Showing papers on "Mathematical model published in 2017"

Energy Balance Climate Models

Abstract: An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved, and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed.

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications *

Abstract: Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. In this review article we will address the two principal components of the cardiovascular system: arterial circulation and heart function. We will systematically describe all aspects of the problem, ranging from data imaging acquisition, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, proposing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiocirculatory system, the multiscale nature of the physiological processes involved, and the need to devise computational methods that are stable, reliable and efficient. Critical issues involve filtering the data, identifying the parameters of mathematical models, devising optimal treatments and accounting for uncertainties. For this reason, we will devote the last part of the paper to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are of paramount importance when solving problems with high complexity, which would otherwise be out of reach.

Mathematical modelling of wave energy converters: A review of nonlinear approaches

Abstract: The wave energy sector has made and is still doing a great effort in order to open up a niche in the energy market, working on several and diverse concepts and making advances in all aspects towards more efficient technologies However, economic viability has not been achieved yet, for which maximisation of power production over the full range of sea conditions is crucial Precise mathematical models are essential to accurately reproduce the behaviour, including nonlinear dynamics, and understand the performance of wave energy converters Therefore, nonlinear models must be considered, which are required for power absorption assessment, simulation of devices motion and model-based control systems Main sources of nonlinear dynamics within the entire chain of a wave energy converter - incoming wave trains, wave-structure interaction, power take-off systems or mooring lines- are identified, with especial attention to the wave-device hydrodynamic interaction, and their influence is studied in the present paper for different types of converters In addition, different approaches to model nonlinear wave-device interaction are presented, highlighting their advantages and drawbacks Besides the traditional Navier-Stokes equations or potential flow methods, ‘new’ methods such as system-identification models, smoothed particle hydrodynamics or nonlinear potential flow methods are analysed

Tilt and azimuth angles in solar energy applications – A review

Abstract: This paper presents a review of tilt angle and azimuth angles in solar energy applications. The paper involves an overview of design parameter, applications, simulations and mathematical techniques covering different usage application. The number of references analysing the tilt angle deployment in the context of the research papers of the different countries currently having operations in solar systems is much more significant. Different kinds of models and test methods of optimum tilt angle in different solar systems have been developed since 1956 which can be distinguished by their particular mathematical models or tracking techniques as shown in the latest researches. The mathematical models allows the calculation of different parameters of the solar radiation, the angle of inclination, and the optimum tilt angle of the collecting surface and the effects acting on the system.

Lost-Circulation Control for Formation-Damage Prevention in Naturally Fractured Reservoir: Mathematical Model and Experimental Study

Abstract: Drill-in fluid loss is the most important cause of formation damage during the drill-in process in fractured tight reservoirs. The addition of lost-circulation material (LCM) into drill-in fluid is the most popular technique for loss control. However, traditional LCM selection is mainly performed by use of the trial-and-error method because of the lack of mathematical models. The present work aims at filling this gap by developing a new mathematical model to characterize the performance of drill-in fluid-loss control by use of LCM during the drill-in process of fractured tight reservoirs. Plugging-zone strength and fracture-propagation pressure are the two main factors affecting drill-in fluid-loss control. The developed mathematical model consists of two submodels: the plugging-zone-strength model and the fracture-propagation-pressure model. Explicit formulae are obtained for LCM selection dependent on the proposed model to control drill-in fluid loss and prevent formation damage. Effects of LCMmechanical and geometrical properties on loss-control performance are analyzed for optimal fracture plugging and propagation control. Laboratory tests on loss-control effect by use of different types and concentrations of LCMs are performed. Different combinations of acid-soluble rigid particles, fibers, and elastic particles are tested to generate a synergy effect for drill-in fluidloss control. The derived model is validated by laboratory data and successfully applied to the field case study in Sichuan Basin, China.

