, Norbert; Theis, Fabian J.; Ehlting, Christian; Bode, Johannes G.; Timmer, Jens; Schilling, Marcel; Klingmüller, Ursula

2017-01-01

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines. PMID:29062282

Simulation of anaerobic digestion processes using stochastic algorithm.

PubMed

Palanichamy, Jegathambal; Palani, Sundarambal

2014-01-01

The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic digestion systems. Although several models have been developed, mostly they suffer from lack of knowledge on constants, complexity and weak generalization. The basis of the deterministic approach for modelling the physico and bio-chemical reactions occurring in the AD system is the law of mass action, which gives the simple relationship between the reaction rates and the species concentrations. The assumptions made in the deterministic models are not hold true for the reactions involving chemical species of low concentration. The stochastic behaviour of the physicochemical processes can be modeled at mesoscopic level by application of the stochastic algorithms. In this paper a stochastic algorithm (Gillespie Tau Leap Method) developed in MATLAB was applied to predict the concentration of glucose, acids and methane formation at different time intervals. By this the performance of the digester system can be controlled. The processes given by ADM1 (Anaerobic Digestion Model 1) were taken for verification of the model. The proposed model was verified by comparing the results of Gillespie's algorithms with the deterministic solution for conversion of glucose into methane through degraders. At higher value of 'τ' (timestep), the computational time required for reaching the steady state is more since the number of chosen reactions is less. When the simulation time step is reduced, the results are similar to ODE solver. It was concluded that the stochastic algorithm is a suitable approach for the simulation of complex anaerobic digestion processes. The accuracy of the results depends on the optimum selection of tau value.

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib.

PubMed

Sobotta, Svantje; Raue, Andreas; Huang, Xiaoyun; Vanlier, Joep; Jünger, Anja; Bohl, Sebastian; Albrecht, Ute; Hahnel, Maximilian J; Wolf, Stephanie; Mueller, Nikola S; D'Alessandro, Lorenza A; Mueller-Bohl, Stephanie; Boehm, Martin E; Lucarelli, Philippe; Bonefas, Sandra; Damm, Georg; Seehofer, Daniel; Lehmann, Wolf D; Rose-John, Stefan; van der Hoeven, Frank; Gretz, Norbert; Theis, Fabian J; Ehlting, Christian; Bode, Johannes G; Timmer, Jens; Schilling, Marcel; Klingmüller, Ursula

2017-01-01

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines.

The analysis of HIV/AIDS drug-resistant on networks

NASA Astrophysics Data System (ADS)

Liu, Maoxing

2014-01-01

In this paper, we present an Human Immunodeficiency Virus (HIV)/Acquired Immune Deficiency Syndrome (AIDS) drug-resistant model using an ordinary differential equation (ODE) model on scale-free networks. We derive the threshold for the epidemic to be zero in infinite scale-free network. We also prove the stability of disease-free equilibrium (DFE) and persistence of HIV/AIDS infection. The effects of two immunization schemes, including proportional scheme and targeted vaccination, are studied and compared. We find that targeted strategy compare favorably to a proportional condom using has prominent effect to control HIV/AIDS spread on scale-free networks.

On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation

PubMed Central

DiStefano, Joseph

2014-01-01

Parameter identifiability problems can plague biomodelers when they reach the quantification stage of development, even for relatively simple models. Structural identifiability (SI) is the primary question, usually understood as knowing which of P unknown biomodel parameters p 1,…, pi,…, pP are-and which are not-quantifiable in principle from particular input-output (I-O) biodata. It is not widely appreciated that the same database also can provide quantitative information about the structurally unidentifiable (not quantifiable) subset, in the form of explicit algebraic relationships among unidentifiable pi. Importantly, this is a first step toward finding what else is needed to quantify particular unidentifiable parameters of interest from new I–O experiments. We further develop, implement and exemplify novel algorithms that address and solve the SI problem for a practical class of ordinary differential equation (ODE) systems biology models, as a user-friendly and universally-accessible web application (app)–COMBOS. Users provide the structural ODE and output measurement models in one of two standard forms to a remote server via their web browser. COMBOS provides a list of uniquely and non-uniquely SI model parameters, and–importantly-the combinations of parameters not individually SI. If non-uniquely SI, it also provides the maximum number of different solutions, with important practical implications. The behind-the-scenes symbolic differential algebra algorithms are based on computing Gröbner bases of model attributes established after some algebraic transformations, using the computer-algebra system Maxima. COMBOS was developed for facile instructional and research use as well as modeling. We use it in the classroom to illustrate SI analysis; and have simplified complex models of tumor suppressor p53 and hormone regulation, based on explicit computation of parameter combinations. It’s illustrated and validated here for models of moderate complexity, with and without initial conditions. Built-in examples include unidentifiable 2 to 4-compartment and HIV dynamics models. PMID:25350289

Toxin effect on protein biosynthesis in eukaryotic cells: a simple kinetic model.

PubMed

Skakauskas, Vladas; Katauskis, Pranas; Skvortsov, Alex; Gray, Peter

2015-03-01

A model for toxin inhibition of protein synthesis inside eukaryotic cells is presented. Mitigation of this effect by introduction of an antibody is also studied. Antibody and toxin (ricin) initially are delivered outside the cell. The model describes toxin internalization from the extracellular into the intracellular domain, its transport to the endoplasmic reticulum (ER) and the cleavage inside the ER into the RTA and RTB chains, the release of RTA into the cytosol, inactivation (depurination) of ribosomes, and the effect on translation. The model consists of a set of ODEs which are solved numerically. Numerical results are illustrated by figures and discussed. Copyright © 2015 Elsevier Inc. All rights reserved.

Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

NASA Astrophysics Data System (ADS)

Feng, Wei; Zhao, Songlin

2018-01-01

In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.

Reduction by invariants and projection of linear representations of Lie algebras applied to the construction of nonlinear realizations

NASA Astrophysics Data System (ADS)

Campoamor-Stursberg, R.

2018-03-01

A procedure for the construction of nonlinear realizations of Lie algebras in the context of Vessiot-Guldberg-Lie algebras of first-order systems of ordinary differential equations (ODEs) is proposed. The method is based on the reduction of invariants and projection of lowest-dimensional (irreducible) representations of Lie algebras. Applications to the description of parameterized first-order systems of ODEs related by contraction of Lie algebras are given. In particular, the kinematical Lie algebras in (2 + 1)- and (3 + 1)-dimensions are realized simultaneously as Vessiot-Guldberg-Lie algebras of parameterized nonlinear systems in R3 and R4, respectively.

Dark Soliton Solutions of Space-Time Fractional Sharma-Tasso-Olver and Potential Kadomtsev-Petviashvili Equations

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Korkmaz, Alper; Bekir, Ahmet

2017-02-01

Dark soliton solutions for space-time fractional Sharma-Tasso-Olver and space-time fractional potential Kadomtsev-Petviashvili equations are determined by using the properties of modified Riemann-Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the \\tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma-Tasso-Olver equation as only one solution for the potential Kadomtsev-Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.

Interplay of symmetries and other integrability quantifiers in finite-dimensional integrable nonlinear dynamical systems

PubMed Central

Mohanasubha, R.; Chandrasekar, V. K.; Lakshmanan, M.

2016-01-01

In this work, we establish a connection between the extended Prelle–Singer procedure and other widely used analytical methods to identify integrable systems in the case of nth-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods, we bring out the interlink between Lie point symmetries, contact symmetries, λ-symmetries, adjoint symmetries, null forms, Darboux polynomials, integrating factors, the Jacobi last multiplier and generalized λ-symmetries corresponding to the nth-order ODEs. We also prove these interlinks with suitable examples. By exploiting these interconnections, the characteristic quantities associated with different methods can be deduced without solving the associated determining equations. PMID:27436964

Sensitivity and specificity of monochromatic photography of the ocular fundus in differentiating optic nerve head drusen and optic disc oedema: optic disc drusen and oedema.

PubMed

Gili, Pablo; Flores-Rodríguez, Patricia; Yangüela, Julio; Orduña-Azcona, Javier; Martín-Ríos, María Dolores

2013-03-01

Evaluation of the efficacy of monochromatic photography of the ocular fundus in differentiating optic nerve head drusen (ONHD) and optic disc oedema (ODE). Sixty-six patients with ONHD, 31 patients with ODE and 70 healthy subjects were studied. Colour and monochromatic fundus photography with different filters (green, red and autofluorescence) were performed. The results were analysed blindly by two observers. The sensitivity, specificity and interobserver agreement (k) of each test were assessed. Colour photography offers 65.5 % sensitivity and 100 % specificity for the diagnosis of ONHD. Monochromatic photography improves sensitivity and specificity and provides similar results: green filter (71.20 % sensitivity, 96.70 % specificity), red filter (80.30 % sensitivity, 96.80 % specificity), and autofluorescence technique (87.8 % sensitivity, 100 % specificity). The interobserver agreement was good with all techniques used: autofluorescence (k = 0.957), green filter (k = 0.897), red filter (k = 0.818) and colour (k = 0.809). Monochromatic fundus photography permits ONHD and ODE to be differentiated, with good sensitivity and very high specificity. The best results were obtained with autofluorescence and red filter study.

Solving ODE Initial Value Problems With Implicit Taylor Series Methods

NASA Technical Reports Server (NTRS)

Scott, James R.

2000-01-01

In this paper we introduce a new class of numerical methods for integrating ODE initial value problems. Specifically, we propose an extension of the Taylor series method which significantly improves its accuracy and stability while also increasing its range of applicability. To advance the solution from t (sub n) to t (sub n+1), we expand a series about the intermediate point t (sub n+mu):=t (sub n) + mu h, where h is the stepsize and mu is an arbitrary parameter called an expansion coefficient. We show that, in general, a Taylor series of degree k has exactly k expansion coefficients which raise its order of accuracy. The accuracy is raised by one order if k is odd, and by two orders if k is even. In addition, if k is three or greater, local extrapolation can be used to raise the accuracy two additional orders. We also examine stability for the problem y'= lambda y, Re (lambda) less than 0, and identify several A-stable schemes. Numerical results are presented for both fixed and variable stepsizes. It is shown that implicit Taylor series methods provide an effective integration tool for most problems, including stiff systems and ODE's with a singular point.

Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes

NASA Astrophysics Data System (ADS)

Calvo, M.; González-Pinto, S.; Montijano, J. I.

2008-09-01

Modern codes for the numerical solution of Initial Value Problems (IVPs) in ODEs are based in adaptive methods that, for a user supplied tolerance [delta], attempt to advance the integration selecting the size of each step so that some measure of the local error is [similar, equals][delta]. Although this policy does not ensure that the global errors are under the prescribed tolerance, after the early studies of Stetter [Considerations concerning a theory for ODE-solvers, in: R. Burlisch, R.D. Grigorieff, J. Schröder (Eds.), Numerical Treatment of Differential Equations, Proceedings of Oberwolfach, 1976, Lecture Notes in Mathematics, vol. 631, Springer, Berlin, 1978, pp. 188-200; Tolerance proportionality in ODE codes, in: R. März (Ed.), Proceedings of the Second Conference on Numerical Treatment of Ordinary Differential Equations, Humbold University, Berlin, 1980, pp. 109-123] and the extensions of Higham [Global error versus tolerance for explicit Runge-Kutta methods, IMA J. Numer. Anal. 11 (1991) 457-480; The tolerance proportionality of adaptive ODE solvers, J. Comput. Appl. Math. 45 (1993) 227-236; The reliability of standard local error control algorithms for initial value ordinary differential equations, in: Proceedings: The Quality of Numerical Software: Assessment and Enhancement, IFIP Series, Springer, Berlin, 1997], it has been proved that in many existing explicit Runge-Kutta codes the global errors behave asymptotically as some rational power of [delta]. This step-size policy, for a given IVP, determines at each grid point tn a new step-size hn+1=h(tn;[delta]) so that h(t;[delta]) is a continuous function of t. In this paper a study of the tolerance proportionality property under a discontinuous step-size policy that does not allow to change the size of the step if the step-size ratio between two consecutive steps is close to unity is carried out. This theory is applied to obtain global error estimations in a few problems that have been solved with the code Gauss2 [S. Gonzalez-Pinto, R. Rojas-Bello, Gauss2, a Fortran 90 code for second order initial value problems, ], based on an adaptive two stage Runge-Kutta-Gauss method with this discontinuous step-size policy.

Cause and cure of sloppiness in ordinary differential equation models.

PubMed

Tönsing, Christian; Timmer, Jens; Kreutz, Clemens

2014-08-01

Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

Qualitative dynamical analysis of chaotic plasma perturbations model

NASA Astrophysics Data System (ADS)

Elsadany, A. A.; Elsonbaty, Amr; Agiza, H. N.

2018-06-01

In this work, an analytical framework to understand nonlinear dynamics of plasma perturbations model is introduced. In particular, we analyze the model presented by Constantinescu et al. [20] which consists of three coupled ODEs and contains three parameters. The basic dynamical properties of the system are first investigated by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Then, the normal form technique and perturbation methods are applied so as to the different types of bifurcations that exist in the model are investigated. It is proved that pitcfork, Bogdanov-Takens, Andronov-Hopf bifurcations, degenerate Hopf and homoclinic bifurcation can occur in phase space of the model. Also, the model can exhibit quasiperiodicity and chaotic behavior. Numerical simulations confirm our theoretical analytical results.

Cause and cure of sloppiness in ordinary differential equation models

NASA Astrophysics Data System (ADS)

Tönsing, Christian; Timmer, Jens; Kreutz, Clemens

2014-08-01

Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

Designing synthetic networks in silico: a generalised evolutionary algorithm approach.

PubMed

Smith, Robert W; van Sluijs, Bob; Fleck, Christian

2017-12-02

Evolution has led to the development of biological networks that are shaped by environmental signals. Elucidating, understanding and then reconstructing important network motifs is one of the principal aims of Systems & Synthetic Biology. Consequently, previous research has focused on finding optimal network structures and reaction rates that respond to pulses or produce stable oscillations. In this work we present a generalised in silico evolutionary algorithm that simultaneously finds network structures and reaction rates (genotypes) that can satisfy multiple defined objectives (phenotypes). The key step to our approach is to translate a schema/binary-based description of biological networks into systems of ordinary differential equations (ODEs). The ODEs can then be solved numerically to provide dynamic information about an evolved networks functionality. Initially we benchmark algorithm performance by finding optimal networks that can recapitulate concentration time-series data and perform parameter optimisation on oscillatory dynamics of the Repressilator. We go on to show the utility of our algorithm by finding new designs for robust synthetic oscillators, and by performing multi-objective optimisation to find a set of oscillators and feed-forward loops that are optimal at balancing different system properties. In sum, our results not only confirm and build on previous observations but we also provide new designs of synthetic oscillators for experimental construction. In this work we have presented and tested an evolutionary algorithm that can design a biological network to produce desired output. Given that previous designs of synthetic networks have been limited to subregions of network- and parameter-space, the use of our evolutionary optimisation algorithm will enable Synthetic Biologists to construct new systems with the potential to display a wider range of complex responses.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part 2; Global Asymptotic Behavior of Time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

An ODE-Based Wall Model for Turbulent Flow Simulations

NASA Technical Reports Server (NTRS)

Berger, Marsha J.; Aftosmis, Michael J.

2017-01-01

Fully automated meshing for Reynolds-Averaged Navier-Stokes Simulations, Mesh generation for complex geometry continues to be the biggest bottleneck in the RANS simulation process; Fully automated Cartesian methods routinely used for inviscid simulations about arbitrarily complex geometry; These methods lack of an obvious & robust way to achieve near wall anisotropy; Goal: Extend these methods for RANS simulation without sacrificing automation, at an affordable cost; Note: Nothing here is limited to Cartesian methods, and much becomes simpler in a body-fitted setting.

Homoclinic Bifurcation in an SIQR Model for Childhood Diseases

NASA Astrophysics Data System (ADS)

Wu, Lih-Ing; Feng, Zhilan

2000-11-01

We consider a system of ODEs which describes the transmission dynamics of childhood diseases. A center manifold reduction at a bifurcation point has the normal form x‧=y, y‧=axy+bx2y+O(4), indicating a bifurcation of codimension greater than two. A three-parameter unfolding of the normal form is studied to capture possible complex dynamics of the original system which is subjected to certain constraints on the state space due to biological considerations. It is shown that the perturbed system produces homoclinic bifurcation.

A Comparison in the Accuracy of Mapping Nuclear Fallout Patterns Using HPAC, HYSPLIT, DELFIC FPT and an AFIT FORTRAN95 Fallout Deposition ode

DTIC Science & Technology

2011-03-01

Capability (HPAC), HPAC 4.04 On-Line Help. Alexandria VA , April 2005. 13. Draxler, Roland R. and G.D. Hess. Description of the HYSPLIT_4 Modeling...Effects of Nuclear Weapons. Alexandria, VA : The United States Department of Defense and the United States Department of Energy, 1977. 18...77: 437-431 (3 March 1996). 25. Moroz , Brian E., Harold L. Beck, Andre Bouville, and Steven L. Simon. “Predictions of Dispersion and Deposition

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

PubMed

Muñoz-Tamayo, R; Puillet, L; Daniel, J B; Sauvant, D; Martin, O; Taghipoor, M; Blavy, P

2018-04-01

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.

