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• The mathematical model on the grounding resistance of the vertical electrode is proposed. • Accuracy of the mathematical model is proved by computer simulation analysis and the field measurement examination in this paper. • The mathematical model can be used in the design of vertical grounding electrode effectively. In this paper, a mathematical model on the grounding resistance of vertical electrode is proposed. The proposed mathematical model is modeled with consideration of the effects of parameters such as the length and diameter of vertical electrode, the soil resistivity and the embedding depth. This mathematical model can be applied effectively to the design of grounding system using vertical electrode in harmonious soil with the resistivity values less than 900Ω∙m. The accuracy of proposed model is proved by the simulation analysis and measurement examination of the electric field in this paper. [ABSTRACT FROM AUTHOR]

• The article proposes a new mathematical model of the inductive displacement sensor. • The model uses composite functions and a multi-objective optimization algorithm to design the coil structure parameters of the sensor. • The model aims to improve the sensor's linearity and sensitivity. • The new design method is verified by numerical simulation and physical experiments. This paper proposes a novel mathematical model that has high accuracy based on a multi-objective optimization algorithm for the inductive displacement sensors, which is popular in industrial production due to their simple design and reliable performance. The proposed model uses composite functions to establish the structural parameters of the coil winding. The non-dominated sorting genetic algorithm II (NSGA-II) is used to solve a series of non-dominated problems related to the coil structure parameters with the goal of achieving superior sensor performance. Density clustering sorting is used to select the desired non-dominated solutions. The designed sensor has a nonlinearity of 0.16%, and numerical simulations and physical experiments confirm the effectiveness of the new design method. [ABSTRACT FROM AUTHOR]

The rotor profile is one of the key factors for improving the performance of the Roots vacuum pump. A novel elliptical rotor profile consisting of the elliptical arc and its conjugate curve is proposed in this paper. The mathematical model of the elliptical rotor profile is established, and profile equations without incurring undercutting and carryover are derived. The elliptical rotor profile is tested using six Roots rotors, including five new elliptical rotors and one conventional circular arc rotor. Additionally, to assess the performance of the elliptical rotor profile, three-dimensional numerical simulations of the above six Roots rotors are conducted, and then the working process of the Roots vacuum pump is analyzed. The results indicate that all the new designs produce higher flow rate than the traditional circular rotor under the same conditions. As the elliptical axial ratio decreases, the area efficiency of the elliptical rotor increases. [ABSTRACT FROM AUTHOR]

This paper presents the mathematical modeling of a liquid-to-water heat pump with scroll compressor, brazed plate heat exchangers, additionally built-in liquid-vapor heat exchanger (LVHX) and a desuperheater for domestic hot water (DHW) production. The refrigerant is the zeotropic mixture R407C and the liquid used in the outdoor loop is a propylene-glycol water mixture. Developed mathematical model is validated on experimental data and used as a tool for the heat pump analysis. Simulation results are obtained for the effect of the degree of superheat at the evaporator outlet, the subcooling degree at the condenser outlet, the effect of using or not the LVHX and the effect of using or not the desuperheater for DHW for typical operating conditions of liquid-to-water heat pumps (EN-14,511-2, 2011) in the cooling and heating modes (low and medium temperature applications). Results show that the effect of the degree of superheat or the decision on the suitability of using or not a LVHX may be different for heat pumps that include or not a desuperheater for DHW. In particular, if DHW is a priority, the use of a LVHX is recommended because it leads to higher COP (or EER) values as well as to higher DHW heating powers. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study of heat and mass transfer in counter-flow indirect evaporative air coolers is presented using an approach proposed by previous work. The mathematical model equations of continuity, momentum, energy and concentration are solved by the finite volume method to obtain the value of primary outlet dimensionless temperature. This mathematical model developed is validated against published data acquired from literature. The key target of presented analysis is to develop a performance correlation based on five dimensionless factors: ratio of channel length to half width of secondary air channel, ratio of water to secondary air mass flow rate, primary air inlet Reynolds number, secondary air inlet dimensionless temperature and water film inlet dimensionless temperature. Numerical simulations are performed by changing the value of each dimensionless factor under a constant value for other parameters. The simulation results are regressed to obtain the empirical constants of the correlation. The value of outlet dimensionless temperature is varied from 0.47 to 0.92. The developed correlation can predict the performance of the counter-flow indirect evaporative air coolers within a discrepancy of 12.6%. The correlation would be helpful to provide a simpler equation to improve the calculation speed within the engineering allowable accuracy range. [ABSTRACT FROM AUTHOR]