Computationally efficient nonlinear Froude–Krylov force calculations for heaving axisymmetric wave energy point absorbers

Abstract: Most wave energy converters (WECs) are described by linear mathematical models, based on the main assumption of small amplitudes of motion. Notwithstanding the computational convenience, linear models can become inaccurate when large motions occur. On the other hand, nonlinear models are often time consuming to simulate, while model-based controllers require system dynamic models which can execute in real time. Therefore, this paper proposes a computationally efficient representation of nonlinear static and dynamic Froude–Krylov forces, valid for any heaving axisymmetric point absorber. Nonlinearities are increased by nonuniform WEC cross sectional area and large displacements induced by energy maximising control strategies, which prevent the device from behaving as a wave follower. Results also show that the power production assessment realized through a linear model can be overly optimistic and control parameters calculations should also reflect the true nonlinear nature of the WEC model.

Control Theoretic Models of Pointing

Abstract: This article presents an empirical comparison of four models from manual control theory on their ability to model targeting behaviour by human users using a mouse: McRuer’s Crossover, Costello’s Surge, second-order lag (2OL), and the Bang-bang model. Such dynamic models are generative, estimating not only movement time, but also pointer position, velocity, and acceleration on a moment-to-moment basis. We describe an experimental framework for acquiring pointing actions and automatically fitting the parameters of mathematical models to the empirical data. We present the use of time-series, phase space, and Hooke plot visualisations of the experimental data, to gain insight into human pointing dynamics. We find that the identified control models can generate a range of dynamic behaviours that captures aspects of human pointing behaviour to varying degrees. Conditions with a low index of difficulty (ID) showed poorer fit because their unconstrained nature leads naturally to more behavioural variability. We report on characteristics of human surge behaviour (the initial, ballistic sub-movement) in pointing, as well as differences in a number of controller performance measures, including overshoot, settling time, peak time, and rise time. We describe trade-offs among the models. We conclude that control theory offers a promising complement to Fitts’ law based approaches in HCI, with models providing representations and predictions of human pointing dynamics, which can improve our understanding of pointing and inform design.

Constructing compact causal mathematical models for complex dynamics

Abstract: From microbial communities, human physiology to social and bio- logical/neural networks, complex interdependent systems display multi-scale spatio-temporal pa erns that are frequently classi ed as non-linear, non-Gaussian, non-ergodic, and/or fractal. Distin- guishing between the sources of nonlinearity, identifying the na- ture of fractality (space versus time) and encapsulating the non- Gaussian characteristics into dynamic causal models remains a ma- jor challenge for studying complex systems. In this paper, we pro- pose a new mathematical strategy for constructing compact yet ac- curate models of complex systems dynamics that aim to scrutinize the causal e ects and in uences by analyzing the statistics of the magnitude increments and the inter-event times of stochastic pro- cesses. We derive a framework that enables to incorporate knowl- edge about the causal dynamics of the magnitude increments and the inter-event times of stochastic processes into a multi-fractional order nonlinear partial di erential equation for the probability to nd the system in a speci c state at one time. Rather than follow- ing the current trends in nonlinear system modeling which pos- tulate speci c mathematical expressions, this mathematical frame- work enables us to connect the microscopic dependencies between the magnitude increments and the inter-event times of one stochas- tic process to other processes and justify the degree of nonlinearity. In addition, the newly presented formalism allows to investigate appropriateness of using multi-fractional order dynamical models for various complex system which was overlooked in the literature. We run extensive experiments on several sets of physiological pro- cesses and demonstrate that the derived mathematical models o er superior accuracy over state of the art techniques.