SEIR model simulation for Hepatitis B

NASA Astrophysics Data System (ADS)

Side, Syafruddin; Irwan, Mulbar, Usman; Sanusi, Wahidah

2017-09-01

Mathematical modelling and simulation for Hepatitis B discuss in this paper. Population devided by four variables, namely: Susceptible, Exposed, Infected and Recovered (SEIR). Several factors affect the population in this model is vaccination, immigration and emigration that occurred in the population. SEIR Model obtained Ordinary Differential Equation (ODE) non-linear System 4-D which then reduces to 3-D. SEIR model simulation undertaken to predict the number of Hepatitis B cases. The results of the simulation indicates the number of Hepatitis B cases will increase and then decrease for several months. The result of simulation using the number of case in Makassar also found the basic reproduction number less than one, that means, Makassar city is not an endemic area of Hepatitis B.

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

PubMed Central

Saberi Nik, Hassan; Rebelo, Paulo

2014-01-01

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results. PMID:25386624

Linear Stability Analysis of an Acoustically Vaporized Droplet

NASA Astrophysics Data System (ADS)

Siddiqui, Junaid; Qamar, Adnan; Samtaney, Ravi

2015-11-01

Acoustic droplet vaporization (ADV) is a phase transition phenomena of a superheat liquid (Dodecafluoropentane, C5F12) droplet to a gaseous bubble, instigated by a high-intensity acoustic pulse. This approach was first studied in imaging applications, and applicable in several therapeutic areas such as gas embolotherapy, thrombus dissolution, and drug delivery. High-speed imaging and theoretical modeling of ADV has elucidated several physical aspects, ranging from bubble nucleation to its subsequent growth. Surface instabilities are known to exist and considered responsible for evolving bubble shapes (non-spherical growth, bubble splitting and bubble droplet encapsulation). We present a linear stability analysis of the dynamically evolving interfaces of an acoustically vaporized micro-droplet (liquid A) in an infinite pool of a second liquid (liquid B). We propose a thermal ADV model for the base state. The linear analysis utilizes spherical harmonics (Ynm, of degree m and order n) and under various physical assumptions results in a time-dependent ODE of the perturbed interface amplitudes (one at the vapor/liquid A interface and the other at the liquid A/liquid B interface). The perturbation amplitudes are found to grow exponentially and do not depend on m. Supported by KAUST Baseline Research Funds.

Stochastic flux analysis of chemical reaction networks

PubMed Central

2013-01-01

Background Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. Results We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. Conclusions We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network. PMID:24314153

Stochastic flux analysis of chemical reaction networks.

PubMed

Kahramanoğulları, Ozan; Lynch, James F

2013-12-07

Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network.

Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model.

PubMed

Laamiri, Imen; Khouaja, Anis; Messaoud, Hassani

2015-03-01

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS). Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

A one-dimensional model for gas-solid heat transfer in pneumatic conveying

NASA Astrophysics Data System (ADS)

Smajstrla, Kody Wayne

A one-dimensional ODE model reduced from a two-fluid model of a higher dimensional order is developed to study dilute, two-phase (air and solid particles) flows with heat transfer in a horizontal pneumatic conveying pipe. Instead of using constant air properties (e.g., density, viscosity, thermal conductivity) evaluated at the initial flow temperature and pressure, this model uses an iteration approach to couple the air properties with flow pressure and temperature. Multiple studies comparing the use of constant or variable air density, viscosity, and thermal conductivity are conducted to study the impact of the changing properties to system performance. The results show that the fully constant property calculation will overestimate the results of the fully variable calculation by 11.4%, while the constant density with variable viscosity and thermal conductivity calculation resulted in an 8.7% overestimation, the constant viscosity with variable density and thermal conductivity overestimated by 2.7%, and the constant thermal conductivity with variable density and viscosity calculation resulted in a 1.2% underestimation. These results demonstrate that gas properties varying with gas temperature can have a significant impact on a conveying system and that the varying density accounts for the majority of that impact. The accuracy of the model is also validated by comparing the simulation results to the experimental values found in the literature.

First integrals and parametric solutions of third-order ODEs admitting {\\mathfrak{sl}(2, {R})}

NASA Astrophysics Data System (ADS)

Ruiz, A.; Muriel, C.

2017-05-01

A complete set of first integrals for any third-order ordinary differential equation admitting a Lie symmetry algebra isomorphic to sl(2, {R}) is explicitly computed. These first integrals are derived from two linearly independent solutions of a linear second-order ODE, without additional integration. The general solution in parametric form can be obtained by using the computed first integrals. The study includes a parallel analysis of the four inequivalent realizations of sl(2, {R}) , and it is applied to several particular examples. These include the generalized Chazy equation, as well as an example of an equation which admits the most complicated of the four inequivalent realizations.

Dual Roles of β-Oxodithioesters in the Copper-Catalyzed Synthesis of Benzo[e]pyrazolo[1,5-c][1,3]thiazine Derivatives.

PubMed

Wen, Li-Rong; Yuan, Wen-Kui; Li, Ming

2015-05-15

A facile and efficient method for the chemoselective synthesis of benzo[e]pyrazolo[1,5-c][1,3]thiazine derivatives has been developed by tandem Ullmann coupling reactions of β-oxodithioesters (ODEs) with 3-(2-bromoaryl)-1H-pyrazoles in C-S bond formation manner, in which ODEs play dual roles as both a substrate and a ligand. A series of benzo[e]pyrazolo[1,5-c][1,3]thiazine derivatives were provided in good to excellent yields with CuI as the copper source in the presence of NaOH in CH3CN at 80 °C under a N2 atmosphere.

ODE/IM correspondence for modified B2(1) affine Toda field equation

NASA Astrophysics Data System (ADS)

Ito, Katsushi; Shu, Hongfei

2017-03-01

We study the massive ODE/IM correspondence for modified B2(1) affine Toda field equation. Based on the ψ-system for the solutions of the associated linear problem, we obtain the Bethe ansatz equations. We also discuss the T-Q relations, the T-system and the Y-system, which are shown to be related to those of the A3 /Z2 integrable system. We consider the case that the solution of the linear problem has a monodromy around the origin, which imposes nontrivial boundary conditions for the T-/Y-system. The high-temperature limit of the T- and Y-system and their monodromy dependence are studied numerically.

EVOLUTION OF THE MAGNETIC FIELD LINE DIFFUSION COEFFICIENT AND NON-GAUSSIAN STATISTICS

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

Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H.

The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with thesemore » underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.« less

Effects of fuel cetane number on the structure of diesel spray combustion: An accelerated Eulerian stochastic fields method

NASA Astrophysics Data System (ADS)

Jangi, Mehdi; Lucchini, Tommaso; Gong, Cheng; Bai, Xue-Song

2015-09-01

An Eulerian stochastic fields (ESF) method accelerated with the chemistry coordinate mapping (CCM) approach for modelling spray combustion is formulated, and applied to model diesel combustion in a constant volume vessel. In ESF-CCM, the thermodynamic states of the discretised stochastic fields are mapped into a low-dimensional phase space. Integration of the chemical stiff ODEs is performed in the phase space and the results are mapped back to the physical domain. After validating the ESF-CCM, the method is used to investigate the effects of fuel cetane number on the structure of diesel spray combustion. It is shown that, depending of the fuel cetane number, liftoff length is varied, which can lead to a change in combustion mode from classical diesel spray combustion to fuel-lean premixed burned combustion. Spray combustion with a shorter liftoff length exhibits the characteristics of the classical conceptual diesel combustion model proposed by Dec in 1997 (http://dx.doi.org/10.4271/970873), whereas in a case with a lower cetane number the liftoff length is much larger and the spray combustion probably occurs in a fuel-lean-premixed mode of combustion. Nevertheless, the transport budget at the liftoff location shows that stabilisation at all cetane numbers is governed primarily by the auto-ignition process.

Dynamics and forecast in a simple model of sustainable development for rural populations.

PubMed

Angulo, David; Angulo, Fabiola; Olivar, Gerard

2015-02-01

Society is becoming more conscious on the need to preserve the environment. Sustainable development schemes have grown rapidly as a tool for managing, predicting and improving the growth path in different regions and economy sectors. We introduce a novel and simple mathematical model of ordinary differential equations (ODEs) in order to obtain a dynamical description for each one of the sustainability components (economy, social development and environment conservation), together with their dependence with demographic dynamics. The main part in the modeling task is inspired by the works by Cobb, Douglas, Brander and Taylor. This is completed through some new insights by the authors. A model application is presented for three specific geographical rural regions in Caldas (Colombia).

Global stability results for a generalized Lotka-Volterra system with distributed delays. Applications to predator-prey and to epidemic systems.

PubMed

Beretta, E; Capasso, V; Rinaldi, F

1988-01-01

The paper contains an extension of the general ODE system proposed in previous papers by the same authors, to include distributed time delays in the interaction terms. The new system describes a large class of Lotka-Volterra like population models and epidemic models with continuous time delays. Sufficient conditions for the boundedness of solutions and for the global asymptotic stability of nontrivial equilibrium solutions are given. A detailed analysis of the epidemic system is given with respect to the conditions for global stability. For a relevant subclass of these systems an existence criterion for steady states is also given.

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

NASA Technical Reports Server (NTRS)

Majda, G.

1985-01-01

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1986-01-01

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Numerical investigation of magnetohydrodynamic slip flow of power-law nanofluid with temperature dependent viscosity and thermal conductivity over a permeable surface

NASA Astrophysics Data System (ADS)

Hussain, Sajid; Aziz, Asim; Khalique, Chaudhry Masood; Aziz, Taha

2017-12-01

In this paper, a numerical investigation is carried out to study the effect of temperature dependent viscosity and thermal conductivity on heat transfer and slip flow of electrically conducting non-Newtonian nanofluids. The power-law model is considered for water based nanofluids and a magnetic field is applied in the transverse direction to the flow. The governing partial differential equations(PDEs) along with the slip boundary conditions are transformed into ordinary differential equations(ODEs) using a similarity technique. The resulting ODEs are numerically solved by using fourth order Runge-Kutta and shooting methods. Numerical computations for the velocity and temperature profiles, the skin friction coefficient and the Nusselt number are presented in the form of graphs and tables. The velocity gradient at the boundary is highest for pseudoplastic fluids followed by Newtonian and then dilatant fluids. Increasing the viscosity of the nanofluid and the volume of nanoparticles reduces the rate of heat transfer and enhances the thickness of the momentum boundary layer. The increase in strength of the applied transverse magnetic field and suction velocity increases fluid motion and decreases the temperature distribution within the boundary layer. Increase in the slip velocity enhances the rate of heat transfer whereas thermal slip reduces the rate of heat transfer.

Toward GPGPU accelerated human electromechanical cardiac simulations

PubMed Central

Vigueras, Guillermo; Roy, Ishani; Cookson, Andrew; Lee, Jack; Smith, Nicolas; Nordsletten, David

2014-01-01

In this paper, we look at the acceleration of weakly coupled electromechanics using the graphics processing unit (GPU). Specifically, we port to the GPU a number of components of Heart—a CPU-based finite element code developed for simulating multi-physics problems. On the basis of a criterion of computational cost, we implemented on the GPU the ODE and PDE solution steps for the electrophysiology problem and the Jacobian and residual evaluation for the mechanics problem. Performance of the GPU implementation is then compared with single core CPU (SC) execution as well as multi-core CPU (MC) computations with equivalent theoretical performance. Results show that for a human scale left ventricle mesh, GPU acceleration of the electrophysiology problem provided speedups of 164 × compared with SC and 5.5 times compared with MC for the solution of the ODE model. Speedup of up to 72 × compared with SC and 2.6 × compared with MC was also observed for the PDE solve. Using the same human geometry, the GPU implementation of mechanics residual/Jacobian computation provided speedups of up to 44 × compared with SC and 2.0 × compared with MC. © 2013 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons, Ltd. PMID:24115492

Computation of restoration of ligand response in the random kinetics of a prostate cancer cell signaling pathway.

PubMed

Dana, Saswati; Nakakuki, Takashi; Hatakeyama, Mariko; Kimura, Shuhei; Raha, Soumyendu

2011-01-01

Mutation and/or dysfunction of signaling proteins in the mitogen activated protein kinase (MAPK) signal transduction pathway are frequently observed in various kinds of human cancer. Consistent with this fact, in the present study, we experimentally observe that the epidermal growth factor (EGF) induced activation profile of MAP kinase signaling is not straightforward dose-dependent in the PC3 prostate cancer cells. To find out what parameters and reactions in the pathway are involved in this departure from the normal dose-dependency, a model-based pathway analysis is performed. The pathway is mathematically modeled with 28 rate equations yielding those many ordinary differential equations (ODE) with kinetic rate constants that have been reported to take random values in the existing literature. This has led to us treating the ODE model of the pathways kinetics as a random differential equations (RDE) system in which the parameters are random variables. We show that our RDE model captures the uncertainty in the kinetic rate constants as seen in the behavior of the experimental data and more importantly, upon simulation, exhibits the abnormal EGF dose-dependency of the activation profile of MAP kinase signaling in PC3 prostate cancer cells. The most likely set of values of the kinetic rate constants obtained from fitting the RDE model into the experimental data is then used in a direct transcription based dynamic optimization method for computing the changes needed in these kinetic rate constant values for the restoration of the normal EGF dose response. The last computation identifies the parameters, i.e., the kinetic rate constants in the RDE model, that are the most sensitive to the change in the EGF dose response behavior in the PC3 prostate cancer cells. The reactions in which these most sensitive parameters participate emerge as candidate drug targets on the signaling pathway. 2011 Elsevier Ireland Ltd. All rights reserved.

Large Diffusivity and Asymptotic Behavior in Parabolic Systems.

DTIC Science & Technology

1985-01-01

interesting ones for the case in which there is an in- variant region E. Any two species Volterra - Lotka model for which the ode’s have a unique stable...qualitative results as in [9], but the rates of decay are not as sharp. Generalizations to functional differential equations are given in Section 4. 2...1, generated by the equation aw/3t = DAW in 1. ..,. ., aw/an = 0 on an. Now, fix a > 3/4. There is a constant k > 0 such that P"~~ ,r*-’ IT(t)wl

Thermal buoyancy on magneto hydrodynamic flow over a vertical saturated porous surface with viscous dissipation

NASA Astrophysics Data System (ADS)

Nirmala, P. H.; Saila Kumari, A.; Raju, C. S. K.

2018-04-01

In the present article, we studied the magnetohydro dynamic flow induced heat transfer from vertical surface embedded in a saturated porous medium in the presence of viscous dissipation. Appropriate similarity transformations are used to transmute the non-linear governing partial differential equations to non-linear ODE. To solve these ordinary differential equations (ODE) we used the well-known integral method of Von Karman type. A comparison has been done and originates to be in suitable agreement with the previous published results. The tabulated and graphical results are given to consider the physical nature of the problem. From this results we found that the magnetic field parameter depreciate the velocity profiles and improves the heat transfer rate of the flow.

Implementation of Rosenbrock methods

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

Shampine, L. F.

1980-11-01

Rosenbrock formulas have shown promise in research codes for the solution of initial-value problems for stiff systems of ordinary differential equations (ODEs). To help assess their practical value, the author wrote an item of mathematical software based on such a formula. This required a variety of algorithmic and software developments. Those of general interest are reported in this paper. Among them is a way to select automatically, at every step, an explicit Runge-Kutta formula or a Rosenbrock formula according to the stiffness of the problem. Solving linear systems is important to methods for stiff ODEs, and is rather special formore » Rosenbrock methods. A cheap, effective estimate of the condition of the linear systems is derived. Some numerical results are presented to illustrate the developments.« less

Integrable cosmological potentials

NASA Astrophysics Data System (ADS)

Sokolov, V. V.; Sorin, A. S.

2017-09-01

The problem of classification of the Einstein-Friedman cosmological Hamiltonians H with a single scalar inflaton field φ, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint H=0, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential V(φ). In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed.

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Stability analysis of BWR nuclear-coupled thermal-hyraulics using a simple model

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

Karve, A.A.; Rizwan-uddin; Dorning, J.J.

1995-09-01

A simple mathematical model is developed to describe the dynamics of the nuclear-coupled thermal-hydraulics in a boiling water reactor (BWR) core. The model, which incorporates the essential features of neutron kinetics, and single-phase and two-phase thermal-hydraulics, leads to simple dynamical system comprised of a set of nonlinear ordinary differential equations (ODEs). The stability boundary is determined and plotted in the inlet-subcooling-number (enthalpy)/external-reactivity operating parameter plane. The eigenvalues of the Jacobian matrix of the dynamical system also are calculated at various steady-states (fixed points); the results are consistent with those of the direct stability analysis and indicate that a Hopf bifurcationmore » occurs as the stability boundary in the operating parameter plane is crossed. Numerical simulations of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter plane to obtain the actual damped and growing oscillations in the neutron number density, the channel inlet flow velocity, and the other phase variables. These indicate that the Hopf bifurcation is subcritical, hence, density wave oscillations with growing amplitude could result from a finite perturbation of the system even where the steady-state is stable. The power-flow map, frequently used by reactor operators during start-up and shut-down operation of a BWR, is mapped to the inlet-subcooling-number/neutron-density (operating-parameter/phase-variable) plane, and then related to the stability boundaries for different fixed inlet velocities corresponding to selected points on the flow-control line. The stability boundaries for different fixed inlet subcooling numbers corresponding to those selected points, are plotted in the neutron-density/inlet-velocity phase variable plane and then the points on the flow-control line are related to their respective stability boundaries in this plane.« less

Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

PubMed

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

Insights into Chemical Transport and Oxidative Processing in the Arctic Springtime

NASA Astrophysics Data System (ADS)

Apel, E. C.; Hornbrook, R. S.; Flocke, F. M.; Hall, S. R.; Hills, A. J.; Montzka, D.; Orlando, J. J.; Turnipseed, A. A.; Ullmann, K.; Weinheimer, A. J.; Mauldin, L.; Riemer, D. D.; Shepson, P. B.; Sive, B. C.; Staebler, R. M.; Blake, N. J.

