Model Of Equations Research Articles

Element Free Galerkin (EFG) Formulation in Solving Kinematic Wave Equation for Hydrological Modelling

Meshfree methods such as Element Free Galerkin Method (EFG) are the cutting edge of numerical methods as it does not require user to perform meshing which often is time consuming and tedious. The method being "meshfree" for the user can theoretically generate more accurate models which follow more complex boundary conditions such as natural rivers etc. The time saving and potential of higher accuracy in modelling makes EFG formulation an interesting research topic. EFG formulation is used to solve kinematic wave equations which is detailed in this paper. Galerkin weighted residual method using EFG’s shape function parameters is used to discretize the partial differential equation (PDE) of kinematic wave equations. To discretize the equations, a forward difference scheme is used for temporal discretization and Picard direct substitution method is employed to solve the nonlinear system at each time step. The formulations are validated by making a comparison between well-established numerical techniques against actual recorded datasets. After which it is found that EFG method agrees with conventional established techniques, thus validating the formulations as useful. To further investigate the usefulness of this formulation, an optimal performance study was also conducted to determine the most optimal shape function parameters. The optimal shape function values improved the performance to where it was found that established methods such as FDM were surpassed and on par with FEM. This shows that EFG is a good alternative for hydrological modelling.

Estimation of River Discharge Outside the Regime of Uniform Flow

The flow discharge computation is based on assumptions about the energy grade line slope and the water level to estimate the stream flow with the hydraulic model of Manning's equation. The purpose of this paper is to improve the river discharge prediction using a modified practical Manning's equation for non-uniform but also for uniform flow conditions by using free surface slope, bed slope, friction coefficient and the flow depth. This paper presents an improvement in the integration of the average velocity in gradually varied flows. To validate the modified equation, experimentations have been carried out in the hydraulic laboratory of Ain Temouchent University (Algeria) for 23 flow discharges through two measurement sections; we have got 46 values of the average velocity, the bed slope and free surface slope. The results compare very well with the experimentations. A very good agreement has been found between measured and computed velocities with a coefficient of determination R2 (97.91% for section A and 99.45% for Section B) with the normalized RMSE low than 2.4%. This could be a very useful contribution for the literature. No closer-form of this modified Manning equation is available in the literature.

Methodology of the PEM FC Gas Diffusion Layer Permeability Determination and Its Description Related to the Fuel Cell Flow Field Design

Hydrogen fuel cells represent an important part of the new energy scheme for low emission society. Development of the more efficient, durable and energy dense systems requires precise information on the numerous aspects, especially on the local distribution of physio-chemical quantities inside the fuel cells stacks. It is extremely difficult to obtain such information experimentally. Therefore, the mathematical modelling represents a feasible alternative. It offers an efficient and versatile way for the acquisition of required information. Accuracy of mathematical model, however, is primarily determined by the accuracy and reliability of the experimental data available. In this particular case, permeability of gas diffusion layer for reactants and products is of interest. Permeability values in porous environment are available experimentally. It is, however, important to keep in mind that permeability value is strongly dependent on the material porosity and thus on a degree of its compression inside the stack. Therefore, permeability value is varying with position over the electrode. Suitable approach, making possible to describe smoothly variation of the gas diffusion layer permeability with degree of its compression, is desirable. Traditional approach is to use corresponding semi-empirical equations. It is a purpose of this work to verify applicability of the Kozeny-Carman equation for this particular case and thus to fill in this gap in the current knowledge.Prior the experimental validation of the Kozeny-Carman equation accuracy, methodology of obtaining sufficiently accurate permeability data needs to be developed. In the first step of this process, permeability cells were designed, characterized by the homogeneous gas flow distribution in the channel, used for positioning of the gas diffusion layer sample, to be characterized. A special attention was paid to the absence of any turbulence domains close to the pressure reading ports, which could cause potential error in the observed pressure values. The figure provided documents results of the cell geometry optimization. Mathematical model calculated gas stream lines shown document fulfilling above stated conditions and thus ensuring reliability of the experimental data obtained. The cell lid determined the channel height itself. A series of lids was produced, allowing study of gas diffusion layers permeability at the different degrees of compression, i.e. porosities. The channel depth accuracy was required to be within tolerance of 2 mm. Pressure drop on the channel was determined by varying the streaming gas flow rate. Hydrogen and nitrogen (simulating air) were used as a test gasses. Permeability of gas diffusion layers were determined based on pressure drops using Darcy’s law. This set of data allowed comparing experimental data with Kozeny-Carman equation behavior. The agreement obtained was sufficient to justify the usage of this type of semi-empirical equation for the flow field mathematical modelling. Corresponding conclusion was in the last step of the study verified by means of the model serpentine flow field attached at the gas diffusion layer at the different degrees of compression. Experimental data obtained have shown very good agreement with the model calculations. It can thus be concluded, that Kozeny-Carman provides sufficient approximation of the gas diffusion permeability values to be used in the mathematical models for design of fuel cells and fuel cells stacks for geometry optimization.The work was supported from European Regional Development Fund-Project "Fuel Cells with Low Platinum Content" (No. CZ.02.1.01/0.0/0.0/16_025/0007414). Figure 1