Regional Coastal Processes Numerical Modeling System: Report 1, Rcpwave-a Linear Wave Propagation Model for Engineering Use

Abstract: : The numerical model documented here, RCPWAVE, can be used to solve wave propagation problems over arbitrary bathymetry. The governing equations solved in the model are the mild slope equation for linear, monochromatic waves, and the equation specifying irrotationality of the wave phase function gradient. Finite difference approximations of these equations are solved to predict wave propagation outside the surf zone. Inside the breaker zone, an empirical method is used to predict wave transformation. This method is based on a hydraulic jump representation of the entire surf zone. The model is verified using laboratory and field data. A user's manual section is provided to aid potential users. This documentation describes job control language files, job submission procedures, sample input and output files, and execution costs.

Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 1: Governing equations and static analysis of flexible beams

Abstract: In the first part of the paper we employ the Sheremetev-Pelekh-Reddy-Levinson hypotheses, which yield a non-linear mathematical model of a beam taking into account geometric and physical non-linearity as well as transverse shear based on the modified couple stress theory. The general model includes both Bernoulli-Euler and Timoshenko models with/without geometric/physical non-linearity, and the size-dependent beam behaviour. In addition, we present results of the development of the relaxation method for solution to numerous static problems. The influence of the size-dependent coefficient on the load-deflection and stress-strain states of the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson mathematical models has been also studied.

Nonlinear Model Reduction by Moment Matching

Abstract: Reduced order models, or model reduction, have been used in many technologically advanced areas to ensure the associated complicated mathematical models remain computable. For instance, reduced order models are used to simulate weather forecast models and in the design of very large scale integrated circuits and networked dynamical systems. For linear systems, the model reduction problem has been addressed from several perspectives and a comprehensive theory exists. Although many results and efforts have been made, at present there is no complete theory of model reduction for nonlinear systems or, at least, not as complete as the theory developed for linear systems. This monograph presents, in a uniform and complete fashion, moment matching techniques for nonlinear systems. This includes extensive sections on nonlinear time-delay systems; moment matching from input/output data and the limitations of the characterization of moment based on a signal generator described by differential equations. Each section is enriched with examples and is concluded with extensive bibliographical notes. This monograph provides a comprehensive and accessible introduction into model reduction for researchers and students working on non-linear systems.

On the new soliton and optical wave structures to some nonlinear evolution equations

Abstract: In this study, with the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is utilized to search for the solutions to some important nonlinear mathematical models arising in nonlinear sciences, namely, the (2 + 1) -dimensional Zakharov-Kuznetsov modified equal width equation, the cubic Boussinesq equation and the modified regularized long wave equation. We successfully obtain some new soliton, singular soliton, singular periodic waves and kink-type solutions with complex hyperbolic structures to these equations. We also present the two- and three-dimensional shapes of all the solutions obtained in this study. We further give the physical meaning of all the obtained solutions. We compare our results with the existing results in the literature.

finite element modelling

Abstract: The work described in this paper represents an effort to demonstrate the validity of the hybrid approach to the analysis of structural deformation. Mathematical modelling was incorporated into the process of reducing data from a digital correlation analysis of a speckled surface. The experimental data was collected both by directly imaging the surface onto a digitizing vidicon system and by transmitting the image through a coherent optical fiber bundle. Considerable savings of time and resources can be realized through the hybrid approach and the strengths of the theoretical and experimental procedures complement each other beautifully. The final results agreed within a few percent of each other and with values obtained by another independent method (high frequency moire), demonstrating the accuracy of the procedure. Hybrid approach The idea of a hybrid approach to structural analysis is not new(1,2,3,4). Although a long history of development can be traced for engineering studies based on mathematical models (finite-difference equations, boundary value integrals, finite element models) and on experimentally obtained data (gaging, optical or acoustical metrology), each method has well known limitations. Mathematical studies depend on the correspondence between some abstract model undergoing specified affects and a real structure subjected to a complex of interacting forces. A detailed model quickly becomes very large and mathematically complex, placing large burdens on the computational and financial resources of the designer. Also, the validity of the results depends on how well boundary conditions have been incorporated into the model. On the other hand, direct experimental methods of analysis often depend on only a few data values, measured at isolated points on the structure. The obtaining of this data for certain critical regions may be difficult or dangerous (complex structures, inaccessible locations, hazardous environments). In such cases, the surface can be illuminated by an incoherent fiber optic bundle and the image transmitted back through a coherent fiber optic bundle to a remote analyzing system. The hybrid method is an attempt to take advantage of the strengths of these two approaches, while minimizing their weaknesses. Basically, the idea is to drastically reduce the finite element mesh required and to incorporate real measured values instead of generalized boundary conditions. Speckle metrology