2015-12-01

Gas-phase volatile organic compounds (VOCs) were measured at several levels between the snow surface and 6 m in the Arctic boundary layer in Barrow, Alaska for the OASIS-2009 field campaign during March and April 2009, as part of the International Polar Year (IPY). Nonmethane hydrocarbons (NMHCs) from C4-C8 and oxygenated VOCs, including alcohols, aldehydes and ketones were quantified multiple times per hour, day and night during the campaign using in-situ fast gas chromatography-mass spectrometry (fast-GC/MS). Samples were also collected in canisters two to three times daily and subsequently analyzed for C2-C8 NMHCs. The NMHCs and aldehydes all showed decreasing mixing ratios with time during the experiment whereas acetone and MEK showed increases. These results are interpreted in the context of a box model and a 3D chemical transport model. After adjusting for seasonal trends in the VOCs, acetone, MEK and 2-pentanone were all negatively correlated with O3, while NMHCs, methanol, ethanol, acetaldehyde, propanal and butanal were all positively correlated with O3. Several ozone depletion events (ODEs) during the study provided an opportunity to investigate the large perturbations due to halogen chemistry on the production and loss of VOCs in the air masses at the sampling site. Notably, aldehyde mixing ratios dropped below the detection limit of the instrument (< 3 pptv) during the ODEs. The NCAR Master Mechanism (MM) (0-D box model), which was updated to include halogen chemistry, was able to reproduce the bromine explosion and showed consistency with key observations including the aldehyde data. Further, no clear positive or negative air-snow flux could be identified for any of the VOCs observed by fast-GC/MS during the study.

Cattaneo-Christov heat flux effect on hydromagnetic radiative Oldroyd-B liquid flow across a cone/wedge in the presence of cross-diffusion

NASA Astrophysics Data System (ADS)

Gnaneswara Reddy, M.

2018-01-01

The present article scrutinizes the prominent characteristics of the Cattaneo-Christov heat flux on magnetohydrodynamic Oldroyd-B radiative liquid flow over two different geometries. The effects of cross-diffusion are considered in the modeling of species and energy equations. Similarity transformations are employed to transmute the governing flow, species and energy equations into a set of nonlinear ordinary differential equations (ODEs) with the appropriate boundary conditions. The final system of dimensionless equations is resolved numerically by utilizing the R-K-Fehlberg numerical approach. The behaviors of all physical pertinent flow controlling variables on the three flow distributions are analyzed through plots. The obtained numerical results have been compared with earlier published work and reveal good agreement. The Deborah numbers γ1 and γ2 have quite opposite effects on velocity and energy fields. The increase in thermal relaxation parameter β corresponds to a decrease in the fluid temperature. This study has salient applications in heat and mass transfer manufacturing system processing for energy conversion.

Optical drift effects in general relativity

NASA Astrophysics Data System (ADS)

Korzyński, Mikołaj; Kopiński, Jarosław

2018-03-01

We consider the question of determining the optical drift effects in general relativity, i.e. the rate of change of the apparent position, redshift, Jacobi matrix, angular distance and luminosity distance of a distant object as registered by an observer in an arbitrary spacetime. We present a fully relativistic and covariant approach, in which the problem is reduced to a hierarchy of ODE's solved along the line of sight. The 4-velocities and 4-accelerations of the observer and the emitter and the geometry of the spacetime along the line of sight constitute the input data. We build on the standard relativistic geometric optics formalism and extend it to include the time derivatives of the observables. In the process we obtain two general, non-perturbative relations: the first one between the gravitational lensing, represented by the Jacobi matrix, and the apparent position drift, also called the cosmic parallax, and the second one between the apparent position drift and the redshift drift. The applications of the results include the theoretical study of the drift effects of cosmological origin (so-called real-time cosmology) in numerical or exact Universe models.

Burning invariant manifolds for reaction fronts in three-dimensional fluid flows

NASA Astrophysics Data System (ADS)

Mitchell, Kevin; Solomon, Tom

2017-11-01

The geometry of reaction fronts that propagate in fully three-dimensional (3D) fluid flows is studied using the tools of dynamical systems theory. The evolution of an infinitesimal front element is modeled as a six-dimensional ODE-three dimensions for the position of the front element and three for the orientation of its unit normal. This generalizes an earlier approach to understanding front propagation in two-dimensional (2D) fluid flows. As in 2D, the 3D system exhibits prominent burning invariant manifolds (BIMs). In 3D, BIMs are two-dimensional dynamically defined surfaces that form one-way barriers to the propagation of reaction fronts within the fluid. Due to the third dimension, BIMs in 3D exhibit a richer topology than their cousins in 2D. In particular, whereas BIMs in both 2D and 3D can originate from fixed points of the dynamics, BIMs in 3D can also originate from limit cycles. Such BIMs form robust tube-like channels that guide and constrain the evolution of the front within the bulk of the fluid. Supported by NSF Grant CMMI-1201236.

COMPUTATION OF ℛ IN AGE-STRUCTURED EPIDEMIOLOGICAL MODELS WITH MATERNAL AND TEMPORARY IMMUNITY.

PubMed

Feng, Zhilan; Han, Qing; Qiu, Zhipeng; Hill, Andrew N; Glasser, John W

2016-03-01

For infectious diseases such as pertussis, susceptibility is determined by immunity, which is chronological age-dependent. We consider an age-structured epidemiological model that accounts for both passively acquired maternal antibodies that decay and active immunity that wanes, permitting reinfection. The model is a 6-dimensional system of partial differential equations (PDE). By assuming constant rates within each age-group, the PDE system can be reduced to an ordinary differential equation (ODE) system with aging from one age-group to the next. We derive formulae for the effective reproduction number ℛ and provide their biological interpretation in some special cases. We show that the disease-free equilibrium is stable when ℛ < 1 and unstable if ℛ > 1.

Stochastic Petri Net extension of a yeast cell cycle model.

PubMed

Mura, Ivan; Csikász-Nagy, Attila

2008-10-21

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.

Exponentially varying viscosity of magnetohydrodynamic mixed convection Eyring-Powell nanofluid flow over an inclined surface

NASA Astrophysics Data System (ADS)

Khan, Imad; Fatima, Sumreen; Malik, M. Y.; Salahuddin, T.

2018-03-01

This paper explores the theoretical study of the steady incompressible two dimensional MHD boundary layer flow of Eyring-Powell nanofluid over an inclined surface. The fluid is considered to be electrically conducting and the viscosity of the fluid is assumed to be varying exponentially. The governing partial differential equations (PDE's) are reduced into ordinary differential equations (ODE's) by applying similarity approach. The resulting ordinary differential equations are solved successfully by using Homotopy analysis method. The impact of pertinent parameters on velocity, concentration and temperature profiles are examined through graphs and tables. Also coefficient of skin friction, Sherwood and Nusselt numbers are illustrated in tabular and graphical form.

Phases and stability of non-uniform black strings

NASA Astrophysics Data System (ADS)

Emparan, Roberto; Luna, Raimon; Martínez, Marina; Suzuki, Ryotaku; Tanabe, Kentaro

2018-05-01

We construct solutions of non-uniform black strings in dimensions from D ≈ 9 all the way up to D = ∞, and investigate their thermodynamics and dynamical stability. Our approach employs the large- D perturbative expansion beyond the leading order, including corrections up to 1 /D 4. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin's critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it.

Dynamic Modeling and Simulation of a Rotational Inverted Pendulum

NASA Astrophysics Data System (ADS)

Duart, J. L.; Montero, B.; Ospina, P. A.; González, E.

2017-01-01

This paper presents an alternative way to the dynamic modeling of a rotational inverted pendulum using the classic mechanics known as Euler-Lagrange allows to find motion equations that describe our model. It also has a design of the basic model of the system in SolidWorks software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the theoretical results, It was made a contrast between the solutions obtained by simulation SimMechanics-Matlab and the system of equations Euler-Lagrange, solved through ODE23tb method included in Matlab bookstores for solving equations systems of the type and order obtained. This article comprises a pendulum trajectory analysis by a phase space diagram that allows the identification of stable and unstable regions of the system.

Dynamic Model for Life History of Scyphozoa

PubMed Central

Xie, Congbo; Fan, Meng; Wang, Xin; Chen, Ming

2015-01-01

A two-state life history model governed by ODEs is formulated to elucidate the population dynamics of jellyfish and to illuminate the triggering mechanism of its blooms. The polyp-medusa model admits trichotomous global dynamic scenarios: extinction, polyps survival only, and both survival. The population dynamics sensitively depend on several biotic and abiotic limiting factors such as substrate, temperature, and predation. The combination of temperature increase, substrate expansion, and predator diminishment acts synergistically to create a habitat that is more favorable for jellyfishes. Reducing artificial marine constructions, aiding predator populations, and directly controlling the jellyfish population would help to manage the jellyfish blooms. The theoretical analyses and numerical experiments yield several insights into the nature underlying the model and shed some new light on the general control strategy for jellyfish. PMID:26114642

Dynamic Model for Life History of Scyphozoa.

PubMed

Xie, Congbo; Fan, Meng; Wang, Xin; Chen, Ming

2015-01-01

A two-state life history model governed by ODEs is formulated to elucidate the population dynamics of jellyfish and to illuminate the triggering mechanism of its blooms. The polyp-medusa model admits trichotomous global dynamic scenarios: extinction, polyps survival only, and both survival. The population dynamics sensitively depend on several biotic and abiotic limiting factors such as substrate, temperature, and predation. The combination of temperature increase, substrate expansion, and predator diminishment acts synergistically to create a habitat that is more favorable for jellyfishes. Reducing artificial marine constructions, aiding predator populations, and directly controlling the jellyfish population would help to manage the jellyfish blooms. The theoretical analyses and numerical experiments yield several insights into the nature underlying the model and shed some new light on the general control strategy for jellyfish.

A New Approach on the Long Term Dynamics of NEO's Under Yarkovsky Effect.

NASA Astrophysics Data System (ADS)

Peláez, Jesús; Urrutxua, Hodei; Bombardelli, Claudio; Perez-Grande, Isabel

2011-12-01

A classical approach to the many-body problem is that of using special perturbation methods. Nowadays and due to the availability of high-speed computers is an essential tool in Space Dynamics which exhibits a great advantage: it is applicable to any orbit involving any number of bodies and all sorts of astrodynamical problems, especially when these problems fall into regions in which general perturbation theories are absent. One such case is, for example, that Near Earth Objects (NEO's) dynamics. In this field, the Group of Tether Dynamics of UPM (GDT) has developed a new regularisation scheme - called DROMO - which is characterised by only 8 ODE. This new regularisation scheme allows a new approach to the dynamics of NEO's in the long term, specially appropriated to consider the influence of the anisotropic thermal emission (Yarkovsky and YORP effects) on the dynamics. A new project, called NEODROMO, has been started in GDT that aims to provide a reliable tool for the long term dynamics of NEO's.

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

A comprehensive complex systems approach to the study and analysis of mammalian cell cycle control system in the presence of DNA damage stress.

PubMed

Abroudi, Ali; Samarasinghe, Sandhya; Kulasiri, Don

2017-09-21

Not many models of mammalian cell cycle system exist due to its complexity. Some models are too complex and hard to understand, while some others are too simple and not comprehensive enough. Moreover, some essential aspects, such as the response of G1-S and G2-M checkpoints to DNA damage as well as the growth factor signalling, have not been investigated from a systems point of view in current mammalian cell cycle models. To address these issues, we bring a holistic perspective to cell cycle by mathematically modelling it as a complex system consisting of important sub-systems that interact with each other. This retains the functionality of the system and provides a clearer interpretation to the processes within it while reducing the complexity in comprehending these processes. To achieve this, we first update a published ODE mathematical model of cell cycle with current knowledge. Then the part of the mathematical model relevant to each sub-system is shown separately in conjunction with a diagram of the sub-system as part of this representation. The model sub-systems are Growth Factor, DNA damage, G1-S, and G2-M checkpoint signalling. To further simplify the model and better explore the function of sub-systems, they are further divided into modules. Here we also add important new modules of: chk-related rapid cell cycle arrest, p53 modules expanded to seamlessly integrate with the rapid arrest module, Tyrosine phosphatase modules that activate Cyc_Cdk complexes and play a crucial role in rapid and delay arrest at both G1-S and G2-M, Tyrosine Kinase module that is important for inactivating nuclear transport of CycB_cdk1 through Wee1 to resist M phase entry, Plk1-Related module that is crucial in activating Tyrosine phosphatases and inactivating Tyrosine kinase, and APC-Related module to show steps in CycB degradation. This multi-level systems approach incorporating all known aspects of cell cycle allowed us to (i) study, through dynamic simulation of an ODE model, comprehensive details of cell cycle dynamics under normal and DNA damage conditions revealing the role and value of the added new modules and elements, (ii) assess, through a global sensitivity analysis, the most influential sub-systems, modules and parameters on system response, such as G1-S and G2-M transitions, and (iii) probe deeply into the relationship between DNA damage and cell cycle progression and test the biological evidence that G1-S is relatively inefficient in arresting damaged cells compared to G2-M checkpoint. To perform sensitivity analysis, Self-Organizing Map with Correlation Coefficient Analysis (SOMCCA) is developed which shows that Growth Factor and G1-S Checkpoint sub-systems and 13 parameters in the modules within them are crucial for G1-S and G2-M transitions. To study the relative efficiency of DNA damage checkpoints, a Checkpoint Efficiency Evaluator (CEE) is developed based on perturbation studies and statistical Type II error. Accordingly, cell cycle is about 96% efficient in arresting damaged cells with G2-M checkpoint being more efficient than G1-S. Further, both checkpoint systems are near perfect (98.6%) in passing healthy cells. Thus this study has shown the efficacy of the proposed systems approach to gain a better understanding of different aspects of mammalian cell cycle system separately and as an integrated system that will also be useful in investigating targeted therapy in future cancer treatments. Copyright © 2017 Elsevier Ltd. All rights reserved.

UML as a cell and biochemistry modeling language.

PubMed

Webb, Ken; White, Tony

2005-06-01

The systems biology community is building increasingly complex models and simulations of cells and other biological entities, and are beginning to look at alternatives to traditional representations such as those provided by ordinary differential equations (ODE). The lessons learned over the years by the software development community in designing and building increasingly complex telecommunication and other commercial real-time reactive systems, can be advantageously applied to the problems of modeling in the biology domain. Making use of the object-oriented (OO) paradigm, the unified modeling language (UML) and Real-Time Object-Oriented Modeling (ROOM) visual formalisms, and the Rational Rose RealTime (RRT) visual modeling tool, we describe a multi-step process we have used to construct top-down models of cells and cell aggregates. The simple example model described in this paper includes membranes with lipid bilayers, multiple compartments including a variable number of mitochondria, substrate molecules, enzymes with reaction rules, and metabolic pathways. We demonstrate the relevance of abstraction, reuse, objects, classes, component and inheritance hierarchies, multiplicity, visual modeling, and other current software development best practices. We show how it is possible to start with a direct diagrammatic representation of a biological structure such as a cell, using terminology familiar to biologists, and by following a process of gradually adding more and more detail, arrive at a system with structure and behavior of arbitrary complexity that can run and be observed on a computer. We discuss our CellAK (Cell Assembly Kit) approach in terms of features found in SBML, CellML, E-CELL, Gepasi, Jarnac, StochSim, Virtual Cell, and membrane computing systems.

Efficient Modeling of Laser-Plasma Accelerators with INF&RNO

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

Benedetti, C.; Schroeder, C. B.; Esarey, E.

2010-06-01

The numerical modeling code INF&RNO (INtegrated Fluid& paRticle simulatioN cOde, pronounced"inferno") is presented. INF&RNO is an efficient 2D cylindrical code to model the interaction of a short laser pulse with an underdense plasma. The code is based on an envelope model for the laser while either a PIC or a fluid description can be used for the plasma. The effect of the laser pulse on the plasma is modeled with the time-averaged poderomotive force. These and other features allow for a speedup of 2-4 orders of magnitude compared to standard full PIC simulations while still retaining physical fidelity. The codemore » has been benchmarked against analytical solutions and 3D PIC simulations and here a set of validation tests together with a discussion of the performances are presented.« less

Efficient Modeling of Laser-Plasma Accelerators with INF&RNO

NASA Astrophysics Data System (ADS)

Benedetti, C.; Schroeder, C. B.; Esarey, E.; Geddes, C. G. R.; Leemans, W. P.

2010-11-01

The numerical modeling code INF&RNO (INtegrated Fluid & paRticle simulatioN cOde, pronounced "inferno") is presented. INF&RNO is an efficient 2D cylindrical code to model the interaction of a short laser pulse with an underdense plasma. The code is based on an envelope model for the laser while either a PIC or a fluid description can be used for the plasma. The effect of the laser pulse on the plasma is modeled with the time-averaged poderomotive force. These and other features allow for a speedup of 2-4 orders of magnitude compared to standard full PIC simulations while still retaining physical fidelity. The code has been benchmarked against analytical solutions and 3D PIC simulations and here a set of validation tests together with a discussion of the performances are presented.