Material and Structural Functionalization of Knitted Fabrics for Sportswear.

Comfort is an important quality criterion, especially for sportswear. It influences well-being, performance and efficiency. The necessary dissipation of heat and air flow, at high metabolic rates, must be designed and planned in advance. The influence of structure, density, mass and thickness of fabric were considered as well as yarn material composition, yarn linear density, yarn evenness and yarn hairiness. The influence of the mentioned parameters on thermal properties and air permeability was calculated. From the correlation analysis, it can be concluded that yarn’s linear density, yarn short fibers hairiness, and mass per unit area of knitted fabric has the greatest impact on heat resistance. The yarn linear density, the yarn hairiness of the longer protruding fibers, and the thickness of the knitted fabric have the greatest impact on air permeability. A statistically significant model of multiple linear regression equations was offered to predict the thermal comfort of knitted fabric.

Innovation and human resources practices in companies of Southern Brazil

Purpose: The purpose of the study is to analyze the relationships between process innovation, human resources practices and the competitive advantage of organizations, through seven research hypotheses. Design/methodology/approach: The methodology used is a descriptive, quantitative study applied to 207 human resources professionals from companies in the south of Brazil, analyzed by the modeling of structural equations. Findings: The hypotheses predicted that process innovation and human resources practices would be positively related to competitive advantage, as well as process innovation would be positively correlated with human resources practices. The results confirmed the direct relationships supported by the hypotheses. Practical implications: Regarding the managerial contributions, the present study brought important information to direct the strategic actions of the companies, integrating process innovation and human resources practices to generate competitive advantage, having human resources management as an important vector for the company strategy, guiding individuals towards the companies’ objectives. Originality/value: The originality of the study consists in the construction of a theoretical framework on the relationships between process innovation, human resources practices and the competitive advantage of organizations, which can be used by other researches and thus advance in the Theory of Administration.

A mathematical model of nonlinear differential equation for controlling global dynamics of coronavirus disease 2019 (COVID-19)

In this paper, we have introduced new mathematical model of Coronavirus Disease (COVID-19) Transmission Model as a system of six nonlinear differential equations to analyze the spread and control of this latest outbreak pandemic disease. This new mathematical model is analysed with the help of optimal control analysis. The main purpose of this optimal control theory which applied to the model is to show the existence of optimal controllers for the nonlinear dynamic system. Based on the assumptions, we also studied and formulate an optimal control model for a coronavirus disease dynamic system in terms of mathematical differential equations in order to focus the effects of prevention and control measures with minimal implementation cost. Then, we established the basic reproduction number , which makes possible to check whether a prominent infectious disease will continue to spread or not in a susceptible population. The paper was also extended to assess the conditions under which the population will be free of disease. In particular, we focus to include in the mathematical model, quarantine procedure applied to both the infected individuals and to the highly risk of total population, which is expected to be useful.