Performance evaluation of coherent Ising machines against classical neural networks

Abstract: The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators and a field programmable gate array circuit. The similar mathematical models were proposed three decades ago by Hopfield et al in the context of classical neural networks. In this article, we compare the computational performance of both models.

Standing waves for a coupled nonlinear Hartree equations with nonlocal interaction

Abstract: Standing wave solutions of coupled nonlinear Hartree equations with nonlocal interaction are considered. Such systems arises from mathematical models in Bose–Einstein condensates theory and nonlinear optics. The existence and non-existence of positive ground state solutions are proved under optimal conditions on parameters, and various qualitative properties of ground state solutions are shown. The uniqueness of the positive solution or the positive ground state solution are also obtained in some cases.

Mathematical models for dispersive electromagnetic waves: An overview

Abstract: In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is devoted to the notions of non-dissipativity and passivity. We consider successively the cases of so-called local media and then of general passive media. The models are studied through energy techniques, spectral theory and dispersion analysis of plane waves. For making the article self-contained, we provide in appendix some useful mathematical background.

Nonlinear-Adaptive Mathematical System Identification

Abstract: By reversing paradigms that normally utilize mathematical models as the basis for nonlinear adaptive controllers, this article describes using the controller to serve as a novel computational approach for mathematical system identification. System identification usually begins with the dynamics, and then seeks to parameterize the mathematical model in an optimization relationship that produces estimates of the parameters that minimize a designated cost function. The proposed methodology uses a DC motor with a minimum-phase mathematical model controlled by a self-tuning regulator without model pole cancelation. The normal system identification process is briefly articulated by parameterizing the system for least squares estimation that includes an allowance for exponential forgetting to deal with time-varying plants. Next, towards the proposed approach, the Diophantine equation is derived for an indirect self-tuner where feedforward and feedback controls are both parameterized in terms of the motor’s math model. As the controller seeks to nullify tracking errors, the assumed plant parameters are adapted and quickly converge on the correct parameters of the motor’s math model. Next, a more challenging non-minimum phase system is investigated, and the earlier implemented technique is modified utilizing a direct self-tuner with an increased pole excess. The nominal method experiences control chattering (an undesirable characteristic that could potentially damage the motor during testing), while the increased pole excess eliminates the control chattering, yet maintains effective mathematical system identification. This novel approach permits algorithms normally used for control to instead be used effectively for mathematical system identification.

Mathematical Model of Shock-Train Path with Complex Background Waves

Abstract: The existence of the complex compression and expansion waves in an isolator induces a special motion path of the shock train. Numerical simulations with two different inlet models are conducted. The results indicate that the local parameters govern the shock train’s motion, and the pressure gradient along the surface plays an extremely important role. The shock train’s location is determined by the entrance condition and backpressure, whereas it is the parameter along the surface that determines its path. The start and end positions of the rapid forward motion are located where the pressure gradient approaches zero. Streamwise parameters and the surface pressure gradient are introduced in Waltrup and Billig’s (“Structure of ShockWaves in Cylindrical Ducts,” AIAA Journal, Vol. 11, No. 10, 1973, pp. 1404–1408) empirical correlation to characterize the rapid forward motion. Then, a mathematical model is established based on Billig’s correlation and surface pressure datasets in the current paper.

