Mathematical modelling and parameter optimization of pulsating heat pipes

Proper heat transfer management is important to key electronic components in microelectronic applications. Pulsating heat pipes (PHP) can be an efficient solution to such heat transfer problems. However, mathematical modelling of a PHP system is still very challenging, due to the complexity and multiphysics nature of the system. In this work, we present a simplified, two-phase heat transfer model, and our analysis shows that it can make good predictions about startup characteristics. Furthermore, by considering parameter estimation as a nonlinear constrained optimization problem, we have used the firefly algorithm to find parameter estimates efficiently. We have also demonstrated that it is possible to obtain good estimates of key parameters using very limited experimental data.     

Mathematical modelling and optimisation of a waste water treatment plant by combined oxygen electrode and biological waste water treatment model

Structured mathematical models of oxygen electrode and biological waste water treatment were combined to optimise the position of electrode in the bioreactor. Parameters sensibility testing of mathematical model has shown that the model was most sensitive to the change of these parameters (in decreasing order of significance): oxygen consumption per unit of BOD_5, specific consumption rate of adsorbed BOD₅, volumetric coefficient of oxygen transfer rate (k_La), and waste water inflow. Two positions of electrode were tested: in the bioreactor and in the bioreactors syphon outlet shaft. Results obtained for the exchange of the oxic/anoxic phase and sludge recycling plant indicated that a reduction of electrical power for the aeration could be achieved if O₂ electrode is placed in the bioreactor tank, compared to position in outlet shaft. Better positioning of electrode has resulted in shortening of the oxic/anoxic cycle by 13% and the daily working time of aerators for 0.5 h per day, respectively. In the same time, the number of oxic/anoxic cycles per day was increased by 29%. In addition, results obtained by mathematical modelling indicated no debasement of chemical composition in out coming purified water if new position will be used.     

Mathematical modelling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint

In this study, mathematical modelling and dynamic response of a flexible robot manipulator with rotating-prismatic joint are investigated. The tip end of the flexible robot manipulator traces a multi-straight-line path under the action of an external driving torque and an axial force. Considered robot manipulator consists of a rotating prismatic joint and a sliding flexible arm with a tip mass. Flexible arm is assumed to be an Euler–Bernoulli beam carrying an end-mass. Equations of motion of the flexible manipulator are obtained by using Lagrange’s equation of motion. Effect of rotary inertia, axial shortening and gravitation is considered in the analysis. Equations of motion are solved by using fourth order Runge–Kutta method. Numerical simulations obtained by using a developed computer program are presented and physical trend of the results are discussed.     

Mathematical modelling,analysis and numerical simulations for the influence of heat shock proteins on tumour invasion

Invasion is a key property of tumour cells for building metastasis. A class of functionally related proteins called heat shock proteins (HSPs), the expression of which is increased when cells are exposed to elevated temperatures or other stress, play an important role in the invasion. In this paper we develop a mathematical model focusing on the effect of HSPs on the tumour cell migration. The resulting multiscale setting accounts both for the microscopic, intracellular level on which these proteins are acting and for the macroscopic level of the cell population. We prove the local existence of a unique positive solution and perform numerical simulations in order to illustrate the behaviour of cancer cells w.r.t. the fibre density of the tissue and the matrix degrading enzymes, along with the effect of HSPs.     

The Edinburgh Mathematical Laboratory and Edmund Taylor Whittaker's role in the early development of numerical analysis in Britain

In 1912, Edmund Taylor Whittaker (1873–1956) was appointed to the Chair of Mathematics at the University of Edinburgh. The following year he opened the Edinburgh Mathematical Laboratory. The purpose of the Laboratory was practical instruction in topics which are now classed together as numerical analysis.In this article I explore the inspiration, purpose, and impact of the Laboratory in the context of early 20th century British applied mathematics.     

Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.     

Estimations of trout density and biomass: a neural networks approach

In this paper, we report the use of artificial neural networks to predict the density and biomass of trout in the Pyrenees mountains from 8 physical parameters of the environment. The results obtained with a three-layered neural network are presented. Studies have been undertaken with 1 or 4 variables in the output layer of the network. Results on the test set (generalization of models) are satisfactory with determination coefficients R² exceeding 0.76.     

