Showing papers on "Mathematical model published in 2014"

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

Abstract: Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor

Abstract: This work is devoted to the investigation of mathematical models of drilling systems described by ordinary differential equations. Here, we continue the study done by the researchers from Eindhoven where the two-mass mathematical model of a drilling system has been investigated (Mihajlovic et al. J. Dyn. Syst. Meas. Control 126(4): 709–720, 2004; de Bruin et al. Automatica 45(2): 405–415, 2009). The modified version of this model, which takes into account a full description of an induction motor, is studied. It is shown that such complex effects as hidden oscillations may appear in these kinds of systems. These effects may lead to drill string failures and breakdowns.

A review of mathematical modeling of fixed-bed columns for carbon dioxide adsorption

Abstract: a b s t r a c t Carbon dioxide emissions must be stabilized to mitigate the unfettered release of greenhouse gases into the atmosphere. The removal of carbon dioxide from flue gases, an important first step in addressing the problem of CO2 emissions, can be achieved through adsorption separation technologies. In most adsorption processes, the adsorbent is in contact with fluid in a fixed bed. Fixed-bed column mathematical models are required to predict the performance of the adsorptive separation of carbon dioxide for optimizing design and operating conditions. A comprehensive mathematical model consists of coupled partial differential equations distributed over time and space that describe material, energy, and the momentum balances together with transport rates and equilibrium equations. Due to the complexities associated with the solution of a coupled stiff partial differential equation system, the use of accurate and efficient simplified models is desirable to decrease the required computational time. The simplified model is primarily established based on the description of mass transfer within adsorption systems. This paper presents a review of efforts over the last three decades toward mathematical modeling of the fixed-bed adsorption of carbon dioxide. The nature of various gas–solid equilibrium relationships as well as different descriptions of the mass transfer mechanisms within the adsorbent particle are reviewed. In addition to mass transfer, other aspects of adsorption in a fixed bed, such as heat and momentum transfer, are also studied. Both single- and multi-component CO2 adsorption systems are discussed in the review. © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Topological sensitivity analysis for systems biology

Abstract: Mathematical models of natural systems are abstractions of much more complicated processes. Developing informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise, and a modicum of luck. Except for cases where physical principles provide sufficient guidance, it will also be generally possible to come up with a large number of potential models that are compatible with a given natural system and any finite amount of data generated from experiments on that system. Here we develop a computational framework to systematically evaluate potentially vast sets of candidate differential equation models in light of experimental and prior knowledge about biological systems. This topological sensitivity analysis enables us to evaluate quantitatively the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.

A review of the mathematical models for predicting the heat and mass transfer process in the liquid desiccant dehumidifier

Abstract: The paper aims to overview various mathematical models for modeling the simultaneous heat and mass transfer process in the liquid desiccant dehumidifier. Firstly, the dehumidification principle is introduced briefly. Then the models are interpreted in terms of two classes of dehumidifiers. For the adiabatic dehumidifier, the models are mainly classified into three types: finite difference model, effectiveness NTU (e–NTU) model, and simplified models. For the internally cooled dehumidifier, there are also three kinds of models: models without considering liquid film thickness, models considering uniform liquid film thickness, and models considering variable liquid film thickness. This review is meaningful for comprehending the development process and research status of the models and choosing suitable models for prediction. In addition, some suggestions are proposed for the model improvement.

Vehicle Dynamics: Modeling and Simulation

Abstract: The authors examine in detail the fundamentals and mathematical descriptions of the dynamics of automobiles. In this context different levels of complexity will be presented, starting with basic single-track models up to complex three-dimensional multi-body models. A particular focus is on the process of establishing mathematical models on the basis of real cars and the validation of simulation results. The methods presented are explained in detail by means of selected application scenarios.

Steady state analysis of Boolean molecular network models via model reduction and computational algebra

Abstract: A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem.