A class of simple bouncing and late-time accelerating cosmologies in f(R) gravity

NASA Astrophysics Data System (ADS)

Kuiroukidis, A.

We consider the field equations for a flat FRW cosmological model, given by Eq. (??), in an a priori generic f(R) gravity model and cast them into a, completely normalized and dimensionless, system of ODEs for the scale factor and the function f(R), with respect to the scalar curvature R. It is shown that under reasonable assumptions, namely for power-law functional form for the f(R) gravity model, one can produce simple analytical and numerical solutions describing bouncing cosmological models where in addition there are late-time accelerating. The power-law form for the f(R) gravity model is typically considered in the literature as the most concrete, reasonable, practical and viable assumption [see S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D 90 (2014) 124083, arXiv:1410.8183 [gr-qc

Time-reversibility and particle sedimentation

NASA Technical Reports Server (NTRS)

Golubitsky, Martin; Krupa, Martin; Lim, Chjan

1991-01-01

This paper studies an ODE model, called the Stokeslet model, and describes sedimentation of small clusters of particles in a highly viscous fluid. This model has a trivial solution in which the n particles arrange themselves at the vertices of a regular n-sided polygon. When n = 3, Hocking and Caflisch et al. (1988) proved the existence of periodic motion (in the frame moving with the center of gravity in the cluster) in which the particles form an isosceles triangle. Here, the study of periodic and quasi-periodic solutions of the Stokeslet model is continued, with emphasis on the spatial and time-reversal symmetry of the model. For three particles, the existence of a second family of periodic solutions and a family of quasi-periodic solutions is proved. It is also indicated how the methods generalize to the case of n particles.

21 CFR 814.100 - Purpose and scope.

Code of Federal Regulations, 2014 CFR

2014-04-01

... concerning: (1) Any pediatric subpopulations (neonates, infants, children, adolescents) that suffer from the... of Orphan Products Development, and (2) Submitting an HDE to the Office of Device Evaluation (ODE...

Investigation of second grade fluid through temperature dependent thermal conductivity and non-Fourier heat flux

NASA Astrophysics Data System (ADS)

Hayat, T.; Ahmad, Salman; Khan, M. Ijaz; Alsaedi, A.; Waqas, M.

2018-06-01

Here we investigated stagnation point flow of second grade fluid over a stretchable cylinder. Heat transfer is characterized by non-Fourier law of heat flux and thermal stratification. Temperature dependent thermal conductivity and activation energy are also accounted. Transformations procedure is applying to transform the governing PDE's into ODE's. Obtained system of ODE's are solved analytically by HAM. Influence of flow variables on velocity, temperature, concentration, skin friction and Sherwood number are analyzed. Obtained outcome shows that velocity enhanced through curvature parameter, viscoelastic parameter and velocities ratio variable. Temperature decays for larger Prandtl number, thermal stratification, thermal relaxation and curvature parameter. Sherwood number and concentration field show opposite behavior for higher estimation of activation energy, reaction rate, curvature parameter and Schmidt number.

Nonlinear Krylov and moving nodes in the method of lines

NASA Astrophysics Data System (ADS)

Miller, Keith

2005-11-01

We report on some successes and problem areas in the Method of Lines from our work with moving node finite element methods. First, we report on our "nonlinear Krylov accelerator" for the modified Newton's method on the nonlinear equations of our stiff ODE solver. Since 1990 it has been robust, simple, cheap, and automatic on all our moving node computations. We publicize further trials with it here because it should be of great general usefulness to all those solving evolutionary equations. Second, we discuss the need for reliable automatic choice of spatially variable time steps. Third, we discuss the need for robust and efficient iterative solvers for the difficult linearized equations (Jx=b) of our stiff ODE solver. Here, the 1997 thesis of Zulu Xaba has made significant progress.

Optical solver for a system of ordinary differential equations based on an external feedback assisted microring resonator.

PubMed

Hou, Jie; Dong, Jianji; Zhang, Xinliang

2017-06-15

Systems of ordinary differential equations (SODEs) are crucial for describing the dynamic behaviors in various systems such as modern control systems which require observability and controllability. In this Letter, we propose and experimentally demonstrate an all-optical SODE solver based on the silicon-on-insulator platform. We use an add/drop microring resonator to construct two different ordinary differential equations (ODEs) and then introduce two external feedback waveguides to realize the coupling between these ODEs, thus forming the SODE solver. A temporal coupled mode theory is used to deduce the expression of the SODE. A system experiment is carried out for further demonstration. For the input 10 GHz NRZ-like pulses, the measured output waveforms of the SODE solver agree well with the calculated results.

Air-snowpack exchange of bromine, ozone and mercury in the springtime Arctic simulated by the 1-D model PHANTAS - Part 2: Mercury and its speciation

NASA Astrophysics Data System (ADS)

Toyota, K.; Dastoor, A. P.; Ryzhkov, A.

2014-04-01

Atmospheric mercury depletion events (AMDEs) refer to a recurring depletion of mercury occurring in the springtime Arctic (and Antarctic) boundary layer, in general, concurrently with ozone depletion events (ODEs). To close some of the knowledge gaps in the physical and chemical mechanisms of AMDEs and ODEs, we have developed a one-dimensional model that simulates multiphase chemistry and transport of trace constituents throughout porous snowpack and in the overlying atmospheric boundary layer (ABL). This paper constitutes Part 2 of the study, describing the mercury component of the model and its application to the simulation of AMDEs. Building on model components reported in Part 1 ("In-snow bromine activation and its impact on ozone"), we have developed a chemical mechanism for the redox reactions of mercury in the gas and aqueous phases with temperature dependent reaction rates and equilibrium constants accounted for wherever possible. Thus the model allows us to study the chemical and physical processes taking place during ODEs and AMDEs within a single framework where two-way interactions between the snowpack and the atmosphere are simulated in a detailed, process-oriented manner. Model runs are conducted for meteorological and chemical conditions that represent the springtime Arctic ABL characterized by the presence of "haze" (sulfate aerosols) and the saline snowpack on sea ice. The oxidation of gaseous elemental mercury (GEM) is initiated via reaction with Br-atom to form HgBr, followed by competitions between its thermal decomposition and further reactions to give thermally stable Hg(II) products. To shed light on uncertain kinetics and mechanisms of this multi-step oxidation process, we have tested different combinations of their rate constants based on published laboratory and quantum mechanical studies. For some combinations of the rate constants, the model simulates roughly linear relationships between the gaseous mercury and ozone concentrations as observed during AMDEs/ODEs by including the reaction HgBr + BrO and assuming its rate constant to be the same as for the reaction HgBr + Br, while for other combinations the results are more realistic by neglecting the reaction HgBr + BrO. Speciation of gaseous oxidized mercury (GOM) changes significantly depending on whether or not BrO is assumed to react with HgBr to form Hg(OBr)Br. Similarly to ozone (reported in Part 1), GEM is depleted via bromine radical chemistry more vigorously in the snowpack interstitial air than in the ambient air. However, the impact of such in-snow sink of GEM is found to be often masked by the re-emissions of GEM from the snow following the photo-reduction of Hg(II) deposited from the atmosphere. GOM formed in the ambient air is found to undergo fast "dry deposition" to the snowpack by being trapped on the snow grains in the top ~1 mm layer. We hypothesize that liquid-like layers on the surface of snow grains are connected to create a network throughout the snowpack, thereby facilitating the vertical diffusion of trace constituents trapped on the snow grains at much greater rates than one would expect inside solid ice crystals. Nonetheless, on the timescale of a week simulated in this study, the signal of atmospheric deposition does not extend notably below the top 1 cm of the snowpack. We propose and show that particulate-bound mercury (PBM) is produced mainly as HgBr42- by taking up GOM into bromide-enriched aerosols after ozone is significantly depleted in the air mass. In the Arctic, "haze" aerosols may thus retain PBM in ozone-depleted air masses, allowing the airborne transport of oxidized mercury from the area of its production farther than in the form of GOM. Temperature dependence of thermodynamic constants calculated in this study for Henry's law and aqueous-phase halide complex formation of Hg(II) species is a critical factor for this proposition, calling for experimental verification. The proposed mechanism may explain observed changes in the GOM-PBM partitioning with seasons, air temperature and the concurrent progress of ozone depletion in the high Arctic. The net deposition of mercury to the surface snow is shown to increase with the thickness of the turbulent ABL and to correspond well with the column amount of BrO in the atmosphere.

SU-D-BRB-06: Treating Glioblastoma Multiforme (GBM) as a Chronic Disease: Implication of Temporal-Spatial Dose Fractionation Optimization Including Cancer Stem Cell Dynamics

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

Yu, V; Nguyen, D; Pajonk, F

Purpose: To explore the feasibility of improving GBM treatment outcome with temporal-spatial dose optimization of an ordinary differential equation (ODE) that models the differentiation and distinct radiosensitivity between cancer stem cells (CSC) and differentiated cancer cells (DCC). Methods: The ODE was formulated into a non-convex optimization problem with the objective to minimize remaining total cancer cells 500 days from the onset of radiotherapy when the total cancer cell number was 3.5×10{sup 7}, while maintaining normal tissue biological effective dose (BED) of 100Gy resulted from standard prescription of 2Gyx30. Assuming spatially separated CSC and DCC, optimization was also performed to exploremore » the potential benefit from dose-painting the two compartments. Dose escalation to a sub-cell-population in the GTV was also examined assuming that a 2 cm margin around the GTV allows sufficient dose drop-off to 100Gy BED. The recurrence time was determined as the time at which the total cancer cell number regrows to 10{sup 9} cells. Results: The recurrence time with variable fractional doses administered once per week, bi-week and month for one year were found to be 615, 593 and 570 days, superior to the standard-prescription recurrence time of 418 days. The optimal dose-fraction size progression for both uniform and dose-painting to the tumor is low and relatively constant in the beginning and gradually increases to more aggressive fractions at end of the treatment course. Dose escalation to BED of 200Gy to the whole tumor alongside with protracted weekly treatment was found to further delay recurrence to 733 days. Dose-painting of 200 and 500Gy BED to CSC on a year-long weekly schedule further extended recurrence to 736 and 1076 days, respectively. Conclusion: GBM treatment outcome can possibly be improved with a chronic treatment approach. Further dose escalation to the entire tumor or CSC targeted killing is needed to achieve total tumor control. This work is supported by the NSF Graduate Research Fellowship (DGE-1144087)« less

Chaos and Robustness in a Single Family of Genetic Oscillatory Networks

PubMed Central

Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav I.

2014-01-01

Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback. PMID:24667178

All-optical 1st- and 2nd-order differential equation solvers with large tuning ranges using Fabry-Pérot semiconductor optical amplifiers.

PubMed

Chen, Kaisheng; Hou, Jie; Huang, Zhuyang; Cao, Tong; Zhang, Jihua; Yu, Yuan; Zhang, Xinliang

2015-02-09

We experimentally demonstrate an all-optical temporal computation scheme for solving 1st- and 2nd-order linear ordinary differential equations (ODEs) with tunable constant coefficients by using Fabry-Pérot semiconductor optical amplifiers (FP-SOAs). By changing the injection currents of FP-SOAs, the constant coefficients of the differential equations are practically tuned. A quite large constant coefficient tunable range from 0.0026/ps to 0.085/ps is achieved for the 1st-order differential equation. Moreover, the constant coefficient p of the 2nd-order ODE solver can be continuously tuned from 0.0216/ps to 0.158/ps, correspondingly with the constant coefficient q varying from 0.0000494/ps(2) to 0.006205/ps(2). Additionally, a theoretical model that combining the carrier density rate equation of the semiconductor optical amplifier (SOA) with the transfer function of the Fabry-Pérot (FP) cavity is exploited to analyze the solving processes. For both 1st- and 2nd-order solvers, excellent agreements between the numerical simulations and the experimental results are obtained. The FP-SOAs based all-optical differential-equation solvers can be easily integrated with other optical components based on InP/InGaAsP materials, such as laser, modulator, photodetector and waveguide, which can motivate the realization of the complicated optical computing on a single integrated chip.

Precipitation of salts in freezing seawater and ozone depletion events: a status report

NASA Astrophysics Data System (ADS)

Morin, S.; Marion, G. M.; von Glasow, R.; Voisin, D.; Bouchez, J.; Savarino, J.

2008-12-01

In springtime, the polar marine boundary layer exhibits drastic ozone depletion events (ODEs), associated with elevated bromine oxide (BrO) mixing ratios. The current interpretation of this peculiar chemistry requires the existence of acid and bromide-enriched surfaces to heterogeneously promote and sustain ODEs. Sander et al. (2006) have proposed that calcium carbonate (CaCO3) precipitation in any seawater-derived medium could potentially decrease its alkalinity, making it easier for atmospheric acids such as HNO3 and H2SO4 to acidify it. We performed simulations using the state-of-the-art FREZCHEM model, capable of handling the thermodynamics of concentrated electrolyte solutions, to try to reproduce their results, and found that when ikaite (CaCO3·6H2O) rather than calcite (CaCO3) precipitates, there is no such effect on alkalinity. Given that ikaite has recently been identified in Antarctic brines (Dieckmann et al., 2008), our results show that great caution should be exercised when using the results of Sander et al. (2006), and reveal the urgent need of laboratory investigations on the actual link(s) between bromine activation and the pH of the surfaces on which it is supposed to take place at subzero temperature. In addition, the evolution of the Cl/Br ratio in the brine during freezing was computed using FREZCHEM, taking into account Br substitutions in Cl-containing salts.

Multiscale modeling of mucosal immune responses

PubMed Central

2015-01-01

Computational modeling techniques are playing increasingly important roles in advancing a systems-level mechanistic understanding of biological processes. Computer simulations guide and underpin experimental and clinical efforts. This study presents ENteric Immune Simulator (ENISI), a multiscale modeling tool for modeling the mucosal immune responses. ENISI's modeling environment can simulate in silico experiments from molecular signaling pathways to tissue level events such as tissue lesion formation. ENISI's architecture integrates multiple modeling technologies including ABM (agent-based modeling), ODE (ordinary differential equations), SDE (stochastic modeling equations), and PDE (partial differential equations). This paper focuses on the implementation and developmental challenges of ENISI. A multiscale model of mucosal immune responses during colonic inflammation, including CD4+ T cell differentiation and tissue level cell-cell interactions was developed to illustrate the capabilities, power and scope of ENISI MSM. Background Computational techniques are becoming increasingly powerful and modeling tools for biological systems are of greater needs. Biological systems are inherently multiscale, from molecules to tissues and from nano-seconds to a lifespan of several years or decades. ENISI MSM integrates multiple modeling technologies to understand immunological processes from signaling pathways within cells to lesion formation at the tissue level. This paper examines and summarizes the technical details of ENISI, from its initial version to its latest cutting-edge implementation. Implementation Object-oriented programming approach is adopted to develop a suite of tools based on ENISI. Multiple modeling technologies are integrated to visualize tissues, cells as well as proteins; furthermore, performance matching between the scales is addressed. Conclusion We used ENISI MSM for developing predictive multiscale models of the mucosal immune system during gut inflammation. Our modeling predictions dissect the mechanisms by which effector CD4+ T cell responses contribute to tissue damage in the gut mucosa following immune dysregulation. PMID:26329787

Multiscale modeling of mucosal immune responses.

PubMed

Mei, Yongguo; Abedi, Vida; Carbo, Adria; Zhang, Xiaoying; Lu, Pinyi; Philipson, Casandra; Hontecillas, Raquel; Hoops, Stefan; Liles, Nathan; Bassaganya-Riera, Josep

2015-01-01

Computational techniques are becoming increasingly powerful and modeling tools for biological systems are of greater needs. Biological systems are inherently multiscale, from molecules to tissues and from nano-seconds to a lifespan of several years or decades. ENISI MSM integrates multiple modeling technologies to understand immunological processes from signaling pathways within cells to lesion formation at the tissue level. This paper examines and summarizes the technical details of ENISI, from its initial version to its latest cutting-edge implementation. Object-oriented programming approach is adopted to develop a suite of tools based on ENISI. Multiple modeling technologies are integrated to visualize tissues, cells as well as proteins; furthermore, performance matching between the scales is addressed. We used ENISI MSM for developing predictive multiscale models of the mucosal immune system during gut inflammation. Our modeling predictions dissect the mechanisms by which effector CD4+ T cell responses contribute to tissue damage in the gut mucosa following immune dysregulation.Computational modeling techniques are playing increasingly important roles in advancing a systems-level mechanistic understanding of biological processes. Computer simulations guide and underpin experimental and clinical efforts. This study presents ENteric Immune Simulator (ENISI), a multiscale modeling tool for modeling the mucosal immune responses. ENISI's modeling environment can simulate in silico experiments from molecular signaling pathways to tissue level events such as tissue lesion formation. ENISI's architecture integrates multiple modeling technologies including ABM (agent-based modeling), ODE (ordinary differential equations), SDE (stochastic modeling equations), and PDE (partial differential equations). This paper focuses on the implementation and developmental challenges of ENISI. A multiscale model of mucosal immune responses during colonic inflammation, including CD4+ T cell differentiation and tissue level cell-cell interactions was developed to illustrate the capabilities, power and scope of ENISI MSM.

Elementary functions in thermodynamic Bethe ansatz

NASA Astrophysics Data System (ADS)

Suzuki, J.