半导体与超晶格的数学模型及其分析Ⅰ:模型

本文论及半导体与超晶格的数学模型方法的一些新近发展动态。介绍了半导体与超晶格的一些背景材料并给出了半导体宏观模型间的层次框架。超晶格中载流子传输的SHE扩散模型也被观察。     

Statistical inference and modelling of momentum in stock prices

The following results are obtained, (i) It is possible to obtain a time series of market data {y(t)} in which the fluctuations in fundamental value have been compensated for. An objective test of the efficient market hypothesis (EMH), which would predict random correlations about a constant value, is thereby possible, (ii) A time series procedure can be used to determine the extent to which the differences in the data and the moving averages are significant. This provides a model of the form y(t)-y(t-l)=0.5{y(t- l)-y(t-2)}+ε(t)+0.8ε(r-1) where ε(t) is the error at time t, and the coefficients 0.5 and 0.8 are determined from the data. One concludes that today's price is not a random perturbation from yesterday's; rather, yesterday's rate of change is a significant predictor of today's rate of change. This confirms the concept of momentum that is crucial to market participants. (iii) The model provides out-of-sample predictions that can be tested statistically. (iv) The model and coefficients obtained in this way can be used to make predictions on laboratory experiments to establish an objective and quantitative link between the experiments and the market data. These methods circumvent the central difficulty in testing market data, namely, that changes in fundamentals obscure intrinsic trends and autocorrelations. This procedure is implemented by considering the ratio of two similar funds (Germany and Future Germany) with the same manager and performing a set of statistical tests that have excluded fluctuations in fundamental factors. For the entire data of the first 1149 days beginning with the introduction of the latter fund, a standard runs test indicates that the data is 29 standard deviations away from that which would be expected under a hypothesis of random fluctuations about the fundamental value. This and other tests provide strong evidence against the efficient market hypothesis and in favour of autocorrelations in the data. An ARIMA time series finds strong evidence (9.6 and 21.6 standard deviations in the two coefficients) that the data is described by a model that involves the first difference, indicating that momentum is the significant factor. The first quarter's data is used to make out-of-sample predictions for the second quarter with results that are significant to 3 standard deviations. Finally, the ARIMA model and coefficients are used to make predictions on laboratory experiments of Porter and Smith in which the intrinsic value is clear. The model's forecasts are decidedly more accurate than that of the null hypothesis of random fluctuations about the fundamental value.     

Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.     

Mathematical modeling and numerical simulation of yarn behavior in a modified ring spinning system

In the paper, yarn dynamical behavior and twist distribution in a modified ring spinning system are investigated. Equations of motion and twist wave propagation are used to obtain the numerical solutions of yarn path, yarn tension and twist distribution in steady state. It is observed that yarn path in the twisting zone has several classic modes corresponding to the yarn tension, and all of the yarn paths are approximately planar curves rather than spatial curves. The angular velocities of yarn at the twisting device are given as well as the twist of yarn in the modified ring spinning system. Experiments are conducted to evaluate the yarn paths and twist distributions under consideration. The theoretical and experimental results have a good agreement.     

Boundary-value problem with moving bounds and dynamic boundary conditions: Diffusion peak of TDS-spectrum of dehydriding

In this paper, we present the boundary-value problem with moving bounds and dynamic boundary conditions that models the kinetics of hydrogen desorption from hydrides of metals. Phase change, desorption processes on the surface, size reduction, and heat absorption on the phase bound are taken into consideration. Computational algorithm based on difference approximations is developed. The results of numerical modeling are presented.     

Efficient numerical algorithm for solving the gravimetry problem of finding a lateral density in a layer: Parallel implementation