Mathematical models for efficiency of inverters used in grid connected photovoltaic systems

Abstract: Abs tract In order to perform a reliable simulation of a photovoltaic system is crucial to know the electrical and thermal characteristics of each component that will be modeled by mathematical models that describe the system operation. This paper presents the development of mathematical models that characterize the inverter used in grid-connected photovoltaic systems. The mathematical models were fitted from experimental tests and they are suitable to be used in computer simulation software. The tests were performed on a set of inverters commercially available at Solar Energy Laboratory at Federal University of Rio Grande do Sul (UFRGS, Brazil) and at Photovoltaic Solar Energy Laboratory at Research Centre for Energy, Environment and Technology (CIEMAT, Spain). From the measured data it was calculated fitting coefficients to the efficiency curve of several inverters. In order to use these mathematical models for simulating other inverters, their own coefficients have to be experimentally determined and entered into the data base of the software in order to provide a full detailed computer simulation.

On the multiscale modeling of vehicular traffic: From kinetic to hydrodynamics

Abstract: This paper deals with the multiscale modeling of vehicular traffic according to a kinetic theory approach, where the microscopic state of vehicles is described by position, velocity and activity, namely a variable suitable to model the quality of the driver-vehicle micro-system. Interactions at the microscopic scale are modeled by methods of game theory, thus leading to the derivation of mathematical models within the framework of the kinetic theory. Macroscopic equations are derived by asymptotic limits from the underlying description at the lower scale. This approach shows the hypothesis under which macroscopic models known in the literature can be derived and how new models can be developed.

Modeling and Experimental Validation of the Frequency Response of Synthetic Jet Actuators

Abstract: A lumped-element mathematical model of the operation of a synthetic jet actuator driven by a thin piezoelectric disk is both analytically and numerically investigated to obtain information about the frequency response of the device. It is shown that the actuator behaves as a two-coupled oscillator system, and simple relationships are given to predict the two peak frequencies, corresponding to the modified Helmholtz and first-mode structural resonance frequencies. The model is validated through experimental tests carried out on three devices having different mechanical and geometrical characteristics, designed primarily to achieve an increasing coupling strength. A strict agreement between overall theoretical scaling laws and numerical computations is also found.

Entangled Polymer Dynamics in Equilibrium and Flow Modeled Through Slip Links

Abstract: The idea that the dynamics of concentrated, high–molecular weight polymers are largely governed by entanglements is now widely accepted and typically understood through the tube model. Here we review alternative approaches, slip-link models, that share some similarities to and offer some advantages over tube models. Although slip links were proposed at the same time as tubes, only recently have detailed, quantitative mathematical models arisen based on this picture. In this review, we focus on these models, with most discussion limited to mathematically well-defined objects that conform to state-of-the-art beyond-equilibrium thermodynamics. These models are connected to each other through successive coarse graining, using nonequilibrium thermodynamics along the way, and with a minimal parameter set. In particular, the most detailed level of description has four parameters, three of which can be determined directly from atomistic simulations. Once the remaining parameter is determined for any system, all p...

The art of model fitting to experimental results

Abstract: Model fitting to experimental results is presented within the context of graduate physics laboratories and generalized to other graduate and post-graduate levels, and diverse research fields. In most cases the analysis of experimental results, in terms of mathematical models available to describe the obtained results, extends beyond the numerical minimization of statistical estimators, like the chi-square, in the model’s parameter space. Dedicated fitting procedures, not easily or directly available in common data analysis software’s packages, are required to obtain the best fitting set of parameters that present a consistent physical meaning. A simple but powerful web-based solution is presented, and its relative advantage in comparison with known commercial and open source solutions is discussed.

Flow rate and time mean speed predictions for the urban freeway network using state space models

Abstract: Short-term predictions of traffic parameters such as flow rate and time mean speed is a crucial element of current ITS structures, yet complicated to formulate mathematically. Classifying states of traffic condition as congestion and non-congestion, the present paper is focused on developing flexible and explicitly multivariate state space models for network flow rate and time mean speed predictions. Based on the spatial–temporal patterns of the congested and non-congested traffic, the NSS model and CSS model are developed by solving the macroscopic traffic flow models, conservation equation and Payne–Whitham model for flow rate and time mean speed prediction, respectively. The feeding data of the proposed models are from historical time series and neighboring detector measurements to improve the prediction accuracy and robustness. Using 2-min measurements from urban freeway network in Beijing, we provide some practical guidance on selecting the most appropriate models for congested and non-congested conditions. The result demonstrates that the proposed models are superior to ARIMA models, which ignores the spatial component of the spatial–temporal patterns. Compared to the ARIMA models, the benefit from spatial contribution is much more evident in the proposed models for all cases, and the accuracy can be improved by 5.62% on average. Apart from accuracy improvement, the proposed models are more robust and the predictions can retain a smoother pattern. Our findings suggest that the NSS model is a better alternative for flow rate prediction under non-congestion conditions, and the CSS model is a better alternative for time mean speed prediction under congestion conditions.