Precision in computations is a considerable challenge to adequately addressing many current scientific or engineering problems. The way in which the numbers are represented constitutes the first step to compute them and determines the validity of the results. The aim of this research is to provide a formal framework and a set of computational primitives to address high precision problems of mathematical calculation in engineering and numerical simulation. The main contribution of this research is a mathematical model to build an exact arithmetical unit able to represent without error rational numbers in positional notation system. The functions under consideration are addition and multiplication because they form an algebraic commutative ring which contains a multiplicative inverse for every non-zero element. This paper reviews other specialized arithmetic units based on existing formats to show ways to make high precision computing. It is proposed a formal framework of the whole arithmetic architecture in which the operators are based. Then, the design of the addition operation is detailed and its hardware implementation is described. Finally, extensive evaluation of this operator is performed to prove its ability for exact processing. [ABSTRACT FROM AUTHOR]

• The mathematical model is useful for analyzing the heat exchanger performance. • The most probable variant of heat exchanger operation is established. • There is a risk of frost accumulation within the fixed-bed regenerator. The paper describes an original mathematical model of heat and mass transfer for a fixed bed regenerator used to determine the effect of internal airflow leakage on heat exchanger efficiency. First, the build and operating principles of a fixed-bed heat exchanger were discussed. The presence of internal leakage was shown along with a proposed solution for its elimination. Then, a mathematical model based on a modified ε-NTU method for numerical simulation and analysis of coupled heat and mass transfer in a fixed-bed heat exchanger was presented. The model was supplemented with an additional detailed submodel designed to determine frost surface temperature and frost growth analysis. Initial numerical simulations of the operation of the model were performed for low outdoor air temperature conditions. Different zones of heat and mass transfer within the regenerator matrix were distinguished. The presence of accumulated frost area and its influence on the course of heat and mass transfer processes was revealed. In addition, the presence of a relative humidity limit curve associated with a mass balance deficiency conditioning the occurrence of frost accumulation was established. [ABSTRACT FROM AUTHOR]

The paper is focuses on the numerical simulation and analysis of coupled heat and mass transfer under ice formation conditions in the cross-flow plate heat exchanger. The simulation is performed using the original mathematical model. The presented model was validated against experimental data. The obtained results showed satisfactory agreement with the data obtained from the experimental measurements. Numerical simulation reveals many unique features of considered heat exchanger connected with the heat and mass transfer occurring in the return air channel under ice formation conditions. The results of computer simulation showed that the efficiency gains are sensitive to various inlet conditions, and allow for estimation of the safe operating conditions for different inlet return airflow parameters, based not only on the exhaust air temperature but also on its relative humidity and different thermal efficiency of the exchanger. Several goals were achieved, including: establishing the most unfavorable operating conditions (from the standpoint of ice formation on the plate surface of the return air channels) for cross-flow plate heat exchanger, which correspond to the inlet value of the return airflow dew point temperature equaled to 0 °C, impact of the ice formation on temperature effectiveness, impact of inlet relative humidity on temperature effectiveness and safe operating conditions and safe operating conditions for variety of inlet exhaust air parameters. [ABSTRACT FROM AUTHOR]

In this paper we propose the use of a random network model for simulating and understanding the epidemics of influenza A(H1N1). The proposed model is used to simulate the transmission process of influenza A(H1N1) in a community region of Venezuela using distributed computing in order to accomplish many realizations of the underlying random process. These large scale epidemic simulations have recently become an important application of high-performance computing. The network model proposed performs better than the traditional epidemic model based on ordinary differential equations since it adjusts better to the irregularity of the real world data. In addition, the network model allows the consideration of many possibilities regarding the spread of influenza at the population level. The results presented here show how well the SEIR model fits the data for the AH1N1 time series despite the irregularity of the data and returns parameter values that are in good agreement with the medical data regarding AH1N1 influenza virus. This versatile network model approach may be applied to the simulation of the transmission dynamics of several epidemics in human networks. In addition, the simulation can provide useful information for the understanding, prediction and control of the transmission of influenza A(H1N1) epidemics. [ABSTRACT FROM AUTHOR]