Van der Pol model in two-delay differential equation representation

The Van der Pol equation is the mathematical model of a second-order ordinary differential equation with cubic nonlinearity. Several studies have been adding time delay to the Van der Pol model. In this paper, the differential equation of the Van der Pol model and the RLC (resistor–inductor–capacitor) circuit are deduced as a delay differential equation. The Van der Pol delay model contains two delays, which allows the re-use of its applications in the suggested equation. The Taylor series was used to deduce ordinary differential equations from the delay differential equations in the case of small delays. Also, the model for Parkinson's disease modification is described as the Van der Pol model. A numerical simulation of the delay differential equations has been done to show the different cases that the delay differential equations can express using the MATLAB program.

Stability of a Rectangular Shape Memory Alloy Plate during the Forward Phase Transition for Thermomechanically Coupled Statement

The stability of rectangular thin plates of Shape Memory Alloys during the forward martensitic phase transition induced by uniform cooling under constant stresses was studied. A model of the constitutive equations of Shape Memory Alloys describing phase structural deformation and taking into account thermomechanical coupling and resistance asymmetry was used. It was shown within the limits of this model that the structural deformation during the loss of stability could not occur. Analytical solutions obtained for different statements of the stability problem were compared. For some statements the curves separating the areas of stability and instability in the plane of stresses had concave parts were obtained. It was shown that increase of the plate thickness brought about rising the influence of the phase deformation on the stability loss process.

RESEARCH ON STOCHASTIC FUZZY DIFFERENTIAL EQUATIONS IN MULTIPLE BLURRED IMAGE REPAIR MODELS

This paper aims to study the processing and repairing methods of blurred images, promote the development of partial differential equations in the field of image processing, and expand the application of stochastic fuzzy differential equations in the field of image processing and repair. This study starts with a typical blurred image repair method. First, a comparative analysis of several common blurred image repair methods including Wiener filtering restoration, inverse filtering restoration, and Lucy–Richardson (L-R) filtering restoration is performed. Second, based on the linear partial differential equation learning model (LPDE), the concept of fuzzy integral is introduced, and an improved stochastic fuzzy partial differential equation learning model (SFCPDE) is proposed. The effect of the learning model before and after improvement on blurred color image processing is compared and analyzed. Finally, based on the total variation (TV) blurred image repair algorithm, an improved TV blurred image repair algorithm is proposed. The comparison and analysis of the repair effects of several blurred image repair algorithms are performed. The results show that there are obvious differences in the repairing methods with or without noise. Inverse filtering works best when there is no noise. L-R filtering has the disadvantage of amplifying noise. Compared with LDPE, the training speed of SFCPDE is significantly improved, and the training error is less than LDPE. The SFCPDE learning model performs better in the processing of blurred color images. After 10 iterations, the improved TV algorithm is significantly better than the TV algorithm and the CDD algorithm in repairing blurred images. The PSNR value of the TV algorithm and the curvature-driven diffusion (CDD) algorithm after 10 iterations corresponds to about 60% of the PSNR value of the improved algorithm. The algorithms and models of stochastic fuzzy partial differential equations proposed in this paper have great application potential in the processing and repair of multiple blurred images.

PSYCHOLOGICAL MEMORY FORGETTING MODEL USING LINEAR DIFFERENTIAL EQUATION ANALYSIS

To solve the problem of insufficient combination of neural mechanism and psychological mechanism in the study of human brain cognitive memory activity, in this exploration, the memory forgetting model in psychology is analyzed and constructed by fractional order model of linear differential equation. The study of memory in cognitive psychology is combined with the neurophysiological mechanism of memory. At the same time, for the stability of long-term memory, a long-term memory neural network model (LTMNNS) is proposed. The validity and accuracy of the model are tested by the recognition of memory eigenvectors. Numerical test and simulation results show that when the difference between any initial values of the system is not more than [Formula: see text], the corresponding system solution difference is not more than [Formula: see text] in the interval [Formula: see text]. Reasoning correctness of fractional order computation model of memory neural network is verified. The LTMNNS algorithm in this exploration guarantees a high number of completed tasks, and the average number of failed tasks is less than MemNNs, DNC and LSTM algorithm. Compared with other models, the proposed LTMNNS has better generalization ability and higher stability.