Modeling the behavior of FRP-confined concrete using dynamic harmony search algorithm

Abstract: The accurate prediction of ultimate conditions for fiber reinforced polymer (FRP)-confined concrete is essential for the reliable structural analysis and design of resulting structural members. Nonlinear mathematical models can be used for accurate calibration of strength and strain enhancement ratios of FRP-confined concrete. In this paper, a new procedure is proposed to calibrate the nonlinear mathematical functions, which involved the use of a dynamic harmony search (DHS) algorithm. The harmony memory is dynamically adjusted based on a novel pitch generation scheme using a dynamic bandwidth and random number with normal standard distribution in DHS. A new design-oriented confinement model is proposed based on three influential factors of FRP area ratio ($$ \rho_{a} $$źa), lateral confinement stiffness ratio ($$ \rho_{E} $$źE), and strain ratio ($$ \rho_{\varepsilon } $$źź). Five nonlinear mathematical design-oriented models are regressed on approximately 1000 axial compression tests of FRP-confined concrete in circular sections based on the proposed DHS algorithm. The proposed models for the prediction of the ultimate axial stress and strain of FRP-confined concrete are compared with the existing models. It has been shown that the DHS algorithm offers the best performance in terms of both accuracy and fast convergence rate in comparison with the other modified versions of harmony search algorithms for optimization problems. The proposed design-oriented model provides improved accuracy over the existing models.

Mathematical models for estimating the degree of influence of major factors on performance and accuracy of coordinate measuring machines

Abstract: Increased productivity of Coordinate Measuring Machines, while providing given level of accuracy, is complex and actual problem of robotics and metrology. Therefore, this article provides a set of mathematical models that allow for prediction of values for performance and accuracy of advanced Coordinate Measuring Machines based on system dynamics method. The analysis of scientific literature and statistical data of exploitation CMMs Global Performance (DEA, Italy), CMM-750 (Lapik, Russia), FARO Arm 9 (FARO Technologies, USA) has identified 25 major factors of the process control and their mutual impact. Of the 16 basic factors are internal system parameters, 6 input actions and 3 external factors. As a result of the system analysis of the research object identifies the main characteristics of coordinate measuring machines that affect performance and measurement accuracy. We have done a general graph of causal relationships between modeled characteristics, on the basis of which is made up and numerically solved a system of nonlinear differential equations. In developing this system of equations is used in statistical data describing the cause-effect relationship between the internal model parameters and environmental factors. These solutions make it possible to practically interpret developed models and methods of system dynamics used in solving the problem.

Comparison of Thermal Performance Equations in Describing Temperature-Dependent Developmental Rates of Insects: (II) Two Thermodynamic Models

Abstract: There are many descriptive statistical models describing the temperature-dependent developmental rates of insects without derivation of biophysical processes; thus, it is difficult to explain how temperature affects development from the thermodynamic mechanisms. Fortunately, two mathematical models (the Sharpe–Schoolfield–Ikemoto [SSI] model and Ratkowsky–Olley–Ross [ROR] model) based on thermodynamics have been built to explain temperature-dependent reaction rates. Despite their differences in construction, both models produce similar functions when used to describe the effect of temperature on the probability of a theoretical rate-controlling enzyme that is in its active state. However, the previous fitting method of the SSI model was unable to achieve global optimization of parameter estimates; that of the ROR model usually underestimates the maximal probability of the rate-controlling enzyme that is in its active state, as found in some empirical data sets. In the present study we improved the fitting methods for these two models. We then used these two models to fit 10 data sets from published references. We found the models based on the improved fitting methods agree with the empirical data well and predict that the maximal probabilities of the rate-controlling enzyme that is in its active state are close to 1. The SSI model produces a slightly better goodness-of-fit value for the model than the ROR model, whereas the latter predicts a more symmetrical curve for the probability of the rate-controlling enzyme that is in its active state. If thermodynamic parameters of two or more different species are to be compared, we recommend that researchers use one or the other of these two models and follow the same fitting methods for all species.