This paper investigates a mathematical simulation of the heat and mass transfer in the two different Maisotsenko Cycle (M-Cycle) heat and mass exchangers used for the indirect evaporative cooling in different air-conditioning systems. A two-dimensional heat and mass transfer model is developed to perform the thermal calculations of the indirect evaporative cooling process, thus quantifying the overall heat exchangers’ performance. The mathematical model was validated against the experimental data. Numerical simulations reveal many unique features of the considered units, enabling an accurate prediction of their performance. Results of the model allow for comparison of the two types of heat exchangers in different applications for air conditioning systems in order to obtain optimal efficiency. [ABSTRACT FROM AUTHOR]

The aim of this article is to present the reason and the process of creating new modified mathematical model of heat pump plate condenser. The fundamental mathematical model is modified according to analytical optimization procedure. The adaptation is carried out by applying the procedure of elimination. The modified mathematical model include 2 governing equations instead of 6. The two governing equations contain 2 unknown dependent variables and 6 known parameters. The modified mathematical model is validated using the comparative method. The compared data are obtained by numerical simulation using fundamental and modified mathematical models. Applying both models the obtained data fully coincided. By using the new modified mathematical model and implementing the optimization process may lead to the determination of the maximum energy efficiency of hot water subsystem. The subsystem comprises a condenser, a circulation pump, a connecting pipeline and the heating units. The objective function in the optimization process is the coefficient of performance, COP, as a function of the mass flow rate of the hot water or of the circulation pump power. The paper offers the implementation of modeling the circulation pump power to achieve the maximum value of the COP. [ABSTRACT FROM AUTHOR]

Abstract: Formation deformation of oil reservoirs is a widespread phenomenon for unconsolidated or abnormal high-pressure formations due to the depletion of reservoir pressure in the process of oil recovery. It may not only result in formation damage, but also have an adverse influence on production performance. In this paper, the deformation behavior of formation and formation damage are analyzed by elastic, elastic–plastic and plastic theory of solid porous media, and a set of expressions is derived to describe the change in porosity and permeability caused by linear or nonlinear deformation. Based on the comprehensive study on deformation of reservoir rock and multiphase flow in porous media, a new three dimensional and three phase-flow mathematical model that is used to predict the changes of porosity and permeability is presented, and the model is solved by the finite-difference method and self-adaptive iterative technique. A field-scale numerical simulator written in FORTRAN code is developed to predict the change trend of porosity and permeability in elastic and elastic–plastic deformation range. The runs of an oil field example with five-spot patterns are calculated on the simulator, and the formation damage and its influence on the pressure profiles in the vicinity around production well are studied under the condition of linear and nonlinear deformation of a reservoir. This work implies that the deformation of oil formation may be elastic, elastic–plastic or plastic in actual oil formation during the oil exploitation. The declines of porosity and permeability induced by the deformation are completely recoverable only for elastic deformation. Furthermore, elastic–plastic and plastic deformation may occur in the vicinity of production wells in unconsolidated formations. It is found that the increase of deformation coefficients presented in this work results in a sharp pressure-drop funnels on the vertical cross profile, which can be interpreted by the permeability decline induced by rock deformation. [Copyright &y& Elsevier]

Abstract: In this paper, a mathematical model and computer simulator were developed for offline sample pretreatment of heavy metal ion based on moving precipitate boundary (MPB) electrophoresis. The simulation indicates that (i) the program can easily accomplish numerical computations, such as the velocities of MPB and elution boundary (EB), and enrichment factor (EF) etc; (ii) the simulator can vividly imitate the dynamics of MPB, EB, precipitate zone, and precipitate-elution; and (iii) the software may simply optimized experimental conditions via the influence factors (e.g., voltage, hydroxyl, hydrogen and metal ions) on the EF. As a proof of concept, copper ion and its precipitate with definite blue color were, respectively chosen as mode heavy metal ion and alkaline precipitate for the relevant experiments of MPB-based sample preconcentration of heavy metal ion in large tube. All of the experimental results manifest the validity of developed mathematical model and the relevant simulation results. The model and simulator advanced herein are of clear significance to the optimization of experimental conditions and understanding of offline MPB- based sample condensation of heavy metal ion. [Copyright &y& Elsevier]

Abstract: In the following paper the dynamic behavior of an indirect regulator is investigated and by means of Bondgraph method a nonlinear mathematical model for the considered regulator is developed. In this model to represent variable truncated cone orifice, a novel scheme has been proposed. Various operating conditions, including various inlet pressures are dynamically simulated while developing the model. Additionally, dynamic sensitivity of the valve is taken into account with respect to some geometrical parameters. Finally, the obtained simulation results are compared with experimental data demonstrating desirable accuracy of the proposed method. [Copyright &y& Elsevier]