The paper is devoted to developing the new time- and memory-efficient algorithm BiCGSTABmem for solving the inverse gravimetry problem of determination of a variable density in a layer using the gravitational data. The problem is in solving the linear Fredholm integral equation of the first kind. After discretization of the domain and approximation of the integral operator, this problem is reduced to solving a large system of linear algebraic equations. It is shown that the matrix of coefficients is the Toeplitz-block-Toeplitz one in the case of the horizontal layer. For calculating and storing the elements of this matrix, we construct an efficient method, which significantly reduces the required memory and time. For the case of the curvilinear layer, we construct a method for approximating the parts of the matrix by a Toeplitz-block-Toeplitz one. This allows us to exploit the same efficient method for storing and processing the coefficient matrix in the case of a curvilinear layer. To solve the system of linear equations, we constructed the parallel algorithm on the basis of the stabilized biconjugated gradient method with using the Toeplitz-block-Toeplitz structure of the matrix. We implemented the BiCGSTAB and BiCGSTABmem algorithms for the Uran cluster supercomputer using the hybrid MPI + OpenMP technology. A model problem with synthetic data was solved for a large grid. It was shown that the new BiCGSTABmem algorithm reduces the computation time in comparison with the BiCGSTAB. Scalability of the parallel algorithm was studied.     

Estimating generalized state density of near-extreme events and its applications in analyzing stock data

This paper studies the generalized state density (GDOS) of near-historical extreme events of a set of independent and identically distributed (i.i.d.) random variables. The generalized density of states is proposed which is defined as a probability density function (p.d.f.). For the underlying distribution in the domain of attraction of the three well-known extreme value distribution families, we show the approximate form of the mean GDOS. Estimates of the mean GDOS are presented when the underlying distribution is unknown and the sample size is sufficiently large. Some simulations have been performed, which are found to agree with the theoretical results. The closing price data of the Dow-Jones industrial index are used to illustrate the obtained results.     

Loss data analysis: Analysis of the sample dependence in density reconstruction by maxentropic methods

The problem of determining probability densities of positive random variables from empirical data is important in many fields, in particular in insurance and risk analysis. The method of maximum entropy has proven to be a powerful tool to determine probability densities from a few values of its Laplace transform. This is so even when the amount of data to compute numerically the Laplace transform is small. But in this case, the variability of the reconstruction due to the sample variability in the available data can lead to quite different results. It is the purpose of this note to quantify as much as possible the variability of the densities reconstructed by means of two maxentropic methods: the standard maximum entropy method and its extension to incorporate data with errors.The issues that we consider are of special interest for the advanced measurement approach in operational risk, which is based on loss data analysis to determine regulatory capital, as well as to determine the loss distribution of risks that occur with low frequency.     

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton–Jacobi–Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka–Volterra models are provided to show the effectiveness of this method.     

Unsteady motion of a spherical bubble in a complex fluid: Mathematical modelling and simulation

The nonlinear response of an oscillatory bubble in a complex fluid is studied. The bubble is immersed in a Newtonian liquid, which may have a dilute volume fraction of anisotropic additives such as fibers or few ppm of macromolecules. The constitutive equation for the fluid is based on a Maxwell model with an extensional viscosity for the viscous contribution. The model is considered new in the study of bubble dynamics in complex fluids. The numerical computation solves a system of three first order ordinary differential equations, including the one associated with the solution of the convolution integral, using a fifth order Runge–Kutta scheme with appropriated time steps. Asymptotic solutions of governing equation are developed for small values of the pressure forcing amplitude and for small values of the elastic parameter. A study of the bubble collapse radius is also presented. We compare the results predicted by our model with other model in the literature and a good agreement is observed. The calculated asymptotic solutions are also used to test the results of the numerical simulations. In addition, the orientation of the additives is considered. The angular probability density function is assumed to be a normal distribution. The results show that the model based on the fully aligned additives with the radial direction overestimates the tendency of the additives to stabilize the bubble motion, since the effect of extensional viscosity occurs due to the particle resistance to the movement throughout its longitudinal direction.     

Dynamic process scheduling and resource allocation in distributed environment: an agent-based modelling and simulation

This paper addresses the issues concerning resource allocation and process scheduling in a dynamic environment, where resources are distributed and availability of them is uncertain. In this context, we introduce a new multi-agent-based resource allocation and process scheduling approach, where agents communicate and cooperate among themselves to produce an optimal schedule. A distributed constraint optimization problem-based model in accordance with Markov Decision Process is proposed in this regard. We overcome the hardship of existing centralized approach and our technique optimizes not only the process completion delay but also the number of resources being idle, which is much more beneficial. Apart from the theoretical approach, we take a case study in its practical application domain to validate our claim. Analysis and experimental results show that this proposed method outperforms the state-of-the-art methods and bridges the gap between theory and its applications.