2015-05-01

Some years ago, Fendley found an explicit solution to the thermodynamic Bethe ansatz (TBA) equation for an N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek explicit solutions for other super-potential cases utilizing the idea from the ODE/IM correspondence. We find that the TBA equations, corresponding to a wider class of super-potentials, admit solutions in terms of elementary functions such as modified Bessel functions and confluent hyper-geometric series. Based on talks given at ‘Infinite Analysis 2014’ (Tokyo, 2014) and at ‘Integrable lattice models and quantum field theories’ (Bad Honnef, 2014).

Modeling and analyzing flow of third grade nanofluid due to rotating stretchable disk with chemical reaction and heat source

NASA Astrophysics Data System (ADS)

Hayat, T.; Ahmad, Salman; Khan, M. Ijaz; Alsaedi, A.

2018-05-01

This article addresses flow of third grade nanofluid due to stretchable rotating disk. Mass and heat transports are analyzed through thermophoresis and Brownian movement effects. Further the effects of heat generation and chemical reaction are also accounted. The obtained ODE's are tackled computationally by means of homotopy analysis method. Graphical outcomes are analyzed for the effects of different variables. The obtained results show that velocity reduces through Reynolds number and material parameters. Temperature and concentration increase with Brownian motion and these decrease by Reynolds number.

Analysis of the incomplete Galerkin method for modelling of smoothly-irregular transition between planar waveguides

NASA Astrophysics Data System (ADS)

Divakov, D.; Sevastianov, L.; Nikolaev, N.

2017-01-01

The paper deals with a numerical solution of the problem of waveguide propagation of polarized light in smoothly-irregular transition between closed regular waveguides using the incomplete Galerkin method. This method consists in replacement of variables in the problem of reduction of the Helmholtz equation to the system of differential equations by the Kantorovich method and in formulation of the boundary conditions for the resulting system. The formulation of the boundary problem for the ODE system is realized in computer algebra system Maple. The stated boundary problem is solved using Maples libraries of numerical methods.

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Dynamic Modeling and Simulation of an Underactuated System

NASA Astrophysics Data System (ADS)

Libardo Duarte Madrid, Juan; Ospina Henao, P. A.; González Querubín, E.

2017-06-01

In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in SOLIDWORKS 3D CAD software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the results obtained, a comparison the CAD model simulated in the environment SimMechanics of MATLAB software with the mathematical model who was consisting of Euler-Lagrange’s equations implemented in Simulink MATLAB, solved with the ODE23tb method, included in the MATLAB libraries for the solution of systems of equations of the type and order obtained. This article also has a topological analysis of pendulum trajectories through a phase space diagram, which allows the identification of stable and unstable regions of the system.

SEIR model simulation for Hepatitis B

NASA Astrophysics Data System (ADS)

Side, Syafruddin; Irwan, Mulbar, Usman; Sanusi, Wahidah

2017-09-01

Mathematical modelling and simulation for Hepatitis B discuss in this paper. Population devided by four variables, namely: Susceptible, Exposed, Infected and Recovered (SEIR). Several factors affect the population in this model is vaccination, immigration and emigration that occurred in the population. SEIR Model obtained Ordinary Differential Equation (ODE) non-linear System 4-D which then reduces to 3-D. SEIR model simulation undertaken to predict the number of Hepatitis B cases. The results of the simulation indicates the number of Hepatitis B cases will increase and then decrease for several months. The result of simulation using the number of case in Makassar also found the basic reproduction number less than one, that means, Makassar city is not an endemic area of Hepatitis B. With approval from the proceedings editor article 020185 titled, "SEIR model simulation for Hepatitis B," is retracted from the public record, as it is a duplication of article 020198 published in the same volume.

Numerical simulation of heat and mass transfer in unsteady nanofluid between two orthogonally moving porous coaxial disks

NASA Astrophysics Data System (ADS)

Ali, Kashif; Akbar, Muhammad Zubair; Iqbal, Muhammad Farooq; Ashraf, Muhammad

2014-10-01

The paper deals with the study of heat and mass transfer in an unsteady viscous incompressible water-based nanofluid (containing Titanium dioxide nanoparticles) between two orthogonally moving porous coaxial disks with suction. A combination of iterative (successive over relaxation) and a direct method is employed for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar ODEs. It has been noticed that the rate of mass transfer at the disks decreases with the permeability Reynolds number whether the disks are approaching or receding. The findings of the present investigation may be beneficial for the electronic industry in maintaining the electronic components under effective and safe operational conditions.

Air-snowpack exchange of bromine, ozone and mercury in the springtime Arctic simulated by the 1-D model PHANTAS - Part 2: Mercury and its speciation

NASA Astrophysics Data System (ADS)

Toyota, K.; Dastoor, A. P.; Ryzhkov, A.

2013-08-01

Atmospheric mercury depletion events (AMDEs) refer to a recurring depletion of mercury in the springtime Arctic (and Antarctic) boundary layer, occurring, in general, concurrently with ozone depletion events (ODEs). To close some of the knowledge gaps in the physical and chemical mechanisms of AMDEs and ODEs, we have developed a one-dimensional model that simulates multiphase chemistry and transport of trace constituents throughout porous snowpack and in the overlying atmospheric boundary layer (ABL). Building on the model reported in a companion paper (Part 1: In-snow bromine activation and its impact on ozone), we have expanded the chemical mechanism to include the reactions of mercury in the gas- and aqueous-phases with temperature dependence of rate and equilibrium constants accounted for wherever possible. Thus the model allows us to study the chemical and physical processes taking place during ODEs and AMDEs within a single framework where two-way interactions between the snowpack and the atmosphere are simulated in a detailed, process-oriented manner. Model runs are conducted for meteorological and chemical conditions representing the springtime Arctic ABL loaded with "haze" sulfate aerosols and the underlying saline snowpack laid on sea ice. Using recent updates for the Hg + Br \\rightleftarrows HgBr reaction kinetics, we show that the rate and magnitude of photochemical loss of gaseous elemental mercury (GEM) during AMDEs exhibit a strong dependence on the choice of reaction(s) of HgBr subsequent to its formation. At 253 K, the temperature that is presumably low enough for bromine radical chemistry to cause prominent AMDEs as indicated from field observations, the parallel occurrence of AMDEs and ODEs is simulated if the reaction HgBr + BrO is assumed to produce a thermally stable intermediate, Hg(OBr)Br, at the same rate constant as the reaction HgBr + Br. On the contrary, the simulated depletion of atmospheric mercury is notably diminished by not allowing the former reaction to occur in the model. Similarly to ozone (reported in the companion paper), GEM is destroyed via bromine radical chemistry more vigorously in the snowpack interstitial air than in the ambient air. However, the impact of such in-snow sink of GEM is found to be often masked by the re-emissions of GEM from the snow following the photo-reduction of Hg(II) deposited from the atmosphere. Gaseous oxidized mercury (GOM) formed in the ambient air is found to undergo fast "dry deposition" to the snowpack by being trapped on the snow grains in the top ~ 1 mm layer. We hypothesize that liquid-like layers on the surface of snow grains are connected to create a network throughout the snowpack, thereby facilitating the vertical diffusion of trace constituents trapped on the snow grains at much greater rates than one would expect inside solid ice crystals. Nonetheless, on the timescale of a week simulated in this study, the signal of atmospheric deposition does not extend notably below the top few centimeters of the snowpack. We propose and show that particulate-bound mercury (PBM) is produced mainly as HgBr42- by taking up GOM into bromide-enriched aerosols after ozone is significantly depleted in the air mass. In the Arctic, "haze" aerosols may thus retain PBM in ozone-depleted air masses, allowing the airborne transport of oxidized mercury from the area of its production farther than in the form of GOM. Temperature dependence of thermodynamic constants calculated in this study for Henry's law and aqueous-phase halide complex formation of Hg(II) species is a critical factor for this proposition, calling for experimental verification. The proposed mechanism may explain a major part of changes in the GOM-PBM partitioning with seasons, air temperature and the concurrent progress of ozone depletion as observed in the high Arctic. The net deposition of mercury to the surface snow is shown to increase with the thickness of the turbulent ABL and to correspond well with the column amount of BrO in the atmosphere.

Differential T cell response against BK virus regulatory and structural antigens: A viral dynamics modelling approach.

PubMed

Blazquez-Navarro, Arturo; Schachtner, Thomas; Stervbo, Ulrik; Sefrin, Anett; Stein, Maik; Westhoff, Timm H; Reinke, Petra; Klipp, Edda; Babel, Nina; Neumann, Avidan U; Or-Guil, Michal

2018-05-01

BK virus (BKV) associated nephropathy affects 1-10% of kidney transplant recipients, leading to graft failure in about 50% of cases. Immune responses against different BKV antigens have been shown to have a prognostic value for disease development. Data currently suggest that the structural antigens and regulatory antigens of BKV might each trigger a different mode of action of the immune response. To study the influence of different modes of action of the cellular immune response on BKV clearance dynamics, we have analysed the kinetics of BKV plasma load and anti-BKV T cell response (Elispot) in six patients with BKV associated nephropathy using ODE modelling. The results show that only a small number of hypotheses on the mode of action are compatible with the empirical data. The hypothesis with the highest empirical support is that structural antigens trigger blocking of virus production from infected cells, whereas regulatory antigens trigger an acceleration of death of infected cells. These differential modes of action could be important for our understanding of BKV resolution, as according to the hypothesis, only regulatory antigens would trigger a fast and continuous clearance of the viral load. Other hypotheses showed a lower degree of empirical support, but could potentially explain the clearing mechanisms of individual patients. Our results highlight the heterogeneity of the dynamics, including the delay between immune response against structural versus regulatory antigens, and its relevance for BKV clearance. Our modelling approach is the first that studies the process of BKV clearance by bringing together viral and immune kinetics and can provide a framework for personalised hypotheses generation on the interrelations between cellular immunity and viral dynamics.

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

Menikoff, Ralph

The Zel’dovich-von Neumann-Doering (ZND) profile of a detonation wave is derived. Two basic assumptions are required: i. An equation of state (EOS) for a partly burned explosive; P(V, e, λ). ii. A burn rate for the reaction progress variable; d/dt λ = R(V, e, λ). For a steady planar detonation wave the reactive flow PDEs can be reduced to ODEs. The detonation wave profile can be determined from an ODE plus algebraic equations for points on the partly burned detonation loci with a specified wave speed. Furthermore, for the CJ detonation speed the end of the reaction zone is sonic.more » A solution to the reactive flow equations can be constructed with a rarefaction wave following the detonation wave profile. This corresponds to an underdriven detonation wave, and the rarefaction is know as a Taylor wave.« less

Control of mechanical systems by the mixed "time and expenditure" criterion

NASA Astrophysics Data System (ADS)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

The optimal controlled motion of a mechanical system, that is determined by the linear system ODE with constant coefficients and piecewise constant control components, is considered. The number of control switching points and the heights of control steps are considered as preset. The optimized functional is combination of classical time criteria and "Expenditure criteria", that is equal to the total area of all steps of all control components. In the absence of control, the solution of the system is equal to the sum of components (frequency components) corresponding to different eigenvalues of the matrix of the ODE system. Admissible controls are those that turn to zero (at a non predetermined time moment) the previously chosen frequency components of the solution. An algorithm for the finding of control switching points, based on the necessary minimum conditions for mixed criteria, is proposed.

Tackling the African “poverty trap”: The Ijebu-Ode experiment

PubMed Central

Mabogunje, Akin L.

2007-01-01

An experiment in poverty reduction began in 1998 in the city of Ijebu-Ode, Nigeria (estimated 1999 population 163,000), where, without the remittances from relatives abroad, an estimated 90% of the population lived below the poverty line of $1.00 (U.S.) per person per day. Central to the experiment was whether poverty can be dramatically reduced through a city consultation process that seeks to mobilize the entire community along with its diaspora. With 7 years of experience, the Ijebu-Ode experiment has been successful in many ways. There is increasing evidence that poverty in the city has been reduced significantly through the microfinancing of existing and new productive activities and the estimated >8,000 jobs these activities have created. Training based on both sustainability science and technology and indigenous practitioner knowledge has been a critical factor in the establishment of cooperatives and the development of new enterprises in specialty crops, small animal, and fish production. Much of this success has been possible as a result of harnessing social capital, especially through the dynamic leadership of the traditional authorities of the city and by the provision of ample loanable funds through the National Poverty Eradication Program of the federal government. The city consultation process itself engendered a participatory focus to the experiment from the beginning and has encouraged sustainabaility. Yet long-term sustainability is still in question as the initial leadership needs replacement, and credit, the heart of the experiment, lacks sufficient collateral. PMID:17942687

Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations.

PubMed

Meshkat, Nicolette; Anderson, Chris; Distefano, Joseph J

2011-09-01

When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input-output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input-output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel. Copyright © 2011 Elsevier Inc. All rights reserved.

Efficient Modeling of Laser-Plasma Accelerators with INF and RNO

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

Benedetti, C.; Schroeder, C. B.; Esarey, E.

2010-11-04

The numerical modeling code INF and RNO (INtegrated Fluid and paRticle simulatioN cOde, pronounced 'inferno') is presented. INF and RNO is an efficient 2D cylindrical code to model the interaction of a short laser pulse with an underdense plasma. The code is based on an envelope model for the laser while either a PIC or a fluid description can be used for the plasma. The effect of the laser pulse on the plasma is modeled with the time-averaged poderomotive force. These and other features allow for a speedup of 2-4 orders of magnitude compared to standard full PIC simulations whilemore » still retaining physical fidelity. The code has been benchmarked against analytical solutions and 3D PIC simulations and here a set of validation tests together with a discussion of the performances are presented.« less

Inferring Broad Regulatory Biology from Time Course Data: Have We Reached an Upper Bound under Constraints Typical of In Vivo Studies?

PubMed Central

Craddock, Travis J. A.; Fletcher, Mary Ann; Klimas, Nancy G.

2015-01-01

There is a growing appreciation for the network biology that regulates the coordinated expression of molecular and cellular markers however questions persist regarding the identifiability of these networks. Here we explore some of the issues relevant to recovering directed regulatory networks from time course data collected under experimental constraints typical of in vivo studies. NetSim simulations of sparsely connected biological networks were used to evaluate two simple feature selection techniques used in the construction of linear Ordinary Differential Equation (ODE) models, namely truncation of terms versus latent vector projection. Performance was compared with ODE-based Time Series Network Identification (TSNI) integral, and the information-theoretic Time-Delay ARACNE (TD-ARACNE). Projection-based techniques and TSNI integral outperformed truncation-based selection and TD-ARACNE on aggregate networks with edge densities of 10-30%, i.e. transcription factor, protein-protein cliques and immune signaling networks. All were more robust to noise than truncation-based feature selection. Performance was comparable on the in silico 10-node DREAM 3 network, a 5-node Yeast synthetic network designed for In vivo Reverse-engineering and Modeling Assessment (IRMA) and a 9-node human HeLa cell cycle network of similar size and edge density. Performance was more sensitive to the number of time courses than to sample frequency and extrapolated better to larger networks by grouping experiments. In all cases performance declined rapidly in larger networks with lower edge density. Limited recovery and high false positive rates obtained overall bring into question our ability to generate informative time course data rather than the design of any particular reverse engineering algorithm. PMID:25984725

Parallel particle filters for online identification of mechanistic mathematical models of physiology from monitoring data: performance and real-time scalability in simulation scenarios.

PubMed

Zenker, Sven

2010-08-01

Combining mechanistic mathematical models of physiology with quantitative observations using probabilistic inference may offer advantages over established approaches to computerized decision support in acute care medicine. Particle filters (PF) can perform such inference successively as data becomes available. The potential of PF for real-time state estimation (SE) for a model of cardiovascular physiology is explored using parallel computers and the ability to achieve joint state and parameter estimation (JSPE) given minimal prior knowledge tested. A parallelized sequential importance sampling/resampling algorithm was implemented and its scalability for the pure SE problem for a non-linear five-dimensional ODE model of the cardiovascular system evaluated on a Cray XT3 using up to 1,024 cores. JSPE was implemented using a state augmentation approach with artificial stochastic evolution of the parameters. Its performance when simultaneously estimating the 5 states and 18 unknown parameters when given observations only of arterial pressure, central venous pressure, heart rate, and, optionally, cardiac output, was evaluated in a simulated bleeding/resuscitation scenario. SE was successful and scaled up to 1,024 cores with appropriate algorithm parametrization, with real-time equivalent performance for up to 10 million particles. JSPE in the described underdetermined scenario achieved excellent reproduction of observables and qualitative tracking of enddiastolic ventricular volumes and sympathetic nervous activity. However, only a subset of the posterior distributions of parameters concentrated around the true values for parts of the estimated trajectories. Parallelized PF's performance makes their application to complex mathematical models of physiology for the purpose of clinical data interpretation, prediction, and therapy optimization appear promising. JSPE in the described extremely underdetermined scenario nevertheless extracted information of potential clinical relevance from the data in this simulation setting. However, fully satisfactory resolution of this problem when minimal prior knowledge about parameter values is available will require further methodological improvements, which are discussed.

Phosphine-free synthesis and characterization of type-II ZnSe/CdS core-shell quantum dots

NASA Astrophysics Data System (ADS)

Ghasemzadeh, Roghayyeh; Armanmehr, Mohammad Hasan; Abedi, Mohammad; Fateh, Davood Sadeghi; Bahreini, Zaker

2018-01-01

A phosphine-free route for synthesis of type-II ZnSe/CdS core-shell quantum dots, using green, low cost and environmentally friendly reagents and phosphine-free solvents such as 1-octadecene (ODE) and liquid paraffin has been reported. Hot-injection technique has been used for the synthesis of ZnSe core quantum dots. The CdS shell quantum dots prepared by reaction of CdO precursor and S powder in 1-octadecene (ODE). The ZnSe/CdS core-shell quantum dots were synthesized via successive ion layer adsorption and reaction (SILAR) technique. The characterization of produced quantum dots were performed by absorption and fluorescence spectroscopy, X-ray diffraction (XRD) and energy dispersive X-ray spectroscopy (EDX) and transmission electron microscopy (TEM). The results showed the formation of type-II ZnSe/CdS core-shell quantum dots with FWHM 32 nm and uniform size distribution.