Solutions for a class of singular quasilinear equations involving critical growth in R2$\mathbb {R}^2$

AbstractUsing a variational approach, we study the existence of solutions for the following class of quasilinear Schrödinger equations: where , , is a positive potential bounded away from zero and can be “large” at infinity, the nonlinearity is allowed to satisfy the exponential critical growth with respect to the Trudinger–Moser inequality. Precisely, behaves like as for some . This model of equation has been proposed in the theory of superfluid films in plasma physics. As for as we know, this the first work involving this class of operators and singular nonlinearities with exponential critical growth. Moreover, we are able to deal with exponents .

A class of lattice Boltzmann models for the Burgers equation with variable coefficient in space and time

<abstract><p>In this paper, we study the numerical results of the Burgers equation with the variable coefficient in space and time and then put forward a lattice Boltzmann model of backward difference solution of nonlinear system. The macroscopic equation is recovered by using the Chapman-Enskog method and the direct Taylor-series expansion method. These two methods can recover the same hydrodynamic equations and analyze various nonlinear systems. In particular, it is much easier to perform error analysis by using the direct Taylor method. In this study, the two methods are used to analyze the Burgers equation with variable coefficient in space and time, the numerical results are discussed and are compared with the analytical solution. The numerical results verify the effectiveness of the model. The stability of the model ensures that we can use larger time step lengths. The improvement of lattice speed can improve the computational performance of the model, and the D1Q7 lattice performance is much better than the D1Q5 lattice performance.</p></abstract>

Linewidth Enhancement Factor Impact on Optical Feedback Mutual Coupled Quantum Dot Lasers

In this article, we numerically study and analyse the roles of linewidth enhancement factor (α) in the dynamic operation of the mutual regime of the transmitter and receiver quantum dot laser lasers supported by optical feedback. A set model of adequate rate equations describing the overall dynamics in a quantum dot system subjected to optical feedback were solved numerically. The results reveal a clear chaotic regime between the receiver and the transmitter lasers at α = 3, which is incredibly advantageous for secure optical communications and encoding decoding data transmission. Moreover, at the other value of linewidth enhancement factors, namely 2, 2.5, 3.5 and 4, the optical regime works in high synchronisation with either periodic or steady state forms.

Modeling of constrained motion

This paper presents an investigation of modeling and solving of differential equations in the study of mechanical systems with holonomic constraints. The 2D and 3D mathematical models of constrained motion are made. The structure of the models consists of nonlinear first or second order differential equations. Cases of free movement and movement with resistance are investigated. Solutions of the Cauchy problem of obtained differential equations were obtained by Runge–Kutta method.

Thermal characteristics of longitudinal fin with Fourier and non-Fourier heat transfer by Fourier sine transforms

The quest for high-performance of heat transfer components on the basis of accommodating shapes, smaller weights, lower costs and little volume has significantly diverted the industries for the enhancement of heat dissipation with variable thermal properties of fins. This manuscript proposes the fractional modeling of Fourier and non-Fourier heat transfer of longitudinal fin via non-singular fractional approach. The configuration of longitudinal fin in terms of one dimension is developed for the mathematical model of parabolic and hyperbolic heat transfer equations. By considering the Fourier and non-Fourier heat transfer from longitudinal fin, the mathematical techniques of Fourier sine and Laplace transforms have been invoked. An analytic approach is tackled for handling the governing equation through special functions for the fractionalized parabolic and hyperbolic heat transfer equations in longitudinal fin. For the sake of comparative analysis of parabolic verses hyperbolic heat conduction of fin temperature, we depicted the distinct graphical illustrations; for instance, 2-dimensional graph, bar chart, contour graphs, heat graph, 3-dimensional graphs and column graphs on for the variants of different rheological impacts of longitudinal fin.