Comparison of dynamic effects of high-speed traffic load on ballasted track using a simplified two-dimensional and full three-dimensional model

Abstract: The vertical dynamic actions transmitted by railway vehicles to the ballasted track infrastructure are evaluated taking into account models with different degrees of detail. In particular, this matter has been studied from a two-dimensional finite-element model to a fully coupled three-dimensional multibody finite-element model. The vehicle and track are coupled via a nonlinear Hertz contact mechanism. The method of Lagrange multipliers is used for the contact constraint enforcement between the wheel and rail. Distributed elevation irregularities are generated based on power spectral density distributions, which are taken into account for the interaction. Due to the contact nonlinearities, the numerical simulations are performed in the time domain, using a direct integration method for the transient problem. The results obtained include contact forces, forces transmitted to the infrastructure (sleeper) by railpads, and envelopes of relevant results for several track irregularities and speed ranges. The main contribution of this work is to identify and discuss coincidences and differences between discrete two-dimensional models and continuum three-dimensional models, as well to assess the validity of evaluating the dynamic loading on the track with simplified two-dimensional models.

A study on optimal design of process parameters in single point incremental forming of sheet metal by combining Box–Behnken design of experiments, response surface methods and genetic algorithms

Abstract: Incremental forming is a sheet metal forming process characterized by high flexibility; for this reason, it is suggested for rapid prototyping and customized products. On the other hand, this process is slower than traditional ones and requires in-depth studies to know the influence and the optimization of certain process parameters. In this paper, a complete optimization procedure starting from modeling and leading to the search of robust optimal process parameters is proposed. A numerical model of single point incremental forming of aluminum truncated cone geometries is developed by means of Finite Element simulation code ABAQUS and validated experimentally. One of the problems to be solved in the metal forming processes of thin sheets is the taking into account of the effects of technological process parameters so that the part takes the desired mechanical and geometrical characteristics. The control parameters for the study included wall inclination angle (α), tool size (D), material thickness (Thini), and vertical step size (In). A total of 27 numerical tests were conducted based on a 4-factor, 3-level Box–Behnken Design of Experiments approach along with FEA. An analysis of variance (ANOVA) test was carried out to obtain the relative importance of each single factor in terms of their main effects on the response variable. The main and interaction effects of the process parameters on sheet thinning rate and the punch forces were studied in more detail and presented in graphical form that helps in selecting quickly the process parameters to achieve the desired results. The main objective of this work is to examine and minimize the sheet thinning rate and the punch loads generated in this forming process. A first optimization procedure is based on the use of graphical response surfaces methodology (RSM). Quadratic mathematical models of the process were formulated correlating for the important controllable process parameters with the considered responses. The adequacies of the models were checked using analysis of variance technique. These analytical formulations allow the identification of the influential parameters of an optimization problem and the reduction of the number of evaluations of the objective functions. Taking the models as objective functions further optimization has been carried out using a genetic algorithm (GA) developed in order to compute the optimum solutions defined by the minimum values of sheet thinning and the punch loads and their corresponding combinations of optimum process parameters. For validation of its accuracy and generalization, the genetic algorithm was tested by using two analytical test functions as benchmarks of which global and local minima are known. It was demonstrated that the developed method can solve high nonlinear problems successfully. Finally, it is observed that the numerical results showed the suitability of the proposed approaches, and some comparative studies of the optimum solutions obtained by these algorithms developed in this work are shown here.

A Markov Chain Channel Model for Active Transport Molecular Communication

Abstract: In molecular communication, small particles such as molecules are used to convey information. These particles are released by a transmitter into a fluidic environment, where they propagate freely (e.g. through diffusion) or through externals means (e.g. different types of active transport) until they arrive at the receiver. Although there are a number of different mathematical models for the diffusion-based molecular communication, active transport molecular communication (ATMC) lacks the necessary theoretical framework. Previous works had to rely almost entirely on full Monte Carlo simulations of these systems. However, full simulations can be time consuming because of the computational complexities involved. In this paper, a Markov channel model has been presented, which could be used to reduce the amount of simulations necessary for studying ATMC without sacrificing accuracy. Moreover, a mathematical formula for calculating the transition probabilities in the Markov chain model is derived to complete our analytical framework. Comparing our proposed models with full simulations, it is shown that these models can be used to calculate parameters such channel capacity accurately in a timely manner.