A parallel time integrator for noisy nonlinear oscillatory systems

NASA Astrophysics Data System (ADS)

Subber, Waad; Sarkar, Abhijit

2018-06-01

In this paper, we adapt a parallel time integration scheme to track the trajectories of noisy non-linear dynamical systems. Specifically, we formulate a parallel algorithm to generate the sample path of nonlinear oscillator defined by stochastic differential equations (SDEs) using the so-called parareal method for ordinary differential equations (ODEs). The presence of Wiener process in SDEs causes difficulties in the direct application of any numerical integration techniques of ODEs including the parareal algorithm. The parallel implementation of the algorithm involves two SDEs solvers, namely a fine-level scheme to integrate the system in parallel and a coarse-level scheme to generate and correct the required initial conditions to start the fine-level integrators. For the numerical illustration, a randomly excited Duffing oscillator is investigated in order to study the performance of the stochastic parallel algorithm with respect to a range of system parameters. The distributed implementation of the algorithm exploits Massage Passing Interface (MPI).

Darcy-Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy

NASA Astrophysics Data System (ADS)

Sajid, T.; Sagheer, M.; Hussain, S.; Bilal, M.

2018-03-01

The present article is about the study of Darcy-Forchheimer flow of Maxwell nanofluid over a linear stretching surface. Effects like variable thermal conductivity, activation energy, nonlinear thermal radiation is also incorporated for the analysis of heat and mass transfer. The governing nonlinear partial differential equations (PDEs) with convective boundary conditions are first converted into the nonlinear ordinary differential equations (ODEs) with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with the help of shooting method and MATLAB built-in bvp4c solver. The impact of different physical parameters like Brownian motion, thermophoresis parameter, Reynolds number, magnetic parameter, nonlinear radiative heat flux, Prandtl number, Lewis number, reaction rate constant, activation energy and Biot number on Nusselt number, velocity, temperature and concentration profile has been discussed. It is viewed that both thermophoresis parameter and activation energy parameter has ascending effect on the concentration profile.

Boundary control of elliptic solutions to enforce local constraints

NASA Astrophysics Data System (ADS)

Bal, G.; Courdurier, M.

We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded from below by a positive constant in the vicinity of a finite number of prescribed points; (ii) the determinant of gradients of n solutions is bounded from below in the vicinity of a finite number of prescribed points. Such constructions find applications in recent hybrid medical imaging modalities. The methodology is based on starting from a controlled setting in which the constraints are satisfied and continuously modifying the coefficients in the second-order elliptic equation. The boundary condition is evolved by solving an ordinary differential equation (ODE) defined via appropriate optimality conditions. Unique continuations and standard regularity results for elliptic equations are used to show that the ODE admits a solution for sufficiently long times.

An inverse problem for a mathematical model of aquaponic agriculture

NASA Astrophysics Data System (ADS)

Bobak, Carly; Kunze, Herb

2017-01-01

Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.

Stochastic Model of Clogging in a Microfluidic Cell Sorter

NASA Astrophysics Data System (ADS)

Fai, Thomas; Rycroft, Chris

2016-11-01

Microfluidic devices for sorting cells by deformability show promise for various medical purposes, e.g. detecting sickle cell anemia and circulating tumor cells. One class of such devices consists of a two-dimensional array of narrow channels, each column containing several identical channels in parallel. Cells are driven through the device by an applied pressure or flow rate. Such devices allows for many cells to be sorted simultaneously, but cells eventually clog individual channels and change the device properties in an unpredictable manner. In this talk, we propose a stochastic model for the failure of such microfluidic devices by clogging and present preliminary theoretical and computational results. The model can be recast as an ODE that exhibits finite time blow-up under certain conditions. The failure time distribution is investigated analytically in certain limiting cases, and more realistic versions of the model are solved by computer simulation.

Bromine atom production and chain propagation during springtime Arctic ozone depletion events in Barrow, Alaska

NASA Astrophysics Data System (ADS)

Thompson, Chelsea R.; Shepson, Paul B.; Liao, Jin; Huey, L. Greg; Cantrell, Chris; Flocke, Frank; Orlando, John

2017-03-01

Ozone depletion events (ODEs) in the Arctic are primarily controlled by a bromine radical-catalyzed destruction mechanism that depends on the efficient production and recycling of Br atoms. Numerous laboratory and modeling studies have suggested the importance of heterogeneous recycling of Br through HOBr reaction with bromide on saline surfaces. On the other hand, the gas-phase regeneration of bromine atoms through BrO-BrO radical reactions has been assumed to be an efficient, if not dominant, pathway for Br reformation and thus ozone destruction. Indeed, it has been estimated that the rate of ozone depletion is approximately equal to twice the rate of the BrO self-reaction. Here, we use a zero-dimensional, photochemical model, largely constrained to observations of stable atmospheric species from the 2009 Ocean-Atmosphere-Sea Ice-Snowpack (OASIS) campaign in Barrow, Alaska, to investigate gas-phase bromine radical propagation and recycling mechanisms of bromine atoms for a 7-day period during late March. This work is a continuation of that presented in Thompson et al. (2015) and utilizes the same model construct. Here, we use the gas-phase radical chain length as a metric for objectively quantifying the efficiency of gas-phase recycling of bromine atoms. The gas-phase bromine chain length is determined to be quite small, at < 1.5, and highly dependent on ambient O3 concentrations. Furthermore, we find that Br atom production from photolysis of Br2 and BrCl, which is predominately emitted from snow and/or aerosol surfaces, can account for between 30 and 90 % of total Br atom production. This analysis suggests that condensed-phase production of bromine is at least as important as, and at times greater than, gas-phase recycling for the occurrence of Arctic ODEs. Therefore, the rate of the BrO self-reaction is not a sufficient estimate for the rate of O3 depletion.

A note on windowing for the waveform relaxation

NASA Technical Reports Server (NTRS)

Zhang, Hong

1994-01-01

The technique of windowing has been often used in the implementation of the waveform relaxations for solving ODE's or time dependent PDE's. Its efficiency depends upon problem stiffness and operator splitting. Using model problems, the estimates for window length and convergence rate are derived. The electiveness of windowing is then investigated for non-stiff and stiff cases respectively. lt concludes that for the former, windowing is highly recommended when a large discrepancy exists between the convergence rate on a time interval and the ones on its subintervals. For the latter, windowing does not provide any computational advantage if machine features are disregarded. The discussion is supported by experimental results.

Rheology of the Cu-H2O nanofluid in porous channel with heat transfer: Multiple solutions

NASA Astrophysics Data System (ADS)

Raza, J.; Rohni, A. M.; Omar, Z.; Awais, M.

2017-02-01

Dynamics of nanofluid comprising a base fluid (water) with copper (Cu) nanoparticles have been considered in channel with porous walls under magnetic field influence. The channel walls are considered to be permeable in order to analyze the wall mass transfer phenomenon. Relevant mathematical modelling has been performed and the derived PDEs are converted into coupled nonlinear ODEs by using suitable transformations. Computations have been made numerically by employing the shooting technique. It is noted that multiple solutions occur for the variation of suction Reynolds number, solid volume fraction and magnetic parameters which are interpreted in detail.

Steady boundary layer slip flow along with heat and mass transfer over a flat porous plate embedded in a porous medium.

PubMed

Aziz, Asim; Siddique, J I; Aziz, Taha

2014-01-01

In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile.

Steady Boundary Layer Slip Flow along with Heat and Mass Transfer over a Flat Porous Plate Embedded in a Porous Medium

PubMed Central

Aziz, Asim; Siddique, J. I.; Aziz, Taha

2014-01-01

In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile. PMID:25531301

Comparative study of Eyring and Carreau fluids in a suspension of dust and nickel nanoparticles with variable conductivity

NASA Astrophysics Data System (ADS)

Mamatha Upadhya, S.; Mahesha; Raju, C. S. K.

2018-04-01

A theoretical analysis is carried out to investigate the magnetohydrodynamic unsteady flow of Eyring-Powell and Carreau non-Newtonian fluids in a suspension of dust and nickel nanoparticles by considering variable thermal conductivity and thermal radiation. Dispersion of nickel nanoparticles in dusty fluids finds applications in heat exchanger systems, rechargeable batteries, chemical catalysts, metallurgy, conducting paints, magnetic recording media, drug delivery, nanofibers, textiles, etc. The initially arising set of physical governing partial differential equations is transformed to ordinary differential equations (ODEs) with the aid of similarity transformations. Consequentially, the nonlinear ODEs are solved numerically through the Runge-Kutta Fehlberg scheme (RKFS). The computational results for non-dimensional temperature and velocity profiles are presented through graphs. Furthermore, the numerical values of friction factor and heat transfer rate are tabulated numerically for the unsteady and steady cases of the Eyring and Carreau fluid cases and of the dusty non-Newtonian (φ=0) and the dusty non-Newtonian nanofluid (φ≠ 0) cases of the unsteady flow. We also validated the present results with previous published studies and found them to be highly satisfactory. The formulated model reveals that the rate of heat transfer is higher in the mixture of the nickel + Eyring-Powell case compared to the nickel + Carreau case. From this we can highlight that, depending on the industrial appliances, we can use heating or cooling processes for Eyring and Carreau fluids, respectively.

Online Doppler Effect Elimination Based on Unequal Time Interval Sampling for Wayside Acoustic Bearing Fault Detecting System

PubMed Central

Ouyang, Kesai; Lu, Siliang; Zhang, Shangbin; Zhang, Haibin; He, Qingbo; Kong, Fanrang

2015-01-01

The railway occupies a fairly important position in transportation due to its high speed and strong transportation capability. As a consequence, it is a key issue to guarantee continuous running and transportation safety of trains. Meanwhile, time consumption of the diagnosis procedure is of extreme importance for the detecting system. However, most of the current adopted techniques in the wayside acoustic defective bearing detector system (ADBD) are offline strategies, which means that the signal is analyzed after the sampling process. This would result in unavoidable time latency. Besides, the acquired acoustic signal would be corrupted by the Doppler effect because of high relative speed between the train and the data acquisition system (DAS). Thus, it is difficult to effectively diagnose the bearing defects immediately. In this paper, a new strategy called online Doppler effect elimination (ODEE) is proposed to remove the Doppler distortion online by the introduced unequal interval sampling scheme. The steps of proposed strategy are as follows: The essential parameters are acquired in advance. Then, the introduced unequal time interval sampling strategy is used to restore the Doppler distortion signal, and the amplitude of the signal is demodulated as well. Thus, the restored Doppler-free signal is obtained online. The proposed ODEE method has been employed in simulation analysis. Ultimately, the ODEE method is implemented in the embedded system for fault diagnosis of the train bearing. The results are in good accordance with the bearing defects, which verifies the good performance of the proposed strategy. PMID:26343657

Incipient nonarteritic anterior ischemic optic neuropathy.

PubMed

Hayreh, Sohan Singh; Zimmerman, M Bridget

2007-09-01

To describe the clinical entity of incipient nonarteritic anterior ischemic optic neuropathy (NAION). Cohort study. Fifty-four patients (60 eyes) seen in our clinic from 1973 through 2000. At their first visit to our clinic, all patients gave a detailed ophthalmic and medical history and underwent a comprehensive ophthalmic evaluation, color fundus photography, and fluorescein fundus angiography. At each follow-up visit (of 49 patients [55 eyes]), the same ophthalmic evaluation was performed, except for fluorescein fundus angiography. Clinical features of incipient NAION. Mean age (+/- standard deviation) of the patients was 58.7+/-15.9 years. Median follow-up time was 6.3 years (interquartile range [IQR], 2.1-8.5). At initial visit, all had optic disc edema (ODE) without any visual loss attributable to NAION. In 55%, the fellow eye had classic NAION; in 25%, incipient progressed to classic NAION (after a median time of 5.8 weeks [IQR, 3.2-10.1]); and in 20%, classic NAION developed after resolution of the first episode of incipient NAION. Patients with incipient, compared with classic, NAION had a greater prevalence of diabetes mellitus (P<0.0001) and lower prevalence of ischemic heart disease (P = 0.046). Patients who progressed to classic NAION versus those who did not were significantly younger (P = 0.025), and their visual acuity worsened in 31% and 0%, respectively, and remained stable in 62% and 98%, respectively; in the eyes with progression, central (in 31%) and peripheral (in 77%) visual fields worsened compared with only 1 eye and 2 eyes, respectively, that did not (P = 0.01 and P<0.0001, respectively); and median time to resolution of ODE in the progressed group was 5.8 weeks (IQR, 4.6-8.7) versus 9.6 weeks (IQR, 6.0-17.7) in those who did not progress. The results show that incipient NAION is a distinct clinical entity, with asymptomatic ODE and no visual loss attributable to NAION. When a patient seeks treatment with asymptomatic ODE, incipient NAION must be borne in mind as a strong possibility in those who have had classic NAION in the fellow eye, in diabetics of all ages, and in those with high risk factors for NAION; this can avoid unnecessary and expensive investigations.

Polynomial mixture method of solving ordinary differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Nallasamy, Kumaresan; Ratnavelu, Kuru; Kamali, M. Z. M.

2017-11-01

In this paper, a numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach that provides mixture of polynomials where iteratively the right mixture will be generated. This mixture provide a generalized formalism of traditional Neural Networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). This can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that Polynomial Mixture Method (PMM) shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al, RK-4, Multi-Agent NN and Neuro Method (NM).

Assessment and management of rib fracture pain in geriatric population: an ode to old age.

PubMed

Wardhan, Richa

2013-10-01

Pain management for traumatic rib fractures has been described in literature, but there is paucity of data when it comes to acute pain management in the elderly, let alone pain resulting from traumatic rib fractures. This article focuses on challenges of assessment of pain in elderly patients and the various options available for pain management including utilization of nerve blocks. Nerve blocks are instrumental in treating rib fracture pain along with utilization of opioids and nonopioids thus formulating a multimodal approach to pain management. The goal is to devise a proper pain management regimen for geriatric patients with rib fractures to decrease the morbidity and mortality associated with it. Developing institutional protocols is one step forward towards quality care for such patients.

Modern aspects of homogeneous-heterogeneous reactions and variable thickness in nanofluids through carbon nanotubes

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Ahmed, Sohail; Muhammad, Taseer; Alsaedi, Ahmed

2017-10-01

This article examines homogeneous-heterogeneous reactions and internal heat generation in Darcy-Forchheimer flow of nanofluids with different base fluids. Flow is generated due to a nonlinear stretchable surface of variable thickness. The characteristics of nanofluid are explored using CNTs (single and multi walled carbon nanotubes). Equal diffusion coefficients are considered for both reactants and auto catalyst. The conversion of partial differential equations (PDEs) to ordinary differential equations (ODEs) is done via appropriate transformations. Optimal homotopy approach is implemented for solutions development of governing problems. Averaged square residual errors are computed. The optimal solution expressions of velocity, temperature and concentration are explored through plots by using several values of physical parameters. Further the coefficient of skin friction and local Nusselt number are examined through graphs.

Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study

PubMed Central

Papadimitriou, Konstantinos I.; Stan, Guy-Bart V.; Drakakis, Emmanuel M.

2013-01-01

This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented. PMID:23393550

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

Efficient modeling of laser-plasma accelerator staging experiments using INF&RNO

NASA Astrophysics Data System (ADS)

Benedetti, C.; Schroeder, C. B.; Geddes, C. G. R.; Esarey, E.; Leemans, W. P.

2017-03-01

The computational framework INF&RNO (INtegrated Fluid & paRticle simulatioN cOde) allows for fast and accurate modeling, in 2D cylindrical geometry, of several aspects of laser-plasma accelerator physics. In this paper, we present some of the new features of the code, including the quasistatic Particle-In-Cell (PIC)/fluid modality, and describe using different computational grids and time steps for the laser envelope and the plasma wake. These and other features allow for a speedup of several orders of magnitude compared to standard full 3D PIC simulations while still retaining physical fidelity. INF&RNO is used to support the experimental activity at the BELLA Center, and we will present an example of the application of the code to the laser-plasma accelerator staging experiment.

Stability analysis of an HIV/AIDS epidemic model with treatment

NASA Astrophysics Data System (ADS)

Cai, Liming; Li, Xuezhi; Ghosh, Mini; Guo, Baozhu

2009-07-01

An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number [real]0. If [real]0<=1, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if [real]0>1. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.