An accurate and efficient multiscale finite-difference frequency-domain method for the scalar Helmholtz equation

Frequency-domain numerical modeling of the seismic wave equation can readily describe frequency-dependent seismic wave behaviors, yet it is computationally challenging to perform in finely discretized or large-scale geologic models. Conventional finite-difference frequency-domain (FDFD) methods for solving the Helmholtz equation usually lead to large linear systems that are difficult to solve with a direct or iterative solver. Parallel strategies and hybrid solvers can partially alleviate the computational burden by improving the performance of the linear system solver. We have developed a novel multiscale FDFD method to eventually construct a dimension-reduced linear system from the scalar Helmholtz equation based on the general framework of heterogeneous multiscale method. The methodology associated with multiscale basis functions in the multiscale finite-element method is applied to the local microscale problems of this multiscale FDFD method. Solved from frequency- and medium-dependent local Helmholtz problems, these multiscale basis functions capture fine-scale medium heterogeneities and are finally incorporated into the dimension-reduced linear system by a coupling of scalar Helmholtz problem solutions at two scales. We use several highly heterogeneous models to verify the performance in terms of the accuracy, efficiency, and memory cost of our multiscale method. The results indicate that our new method can solve the scalar Helmholtz equation in complicated models with high accuracy and quite low time and memory costs compared to the conventional FDFD methods.

Mathematical Analysis of a Diarrhoea Model in the Presence of Vaccination and Treatment Waves with Sensitivity Analysis


 
 
 In this study, the diarrhoea model is developed based on basic mathematical modelling techniques leading to a system (five compartmental model) of ordinary differential equations (ODEs). Mathematical analysis of the model is then carried out on the uniqueness and existence of the model to know the region where the model is epidemiologically feasible. The equilibrium points of the model and the stability of the disease-free state were also derived by finding the reproduction number. We then progressed to running a global sensitivity analysis on the reproduction number with respect to all the parameters in it, and four (4) parameters were found sensitive. The work was concluded with numerical simulations on Maple 18 using Runge-Kutta method of order four (4) where the values of six (6) parameters present in the model were each varied successively while all other parameters were held constant so as to know the behaviour and effect of the varied parameter on how diarrhoea spreads in the population. The results from the sensitivity analysis and simulations were found to be in sync.
 
 

ORGANIZATIONAL AND FINANCIAL DETERMINANTS OF THE INNOVATIVE COMPONENT OF THE COUNTRY’S COMPETITIVENESS

Abstract. The article identifies the impact of sources of funding for innovation in the country on economic growth through economic and mathematical modeling and construction of regression equations between GDP and funding for innovation and research costs with the construction of a multifactor regression equation. As a result of regression analysis, it was found that the most significant impact on the resulting indicator have such variables as capital investment from state and local budgets and research and development costs. Using the method of extrapolation, GDP growth was forecast for 4 years, and it was found that capital investment from own funds of enterprises and organizations will grow by 24,08%, capital investment from state and local budgets by 28,42%, research costs and development by 22,76% for the analyzed period.Subject to compliance with the projected values of the financial determinants of the innovative component of increasing the country’s competitiveness, the volume of estimated GDP in actual prices for the forecast period will increase by 936039,011 million UAH or 23,26%. The reasons for the low level of the state of the innovation sphere in the domestic economy are outlined: underdevelopment of the market of innovative products due to low indicators of development of integration processes in it; weakness of relations that determine the innovative nature of economic development; low motivation of the industrial sector in innovative development; the supply of technological innovations created by national industrial companies and research institutions in the domestic market is limited; high cost of development and implementation, high interest rates on the investment portfolio, a long payback period, the focus of financial institutions on the issuance of «short loans», usually consumer loans for technological renewal of industrial sectors. To resolve such contradictions, the system-forming factors of a set of measures to intensify integration processes in the innovation sphere of Ukraine were proposed. Systematized foreign experience in scientific, technical and innovation policy, as well as commercialization of innovations, taking into account which proposed conceptual guidelines for organizational and financial support of the effectiveness of the innovative component of competitiveness: economic mechanisms (direct budget investments; preferential lending; integration with foreign institutions; financial activities; increase the share of GDP aimed at financing innovation processes, development of an effective set of measures to attract international grants and household savings as investments to implement the concept of innovative development of the country’s economy, etc.); organizational mechanisms (formation of integration clusters using the potential of education, business, government, public; state assistance in the development of innovation infrastructure, etc.). Keywords:innovations, financial support of innovative development, country competitiveness, innovation system, cluster, regression, correlation, integration processes. JEL Classification O11, O19, O16, O33, E62, F20 Formulas: 1; fig.: 5; tabl.: 3; bibl.: 12.