A mathematical model of the synchronous reluctance machine with independent control along the excitation line

Abstract: A mathematical model of a synchronous reluctance machine with independent regulation along the excitation line is presented. The electromechanical converter unit is presented as a system with distributed parameters and designed by the finite element method, while the semiconductor converter is approximated with a continuous dynamic element. The case of regulated induction electric drives is used to show by statistical methods that the results produced by the calculation according to the proposed mathematical model at loads from 0 to M N are close to the figures calculated using common calculation procedures. It is shown that, because of the very roughly considered saturation of the magnetic system, it is incorrect to use common mathematical models in the design of induction electric drives in the critical and supercritical torque regions. For this reason, the developed mathematical model can also be used in the design of common electric drives in the torque overload area.

Model-based Diagnosis of an Automotive Electric Power Generation and Storage System

Abstract: This paper presents mathematical models, design and experimental validation, and calibration of a model-based diagnostic algorithm for an electric-power generation and storage automotive system, including a battery and an alternator with a rectifier and a voltage regulator. Mathematical models of these subsystems are derived, based on the physics of processes involved as characterized by time-varying nonlinear ordinary differential equations. The diagnostic problem focuses on detection and isolation of a specific set of alternator faults, including belt slipping, rectifier fault, and voltage regulator fault. The proposed diagnostic approach is based on the generation of residuals obtained using system models and comparing predicted and measured value of selected variables, including alternator output current, field voltage, and battery voltage. An equivalent input-output alternator model, which is used in the diagnostic scheme, is also formulated and parameterized. The test bench used for calibration of thresholds of the diagnostic algorithm and overall validation process are discussed. The effectiveness of the fault diagnosis algorithm and threshold selection is experimentally demonstrated.

Application of Finite Mixture of Regression Model with Varying Mixing Probabilities to Estimation of Urban Arterial Travel Times

Abstract: Travel time along an urban arterial is greatly affected by traffic signals. Most studies on urban travel time use statistical models to obtain the distribution directly without incorporating the effects of traffic signal timing. In this study, a finite mixture of regression model with varying mixing probabilities (weights) was proposed to gain a better understanding of urban travel time distribution through consideration of signal timing. Standard finite mixture models with constant mixing probabilities have a limited ability to adapt to underlying random structural changes for observed travel times. The model developed in this study can capture such dynamics by (a) modeling the mixing probabilities as a function of the explanatory variables associated with signal timing and (b) establishing a linear regression between the mean of each component and signal timing. The finite mixture of regression model was applied to the travel time data collected by the automatic vehicle identification system on one urba...

OpenFCST: An Open-Source Mathematical Modelling Software for Polymer Electrolyte Fuel Cells

Abstract: OpenFCST (open-source fuel cell simulation toolbox) is an open-source, finite element method based, multi-dimensional mathematical modeling software for polymer electrolyte fuel cells. The aim of the software is to develop a platform for collaborative development of fuel cell mathematical models. The philosophy, structure and main components of openFCST are presented. OpenFCST currently includes physical models for gas, electron, ion, ionomer-bound water and heat transport. It also contains effective transport media relations to estimate transport properties for gas diffusion layers, micro-porous layers and catalyst layers as well as several kinetic models for the fuel cell electrochemical reactions. OpenFCST has been structured as a toolbox such that it is easier for new users to integrate new physical models with existing framework. OpenFCST is used to analyze the impact of different kinetic models on a multidimensional cathode model and to study the main differences between a macro-homogeneous and several agglomerate models. Finally, openFCST is used to develop a three-dimensional model of a patterned catalyst layer. Results show that multi-step kinetic models improve fuel cell performance predictions, macro-homogeneous and ionomer-filled agglomerate models show similar performance for 100 nm radii agglomerates up to current densities of 2 A/cm2, and water-filled agglomerate models require negative surface charges to exist at the pore walls in order to provide results in-line with experimental data. Finally, a patterned catalyst layer with micro-pores is shown to improve electrode performance.