Polar boundary layer bromine explosion and ozone depletion events in the chemistry-climate model EMAC v2.52: implementation and evaluation of AirSnow algorithm

NASA Astrophysics Data System (ADS)

Falk, Stefanie; Sinnhuber, Björn-Martin

2018-03-01

Ozone depletion events (ODEs) in the polar boundary layer have been observed frequently during springtime. They are related to events of boundary layer enhancement of bromine. Consequently, increased amounts of boundary layer volume mixing ratio (VMR) and vertical column densities (VCDs) of BrO have been observed by in situ observation, ground-based as well as airborne remote sensing, and from satellites. These so-called bromine explosion (BE) events have been discussed serving as a source of tropospheric BrO at high latitudes, which has been underestimated in global models so far. We have implemented a treatment of bromine release and recycling on sea-ice- and snow-covered surfaces in the global chemistry-climate model EMAC (ECHAM/MESSy Atmospheric Chemistry) based on the scheme of Toyota et al. (2011). In this scheme, dry deposition fluxes of HBr, HOBr, and BrNO3 over ice- and snow-covered surfaces are recycled into Br2 fluxes. In addition, dry deposition of O3, dependent on temperature and sunlight, triggers a Br2 release from surfaces associated with first-year sea ice. Many aspects of observed bromine enhancements and associated episodes of near-complete depletion of boundary layer ozone, both in the Arctic and in the Antarctic, are reproduced by this relatively simple approach. We present first results from our global model studies extending over a full annual cycle, including comparisons with Global Ozone Monitoring Experiment (GOME) satellite BrO VCDs and surface ozone observations.

Sensitivity analysis of dynamic biological systems with time-delays.

PubMed

Wu, Wu Hsiung; Wang, Feng Sheng; Chang, Maw Shang

2010-10-15

Mathematical modeling has been applied to the study and analysis of complex biological systems for a long time. Some processes in biological systems, such as the gene expression and feedback control in signal transduction networks, involve a time delay. These systems are represented as delay differential equation (DDE) models. Numerical sensitivity analysis of a DDE model by the direct method requires the solutions of model and sensitivity equations with time-delays. The major effort is the computation of Jacobian matrix when computing the solution of sensitivity equations. The computation of partial derivatives of complex equations either by the analytic method or by symbolic manipulation is time consuming, inconvenient, and prone to introduce human errors. To address this problem, an automatic approach to obtain the derivatives of complex functions efficiently and accurately is necessary. We have proposed an efficient algorithm with an adaptive step size control to compute the solution and dynamic sensitivities of biological systems described by ordinal differential equations (ODEs). The adaptive direct-decoupled algorithm is extended to solve the solution and dynamic sensitivities of time-delay systems describing by DDEs. To save the human effort and avoid the human errors in the computation of partial derivatives, an automatic differentiation technique is embedded in the extended algorithm to evaluate the Jacobian matrix. The extended algorithm is implemented and applied to two realistic models with time-delays: the cardiovascular control system and the TNF-α signal transduction network. The results show that the extended algorithm is a good tool for dynamic sensitivity analysis on DDE models with less user intervention. By comparing with direct-coupled methods in theory, the extended algorithm is efficient, accurate, and easy to use for end users without programming background to do dynamic sensitivity analysis on complex biological systems with time-delays.

Modeling the flux of metabolites in the juvenile hormone biosynthesis pathway using generalized additive models and ordinary differential equations.

PubMed

Martínez-Rincón, Raúl O; Rivera-Pérez, Crisalejandra; Diambra, Luis; Noriega, Fernando G

2017-01-01

Juvenile hormone (JH) regulates development and reproductive maturation in insects. The corpora allata (CA) from female adult mosquitoes synthesize fluctuating levels of JH, which have been linked to the ovarian development and are influenced by nutritional signals. The rate of JH biosynthesis is controlled by the rate of flux of isoprenoids in the pathway, which is the outcome of a complex interplay of changes in precursor pools and enzyme levels. A comprehensive study of the changes in enzymatic activities and precursor pool sizes have been previously reported for the mosquito Aedes aegypti JH biosynthesis pathway. In the present studies, we used two different quantitative approaches to describe and predict how changes in the individual metabolic reactions in the pathway affect JH synthesis. First, we constructed generalized additive models (GAMs) that described the association between changes in specific metabolite concentrations with changes in enzymatic activities and substrate concentrations. Changes in substrate concentrations explained 50% or more of the model deviances in 7 of the 13 metabolic steps analyzed. Addition of information on enzymatic activities almost always improved the fitness of GAMs built solely based on substrate concentrations. GAMs were validated using experimental data that were not included when the model was built. In addition, a system of ordinary differential equations (ODE) was developed to describe the instantaneous changes in metabolites as a function of the levels of enzymatic catalytic activities. The results demonstrated the ability of the models to predict changes in the flux of metabolites in the JH pathway, and can be used in the future to design and validate experimental manipulations of JH synthesis.

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

PubMed

Akimenko, Vitalii; Anguelov, Roumen

2017-12-01

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

Noetherian symmetries of noncentral forces with drag term

NASA Astrophysics Data System (ADS)

Ghose-Choudhury, A.; Guha, Partha; Paliathanasis, Andronikos; Leach, P. G. L.

We consider the Noetherian symmetries of second-order ODEs subjected to forces with nonzero curl. Both position and velocity dependent forces are considered. In the former case, the first integrals are shown to follow from the symmetries of the celebrated Emden-Fowler equation.

Modelling toxin effects on protein biosynthesis in eukaryotic cells.

PubMed

Skakauskas, Vladas; Katauskis, Pranas

2017-08-01

We present a rather generic model for toxin (ricin) inhibition of protein biosynthesis in eukaryotic cells. We also study reduction of the ricin toxic effects with application of antibodies against the RTB subunit of ricin molecules. Both species initially are delivered extracellularly. The model accounts for the pinocytotic and receptor-mediated toxin endocytosis and the intact toxin exocytotic removal out of the cell. The model also includes the lysosomal toxin destruction, the intact toxin motion to the endoplasmic reticulum (ER) for separation of its molecules into the RTA and RTB subunits, and the RTA chain translocation into the cytosol. In the cytosol, one portion of the RTA undergoes degradation via the ERAD. The other its portion can inactivate ribosomes at a large rate. The model is based on a system of deterministic ODEs. The influence of the kinetic parameters on the protein concentration and antibody protection factor is studied in detail. Copyright © 2017 Elsevier Ltd. All rights reserved.

Nonlinear optimal control policies for buoyancy-driven flows in the built environment

NASA Astrophysics Data System (ADS)

Nabi, Saleh; Grover, Piyush; Caulfield, Colm

2017-11-01

We consider optimal control of turbulent buoyancy-driven flows in the built environment, focusing on a model test case of displacement ventilation with a time-varying heat source. The flow is modeled using the unsteady Reynolds-averaged equations (URANS). To understand the stratification dynamics better, we derive a low-order partial-mixing ODE model extending the buoyancy-driven emptying filling box problem to the case of where both the heat source and the (controlled) inlet flow are time-varying. In the limit of a single step-change in the heat source strength, our model is consistent with that of Bower et al.. Our model considers the dynamics of both `filling' and `intruding' added layers due to a time-varying source and inlet flow. A nonlinear direct-adjoint-looping optimal control formulation yields time-varying values of temperature and velocity of the inlet flow that lead to `optimal' time-averaged temperature relative to appropriate objective functionals in a region of interest.

Uniform Persistence and Global Stability for a Brain Tumor and Immune System Interaction

NASA Astrophysics Data System (ADS)

Khajanchi, Subhas

This paper describes the synergistic interaction between the growth of malignant gliomas and the immune system interactions using a system of coupled ordinary differential equations (ODEs). The proposed mathematical model comprises the interaction of glioma cells, macrophages, activated Cytotoxic T-Lymphocytes (CTLs), the immunosuppressive factor TGF-β and the immuno-stimulatory factor IFN-γ. The dynamical behavior of the proposed system both analytically and numerically is investigated from the point of view of stability. By constructing Lyapunov functions, the global behavior of the glioma-free and the interior equilibrium point have been analyzed under some assumptions. Finally, we perform numerical simulations in order to illustrate our analytical findings by varying the system parameters.

Modeling and vibration control of the flapping-wing robotic aircraft with output constraint

NASA Astrophysics Data System (ADS)

He, Wei; Mu, Xinxing; Chen, Yunan; He, Xiuyu; Yu, Yao

2018-06-01

In this paper, we propose the boundary control for undesired vibrations suppression with output constraint of the flapping-wing robotic aircraft (FWRA). We also present the dynamics of the flexible wing of FWRA with governing equations and boundary conditions, which are partial differential equations (PDEs) and ordinary differential equations (ODEs), respectively. An energy-based barrier Lyapunov function is introduced to analyze the system stability and prevent violation of output constraint. With the effect of the proposed boundary controller, distributed states of the system remain in the constrained spaces. Then the IBLF-based boundary controls are proposed to assess the stability of the FWRA in the presence of output constraint.

Solving Differential Equations in R: Package deSolve

EPA Science Inventory

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

Effect of Chemicals on Morphology and Luminescence of CdSe Quantum Dots.

PubMed

Zhang, Xiao; Li, Xiaoyu; Zhang, Ruili; Yang, Ping

2015-04-01

CdSe quantum dots (QDs) with several morphologies were fabricated using various reaction sys- tems. In a trioctylamine (TOA) and octadecylphosphonic acid (ODPA) system, yellow-emitting (a photoluminescence (PL) peak wavelength of 583 nm) CdSe QDs revealed rod morphology and nar- row size distribution. When ODPA was replaced by tetradecylphosphonic acid (TDPA), red-emitting CdSe rods (a PL peak wavelength of 653 nm) with broad size distribution were fabricated. This is ascribed that the short carbon chain accelerated the growth of CdSe QDs. As a result, the use of ODPA resulted in CdSe QDs with high PL efficiency (3.1%). Furthermore, cubic-like CdSe QDs were created in a stearic acid (SA) and octadecene (ODE) reaction system. The PL efficiency of the QDs is low (0.2%). When hexadecylamine (HDA) was added in such SA and ODE reaction system, spherical CdSe QDs with narrow size distribution and high PL efficiency (3.4%) were prepared.

Sound-turbulence interaction in transonic boundary layers

NASA Astrophysics Data System (ADS)

Lelostec, Ludovic; Scalo, Carlo; Lele, Sanjiva

2014-11-01

Acoustic wave scattering in a transonic boundary layer is investigated through a novel approach. Instead of simulating directly the interaction of an incoming oblique acoustic wave with a turbulent boundary layer, suitable Dirichlet conditions are imposed at the wall to reproduce only the reflected wave resulting from the interaction of the incident wave with the boundary layer. The method is first validated using the laminar boundary layer profiles in a parallel flow approximation. For this scattering problem an exact inviscid solution can be found in the frequency domain which requires numerical solution of an ODE. The Dirichlet conditions are imposed in a high-fidelity unstructured compressible flow solver for Large Eddy Simulation (LES), CharLESx. The acoustic field of the reflected wave is then solved and the interaction between the boundary layer and sound scattering can be studied.

On the complete and partial integrability of non-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

1984-11-01

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

Ode to Mexican Artists

ERIC Educational Resources Information Center

Villeneuve, Pat; Erickson, Mary

2004-01-01

This article presents a thematic, inquiry-based Instructional Resource for secondary students. This instructional resource uses thematic inquiry to facilitate transfer of knowledge. A theme is a general topic that can help students see relationships and make connections--and transfer information to new situations. Students may be more willing and…

NASA Aerodynamics Program Annual Report 1991

DTIC Science & Technology

1992-04-01

results have been compared relation effort on an AH-1G Cobr : helicopter v- ,,odeI wind tunnel data at different has been completed. Computational...The computational studies cant discovery . Preliminary water-channel have shown the trapped vortex to be a viable and wind-tunnel tests have shown the

Quantum Analog Computing

NASA Technical Reports Server (NTRS)

Zak, M.

1998-01-01

Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.

Mud, Macrofauna and Microbes: An ode to benthic organism-abiotic interactions at varying scales

EPA Science Inventory

Benthic environments are dynamic habitats, subject to variable sources and rates of sediment delivery, reworking from the abiotic and biotic processes, and complex biogeochemistry. These activities do not occur in a vacuum, and interact synergistically to influence food webs, bi...

A Simulation of Cooperation and Competition in Insurgent Networks

NASA Astrophysics Data System (ADS)

Gabbay, Michael

2014-03-01

Insurgencies are often characterized by multiple groups who share a common foe in the national government but have independent organizations which may differ with respect to social identities, ideologies, strategies, and their use of violence. These groups may cooperate in various ways such as conducting joint attacks, pooling resources, and establishing formal alliances or mergers. However, they may also compete with each other over popular support, recruitment of fighters, funding, allies, and ultimately military dominance. A network coevolution model of insurgent factional dynamics is presented which accounts for factors driving cooperation and competition. The model is formulated as a system of coupled ODEs which evolves network ties between insurgent groups along with group policies concerning the targets of violence. Simulation results are presented showing sharp transitions in network structure as model parameters are varied. Connections are drawn between the model results and empirical data from the Iraqi insurgency. This work was supported by the Office of Naval Research under grant N00014-13-1-0381.

Authorizing Charters: Helping Mom-and-Pops in Ohio

ERIC Educational Resources Information Center

Ryan, Terry; Lafferty, Michael B.; Finn, Chester E., Jr.

2010-01-01

The Thomas B. Fordham Foundation's long and deep immersion in Ohio education policy, particularly in the charter-school realm, includes a half decade of direct experience as "authorizer" of several charters. Initially, the Ohio Department of Education (ODE) was chief authorizer of charter schools in the Buckeye State. After the state…

Application of Power Geometry and Normal Form Methods to the Study of Nonlinear ODEs

NASA Astrophysics Data System (ADS)

Edneral, Victor

2018-02-01

This paper describes power transformations of degenerate autonomous polynomial systems of ordinary differential equations which reduce such systems to a non-degenerative form. Example of creating exact first integrals of motion of some planar degenerate system in a closed form is given.

MACSYMA's symbolic ordinary differential equation solver

NASA Technical Reports Server (NTRS)

Golden, J. P.

1977-01-01

The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.

Exploring Ohio's Private Education Sector. School Survey Series

ERIC Educational Resources Information Center

Catt, Andrew D.

2014-01-01

Exploring Ohio's Private Education Sector is the second entry in the Friedman Foundation for Educational Choice's "School Survey Series." This report synthesizes information on Ohio's private schools collected by the U.S. Department of Education and the Ohio Department of Education (ODE). Two appendices provide supplementary tables and…

Small Internal Combustion Engine Testing for a Hybrid-Electric Remotely-Piloted Aircraft

DTIC Science & Technology

2011-03-01

differential equations (ODEs) were formed and solved for numerically using various solvers in MATLAB . From these solutions, engine performance...program 5. □ Make sure eddy-current absorber and sprockets are free of debris and that no loose materials are close enough to become entangled

Development of an Urban Search and Rescue Robot

DTIC Science & Technology

2003-01-01

is a magnetorheological (MR) fluids shock absorber. The nature of this fluid is such that its compliance can be electronically adjusted thousands...simulators. First, ODE is still a work in progress. The user manual is far from finished and modifications to the coded library come out quite frequently...

Ode to an Animal

ERIC Educational Resources Information Center

Nelken, Miranda

2008-01-01

People know little about the non-domesticated animals that live around them. Somehow, they seem remote. In stories they hear about them, animals are often acting, speaking, and dressing like people. This article presents a lesson where students learn about the native species of their area while exploring the concept of interdependence through…

The development of the deterministic nonlinear PDEs in particle physics to stochastic case

NASA Astrophysics Data System (ADS)

Abdelrahman, Mahmoud A. E.; Sohaly, M. A.

2018-06-01

In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.

Pedagogical Potentialities in the Dynamic Symbolism of Videocy.

ERIC Educational Resources Information Center

Fantaousakis, Chrysoula

2001-01-01

Examines the communicative effectiveness of content presented in the audiovisual ode of discourse. Ninety children viewed individually four scenes from an audiovisual cartoon in three grade levels. Questions the value placed on the audiovisual mode of communication and addresses its power to organize and present cultural knowledge. (Author/VWL)

Ode to Sparklepony: Gamification in Action

ERIC Educational Resources Information Center

Sierra, Wendi; Stedman, Kyle D.