Epidemic prediction of dengue fever based on vector compartment model and Markov chain Monte Carlo method

BackgroundDengue epidemics is affected by vector-human interactive dynamics. Infectious disease prevention and control emphasize the timing intervention at the right diffusion phase. In such a way, control measures can be cost-effective, and epidemic incidents can be controlled before devastated consequence occurs. However, timing relations between a measurable signal and the onset of the pandemic are complex to be discovered, and the typical lag period regression is difficult to capture in these complex relations. This study investigates the dynamic diffusion pattern of the disease in terms of a probability distribution. We estimate the parameters of an epidemic compartment model with the cross-infection of patients and mosquitoes in various infection cycles. We comprehensively study the incorporated meteorological and mosquito factors that may affect the epidemic of dengue fever to predict dengue fever epidemics.ResultsWe develop a dual-parameter estimation algorithm for a composite model of the partial differential equations for vector-susceptible-infectious-recovered with exogeneity compartment model, Markov chain Montel Carlo method, and boundary element method to evaluate the epidemic periodicity under the effect of environmental factors of dengue fever, given the time series data of 2000–2016 from three cities with a population of 4.7 million. The established computer model of “energy accumulation-delayed diffusion-epidemics” is proven to be effective to predict the future trend of reported and unreported infected incidents. Our artificial intelligent algorithm can inform the authority to cease the larvae at the highest vector infection time. We find that the estimated dengue report rate is about 20%, which is close to the number of official announcements, and the percentage of infected vectors increases exponentially yearly. We suggest that the executive authorities should seriously consider the accumulated effect among infected populations. This established epidemic prediction model of dengue fever can be used to simulate and evaluate the best time to prevent and control dengue fever.ConclusionsGiven our developed model, government epidemic prevention teams can apply this platform before they physically carry out the prevention work. The optimal suggestions from these models can be promptly accommodated when real-time data have been continuously corrected from clinics and related agents.

Denoising of Tourist Street Scene Image Based on ROF Model of Second-Order Partial Differential Equation

The noise pollution in tourist street view images is caused by various reasons. A major challenge that researchers have been facing is to find a way to effectively remove noise. Although in the past few decades people have proposed many methods of denoising tourist street scene images, the research on denoising technology of tourist street scene images is still not outdated. There is no doubt that it has become a basic and important research topic in the field of digital image processing. The evolutionary diffusion method based on partial differential equations is helpful to improve the quality of noisy tourist street scene images. This method can process tourist street scene images according to people’s expected diffusion behavior. The adaptive total variation model proposed in this paper is improved on the basis of the total variation model and the Gaussian thermal diffusion model. We analyze the classic variational PDE-based denoising model and get a unified variational PDE energy functional model. We also give a detailed analysis of the diffusion performance of the total variational model and then propose an adaptive total variational diffusion model. By improving the diffusion coefficient and introducing a curvature operator that can distinguish details such as edges, it can effectively denoise the tourist street scene image, and it also has a good effect on avoiding the step effect. Through the improvement of the ROF model, the loyalty term and regular term of the model are parameterized, the adaptive total variation denoising model of this paper is established, and a detailed analysis is carried out. The experimental results show that compared with some traditional denoising models, the model in this paper can effectively suppress the step effect in the denoising process, while protecting the texture details of the edge area of the tourist street scene image. In addition, the model in this paper is superior to traditional denoising models in terms of denoising performance and texture structure protection.