2012-01-01

Games are becoming increasingly prevalent in education, both in traditional school settings and beyond. In this Disputatio webtext, we look specifically at one application of games for pedagogical use: gamification. Rather than introducing a pre-existing game into the learning spaces, gamification adds elements of games into educational (or other)…

On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

ERIC Educational Resources Information Center

Savoye, Philippe

2009-01-01

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

High precision series solutions of differential equations: Ordinary and regular singular points of second order ODEs

NASA Astrophysics Data System (ADS)

Noreen, Amna; Olaussen, Kåre

2012-10-01

A subroutine for a very-high-precision numerical solution of a class of ordinary differential equations is provided. For a given evaluation point and equation parameters the memory requirement scales linearly with precision P, and the number of algebraic operations scales roughly linearly with P when P becomes sufficiently large. We discuss results from extensive tests of the code, and how one, for a given evaluation point and equation parameters, may estimate precision loss and computing time in advance. Program summary Program title: seriesSolveOde1 Catalogue identifier: AEMW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 991 No. of bytes in distributed program, including test data, etc.: 488116 Distribution format: tar.gz Programming language: C++ Computer: PC's or higher performance computers. Operating system: Linux and MacOS RAM: Few to many megabytes (problem dependent). Classification: 2.7, 4.3 External routines: CLN — Class Library for Numbers [1] built with the GNU MP library [2], and GSL — GNU Scientific Library [3] (only for time measurements). Nature of problem: The differential equation -s2({d2}/{dz2}+{1-ν+-ν-}/{z}{d}/{dz}+{ν+ν-}/{z2})ψ(z)+{1}/{z} ∑n=0N vnznψ(z)=0, is solved numerically to very high precision. The evaluation point z and some or all of the equation parameters may be complex numbers; some or all of them may be represented exactly in terms of rational numbers. Solution method: The solution ψ(z), and optionally ψ'(z), is evaluated at the point z by executing the recursion A(z)={s-2}/{(m+1+ν-ν+)(m+1+ν-ν-)} ∑n=0N Vn(z)A(z), ψ(z)=ψ(z)+A(z), to sufficiently large m. Here ν is either ν+ or ν-, and Vn(z)=vnz. The recursion is initialized by A(z)=δzν,for n=0,1,…,N ψ(z)=A0(z). Restrictions: No solution is computed if z=0, or s=0, or if ν=ν- (assuming Reν+≥Reν-) with ν+-ν- an integer, except when ν+-ν-=1 and v =0 (i.e. when z is an ordinary point for zψ(z)). Additional comments: The code of the main algorithm is in the file seriesSolveOde1.cc, which "#include" the file checkForBreakOde1.cc. These routines, and the programs using them, must "#include" the file seriesSolveOde1.cc. Running time: On a Linux PC that is a few years old, at y=√{10} to an accuracy of P=200 decimal digits, evaluating the ground state wavefunction of the anharmonic oscillator (with the eigenvalue known in advance); (cf. Eq. (6)) takes about 2 ms, and about 40 min at an accuracy of P=100000 decimal digits. References: [1] B. Haible and R.B. Kreckel, CLN — Class Library for Numbers, http://www.ginac.de/CLN/ [2] T. Granlund and collaborators, GMP — The GNU Multiple Precision Arithmetic Library, http://gmplib.org/ [3] M. Galassi et al., GNU Scientific Library Reference Manual (3rd Ed.), ISBN 0954612078., http://www.gnu.org/software/gsl/

Epigenetic battle of the sexes. Comment on: ;Epigenetic game theory: How to compute the epigenetic control of maternal-to-zygotic transition; by Qian Wang et al.

NASA Astrophysics Data System (ADS)

Wu, Song

2017-03-01

Qian Wang et al. present an interesting framework, named epigenetic game theory, for modeling sex-based epigenetic dynamics during embryogenesis from a new viewpoint of evolutionary game theory [1]. That is, epigenomes of sperms and oocytes may coordinate through either cooperation or competition, or both, to affect the fitness of embryos. The work uses a set of ordinary differential equations (ODEs) to describe longitudinal trajectories of DNA methylation levels in both parental and maternal gametes and their dependence on each other. The insights gained from this review, i.e. dynamic methylation profiles and their interaction are potentially important to many fields, such as biomedicine and agriculture.

Impact of chemical reaction in fully developed radiated mixed convective flow between two rotating disk

NASA Astrophysics Data System (ADS)

Hayat, T.; Khan, M. Waleed Ahmed; Khan, M. Ijaz; Waqas, M.; Alsaedi, A.

2018-06-01

Flow of magnetohydrodynamic (MHD) viscous fluid between two rotating disks is modeled. Angular velocities of two disks are different. Flow is investigated for nonlinear mixed convection. Heat transfer is analyzed for nonlinear thermal radiation and heat generation/absorption. Chemical reaction is also implemented. Convective conditions of heat and mass transfer are studied. Transformations used lead to reduction of PDEs into the ODEs. The impacts of important physical variables like Prandtl number, Reynold number, Hartman number, mixed convection parameter, chemical reaction and Schmidt number on velocities, temperature and concentration are elaborated. In addition velocity and temperature gradients are physically interpreted. Our obtained results indicate that radial, axial and tangential velocities decrease for higher estimation of Hartman number.

Modeling multi-GeV class laser-plasma accelerators with INF&RNO

NASA Astrophysics Data System (ADS)

Benedetti, Carlo; Schroeder, Carl; Bulanov, Stepan; Geddes, Cameron; Esarey, Eric; Leemans, Wim

2016-10-01

Laser plasma accelerators (LPAs) can produce accelerating gradients on the order of tens to hundreds of GV/m, making them attractive as compact particle accelerators for radiation production or as drivers for future high-energy colliders. Understanding and optimizing the performance of LPAs requires detailed numerical modeling of the nonlinear laser-plasma interaction. We present simulation results, obtained with the computationally efficient, PIC/fluid code INF&RNO (INtegrated Fluid & paRticle simulatioN cOde), concerning present (multi-GeV stages) and future (10 GeV stages) LPA experiments performed with the BELLA PW laser system at LBNL. In particular, we will illustrate the issues related to the guiding of a high-intensity, short-pulse, laser when a realistic description for both the laser driver and the background plasma is adopted. Work Supported by the U.S. Department of Energy under contract No. DE-AC02-05CH11231.

Hysteresis in coral reefs under macroalgal toxicity and overfishing.

PubMed

Bhattacharyya, Joydeb; Pal, Samares

2015-03-01

Macroalgae and corals compete for the available space in coral reef ecosystems.While herbivorous reef fish play a beneficial role in decreasing the growth of macroalgae, macroalgal toxicity and overfishing of herbivores leads to proliferation of macroalgae. The abundance of macroalgae changes the community structure towards a macroalgae-dominated reef ecosystem. We investigate coral-macroalgal phase shifts by means of a continuous time model in a food chain. Conditions for local asymptotic stability of steady states are derived. It is observed that in the presence of macroalgal toxicity and overfishing, the system exhibits hysteresis through saddle-node bifurcation and transcritical bifurcation. We examine the effects of time lags in the liberation of toxins by macroalgae and the recovery of algal turf in response to grazing of herbivores on macroalgae by performing equilibrium and stability analyses of delay-differential forms of the ODE model. Computer simulations have been carried out to illustrate the different analytical results.

Quality factors and local adaption (with applications in Eulerian hydrodynamics)

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

Crowley, W.P.

1992-06-17

Adapting the mesh to suit the solution is a technique commonly used for solving both ode's and pde's. For Lagrangian hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For Eulerian hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to Eulerian hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh elements. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less

OD-ing on Reality: An Interview with Alex Flinn

ERIC Educational Resources Information Center

Lesesne, Teri S.

2005-01-01

Alex Flinn discusses her debut novel, Breathing Underwater, which received much critical acclaim. She absolutely felt like her second book was being compared to Breathing Underwater at first. Breaking Point (which was completed before Breathing Underwater was published) was very different in tone. It was darker. The voice was different. The ending…

A CURRICULUM FOR ENGLISH, STUDENT PACKET, GRADE 9.

ERIC Educational Resources Information Center

Nebraska Univ., Lincoln. Curriculum Development Center.

THE FIRST UNIT OF THE STUDENT PACKET FOR GRADE NINE OF THE NEBRASKA ENGLISH CURRICULUM IS A STUDY OF THE RELATIONSHIPS WHICH EXIST BETWEEN AUTHOR AND AUDIENCE, AND AN EXAMINATION OF THE EPIGRAM, LIMERICK, PARABLE, FABLE, AND ODE. WITH THIS BACKGROUND, STUDENTS CONSIDER "ON AVARICE" AND "ANIMAL FARM" AS EXAMPLES OF FORMAL AND…

Ode to Moore

ERIC Educational Resources Information Center

Wilbert, Nancy Corrigan

2011-01-01

Best known for his monumental abstract sculptures of reclining figures, Henry Moore's forms are generally pierced or have a hollow space within them. Some say that these "organic undulating forms" are reminiscent of the landscape of his home in Yorkshire, England. Moore was a giant in the world of sculpture and his large cast bronzes and marble…

The Gift Code User Manual. Volume I. Introduction and Input Requirements

DTIC Science & Technology

1975-07-01

REPORT & PERIOD COVERED ‘TII~ GIFT CODE USER MANUAL; VOLUME 1. INTRODUCTION AND INPUT REQUIREMENTS FINAL 6. PERFORMING ORG. REPORT NUMBER ?. AuTHOR(#) 8...reverua side if neceaeary and identify by block number] (k St) The GIFT code is a FORTRANcomputerprogram. The basic input to the GIFT ode is data called

Open and Distance Learning in the Developing World. Routledge Studies in Distance Education.

ERIC Educational Resources Information Center

Perraton, Hilary

This book contains 10 chapters that analyze and synthesize the progress of open and distance education (ODE) in the developing world. Most chapters include case studies of programs in a variety of countries. "Introduction: Golden Goose or Ugly Duckling" briefly delineates the history of the field. "Nonformal Education: The Light…

Detection of Failure Progression in Cross-Ply Graphite/Epoxy during Fatigue through Acoustic Emission. Volume 1

DTIC Science & Technology

1989-11-01

ELECTE Jonathan Awerbuch MAY 2 6 1992William F. Ecldes m Donald L. Erdman A D Drexel University Department of Mechanical Engineering and Mechanics...17 2.8 References . ............. ................................. 17 M . EXPERIMENTAL PROCEDURE...90 6.7 On the Correspondence Between Event Intensities and M odes of Damage

Neutron Imaging of Lithium Concentration for Validation of Li-Ion Battery State of Charge Estimation

DTIC Science & Technology

2010-12-01

2008: Understanding liq- uid water distribution and removal phenomena in an op- erating pemfc via neutron radiography. Journal of The...2008: Measurement of liq- uid water accumulation in a pemfc with dead-ended an- ode. Journal of The Electrochemical Society, 155 (11), B1168–B1178

'Butterfly effect' in porous Bénard convection heated from below

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

Siri, Z.; Liew, K. Y.; Ibrahim, R. I.

2014-07-10

Transition from steady to chaos for the onset of Bénard convection in porous medium was analyzed. The governing equation is reduced to ordinary differential equation and solved using built in MATLAB ODE45. The transition from steady to chaos take over from a limit cycle followed by homoclinic explosion.

High-Fidelity Real-Time Trajectory Optimization for Reusable Launch Vehicles

DTIC Science & Technology

2006-12-01

6.20 Max DR Yawing Moment History. ...............................................................270 Figure 6.21 Snapshot from MATLAB “Profile...Propagation using “ode45” (Euler Angles)...........................................330 Figure 6.114 Interpolated Elevon Controls using Various MATLAB ...Schemes.................332 Figure 6.115 Interpolated Flap Controls using Various MATLAB Schemes.....................333 Figure 6.116 Interpolated

The Shaped Charge Concept. Part 2. The History of Shaped Charges

DTIC Science & Technology

1990-09-01

research of Evans. Ubbel•ode. LAmurd-Jones, Devonihire, and An&ew. 1hW U.K. Mufied cadmium liners (which probably produce molten jets) msd steel liners...34 Mathematical Jet Theory of Lined Hollow Charges." BRL Report No. 370, U.S. Army Ballistic Research Laboratory. Aberdeen Proving Ground, MD, 18 June

Oregon American Indian Alaska Native Education State Plan.

ERIC Educational Resources Information Center

Castillo, Susan

This state plan presents Oregon's 11 educational goals for American Indian/Alaska Native (AI/AN) education, which have been revised and detailed by the statewide Indian Education Council. The goals support the policy of the Oregon Department of Education (ODE), the educational philosophy of the AI/AN community, and the Indian Student Bill of…

Experimental and analytical investigation of inertial propulsion mechanisms and motion simulation of rigid multi-body mechanical systems

NASA Astrophysics Data System (ADS)

Almesallmy, Mohammed

Methodologies are developed for dynamic analysis of mechanical systems with emphasis on inertial propulsion systems. This work adopted the Lagrangian methodology. Lagrangian methodology is the most efficient classical computational technique, which we call Equations of Motion Code (EOMC). The EOMC is applied to several simple dynamic mechanical systems for easier understanding of the method and to aid other investigators in developing equations of motion of any dynamic system. In addition, it is applied to a rigid multibody system, such as Thomson IPS [Thomson 1986]. Furthermore, a simple symbolic algorithm is developed using Maple software, which can be used to convert any nonlinear n-order ordinary differential equation (ODE) systems into 1st-order ODE system in ready format to be used in Matlab software. A side issue, but equally important, we have started corresponding with the U.S. Patent office to persuade them that patent applications, claiming gross linear motion based on inertial propulsion systems should be automatically rejected. The precedent is rejection of patent applications involving perpetual motion machines.

Arrhenius Rate: constant volume burn

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

Menikoff, Ralph

A constant volume burn occurs for an idealized initial state in which a large volume of reactants at rest is suddenly raised to a high temperature and begins to burn. Due to the uniform spatial state, there is no fluid motion and no heat conduction. This reduces the time evolu tion to an ODE for the reaction progress variable. With an Arrhenius reaction rate, two characteristics of thermal ignition are illustrated: induction time and thermal runaway. The Frank-Kamenetskii approximation then leads to a simple expression for the adiabatic induction time. For a first order reaction, the analytic solution is derivedmore » and used to illustrate the effect of varying the activation temperature; in particular, on the induction time. In general, the ODE can be solved numerically. This is used to illustrate the effect of varying the reaction order. We note that for a first order reaction, the time evolution of the reaction progress variable has an exponential tail. In contrast, for a reaction order less than one, the reaction completes in a nite time. The reaction order also affects the induction time.« less

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

Preface of the "Symposium on Mathematical Models and Methods to investigate Heterogeneity in Cell and Cell Population Biology"

NASA Astrophysics Data System (ADS)

Clairambault, Jean

2016-06-01

This session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria.

Dynamics of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells.

PubMed

Katri, Patricia; Ruan, Shigui

2004-11-01

Stilianakis and Seydel (Bull. Math. Biol., 1999) proposed an ODE model that describes the T-cell dynamics of human T-cell lymphotropic virus I (HTLV-I) infection and the development of adult T-cell leukemia (ATL). Their model consists of four components: uninfected healthy CD4+ T-cells, latently infected CD4+ T-cells, actively infected CD4+ T-cells, and ATL cells. Mathematical analysis that completely determines the global dynamics of this model has been done by Wang et al. (Math. Biosci., 2002). In this note, we first modify the parameters of the model to distinguish between contact and infectivity rates. Then we introduce a discrete time delay to the model to describe the time between emission of contagious particles by active CD4+ T-cells and infection of pure cells. Using the results in Culshaw and Ruan (Math. Biosci., 2000) in the analysis of time delay with respect to cell-free viral spread of HIV, we study the effect of time delay on the stability of the endemically infected equilibrium. Numerical simulations are presented to illustrate the results.

A lumped model of venting during thermal runaway in a cylindrical Lithium Cobalt Oxide lithium-ion cell

NASA Astrophysics Data System (ADS)

Coman, Paul T.; Rayman, Sean; White, Ralph E.

2016-03-01

This paper presents a mathematical model built for analyzing the intricate thermal behavior of a 18650 LCO (Lithium Cobalt Oxide) battery cell during thermal runaway when venting of the electrolyte and contents of the jelly roll (ejecta) is considered. The model consists of different ODEs (Ordinary Differential Equations) describing reaction rates and electrochemical reactions, as well as the isentropic flow equations for describing electrolyte venting. The results are validated against experimental findings from Golubkov et al. [1] [Andrey W. Golubkov, David Fuchs, Julian Wagner, Helmar Wiltsche, Christoph Stangl, Gisela Fauler, Gernot Voitice Alexander Thaler and Viktor Hacker, RSC Advances, 4:3633-3642, 2014] for two cases - with flow and without flow. The results show that if the isentropic flow equations are not included in the model, the thermal runaway is triggered prematurely at the point where venting should occur. This shows that the heat dissipation due to ejection of electrolyte and jelly roll contents has a significant contribution. When the flow equations are included, the model shows good agreement with the experiment and therefore proving the importance of including venting.

PKPD model of interleukin-21 effects on thermoregulation in monkeys--application and evaluation of stochastic differential equations.

PubMed

Overgaard, Rune Viig; Holford, Nick; Rytved, Klaus A; Madsen, Henrik

2007-02-01

To describe the pharmacodynamic effects of recombinant human interleukin-21 (IL-21) on core body temperature in cynomolgus monkeys using basic mechanisms of heat regulation. A major effort was devoted to compare the use of ordinary differential equations (ODEs) with stochastic differential equations (SDEs) in pharmacokinetic pharmacodynamic (PKPD) modelling. A temperature model was formulated including circadian rhythm, metabolism, heat loss, and a thermoregulatory set-point. This model was formulated as a mixed-effects model based on SDEs using NONMEM. The effects of IL-21 were on the set-point and the circadian rhythm of metabolism. The model was able to describe a complex set of IL-21 induced phenomena, including 1) disappearance of the circadian rhythm, 2) no effect after first dose, and 3) high variability after second dose. SDEs provided a more realistic description with improved simulation properties, and further changed the model into one that could not be falsified by the autocorrelation function. The IL-21 induced effects on thermoregulation in cynomolgus monkeys are explained by a biologically plausible model. The quality of the model was improved by the use of SDEs.

Oregon School and District Report Card Policy and Technical Manual

ERIC Educational Resources Information Center

Oregon Department of Education, 2012

2012-01-01

The school and district report cards were created by the 1999 Oregon Legislature. The legislation requires that the Oregon Department of Education (ODE) produce and issue a report card to all public schools and districts in the state. The report cards are designed to: (1) Communicate the many good things occurring in Oregon's public schools; (2)…

Teaching a Faulkner Novel Using Research from the Discipline of English.

ERIC Educational Resources Information Center

Ford, Daniel G.

Students cannot be trained to perceive the complicated richness of literary art, but they may be educated to align their sensibilities with writer's clues when a literary work requires an intuitive reading. For instance, William Faulkner admired Keats's "Ode to a Grecian Urn" and various commentators have noted the urn-like imagery in…