Abstract: A two-dimensional transitory mathematical model developed in a previous paper is expanded and applied to represent the extraction process of oil and its minor compounds (phospholipids, tocopherols and waxes) in a De Smet industrial extractor. Diffusivities and equilibrium parameters are obtained from experimental batch extractions. The mathematical model is solved numerically to predict the concentration of oil and minor compounds in miscella and collets in the different sections of the extractor. The concentration of phospholipids and crystallized waxes in the solid decreases slowly, being sharper at the end of the process. Tocopherols and triacylglycerols are extracted more quickly at 60°C. Numerical simulations of the extraction process reveal that it would be possible to obtain oil with smaller concentrations of phospholipids and waxes, working at 60°C and using fewer stages. Since the last stages do not produce a significant increment of the oil yield at 60°C, the model results show that the extractor is over dimensioned. [Copyright &y& Elsevier]

Abstract: In this paper the dynamics of a spacecraft with a system of stabilization out-of-operation is studied. The deployment of the ring flexible antenna is performed after placing the spacecraft into orbit and damping the initially undesired rotations by a special jet-propelled system. Basically the antenna is a pre-stressed tape reeled on a special drum. Deploying from the drum, the tape takes the shape of an elastic ring of 30m in diameter. The objective of the study is the mechanical and computational modelling of the spacecraft dynamics. The equations of motion are derived in Lagrangian form. Numerical simulations of operational mode of the system are performed. As it is shown in main result, which restrictions must be imposed on parameters of the process of deployment for maintenance of the shape of the deployed design. [Copyright &y& Elsevier]

Abstract: Guyton’s original integrative physiology model was a milestone in integrative physiology, combining significant physiological knowledge with an engineering perspective to develop a computational diagrammatic model. It is still used in research and teaching, with a small number of variants on the model also in circulation. However, though new research has added significantly to the knowledge represented by Guyton’s model, and significant advances have been made in computing and simulation software, an accepted common platform to integrate this new knowledge has not emerged. This paper discusses the issues in the selection of a suitable platform, together with a number of current possibilities, and suggests a graphical computing environment for modelling and simulation. By way of example, a validated version of Guyton’s 1992 model, implemented in the ubiquitous Simulink environment, is presented which provides a hierarchical representation amenable to extension and suitable for teaching and research uses. It is designed to appeal to the biomedical engineer and physiologist alike. [Copyright &y& Elsevier]

Abstract: Worms spreading via both Web-based scanning and removable devices account for a major part of threats on internet. However, their dynamical behavior and controlling methods remain unclear. As a result, we present a computer worm model incorporating specific features unique to those worms, in this paper. The threshold value determining whether the worms die out is obtained. Theoretical analysis shows that if the disease-free equilibrium is globally asymptotically stable; otherwise, the disease will be prevalent. Additionally, some control strategies are given. Our results are illustrated by numerical simulations. [Copyright &y& Elsevier]

Abstract: In this paper we have proposed and analyzed a non-linear mathematical model for unemployment by considering three variables, namely the numbers of unemployed, temporarily employed and regularly employed persons. The model is studied using the stability theory of differential equations. It is found that the model has only one equilibrium, which is non-linearly stable under certain conditions. Numerical simulation of the model has been carried out to confirm the analytical results. [Copyright &y& Elsevier]

Abstract: A scalable new model is developed for the analysis of multiple effect evaporator (MEE) systems with the induction of condensate flashing. It uses the concepts of stream analysis and temperature path for the formulation of model equations. In addition to above the model also takes into account boiling point rise and variable physico-thermal properties of steam/vapor condensate and liquor while simulating the MEE system. The present model consists of linear equations, which are automatically generated through temperature path. To establish the reliability of the present model it was run for four different case studies and the results are compared well with the published models. This paper shows the trade-off between annual capital and operating costs, which decides optimum number of flash tanks as well as their positions in the MEE system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, considering that reassembly of a system and/or using anti-virus software will take a period of time, we introduce a time delay for modeling this period of time. Also, considering that at different times the propagation of a worm shows different characteristics, we build a section model for Internet worm propagation depending on a two-factor model. We first consider the stability of the positive equilibrium and the existence of a local Hopf bifurcation. In succession, using the normal form theory and center manifold argument, we derive explicit formulas determining the stability, direction and other properties of bifurcation periodic solutions. Finally, a numerical simulation is presented. The techniques of analysis of the mathematical model provide a theoretical foundation for control and forecasting for Internet worms. [Copyright &y& Elsevier]

Abstract: A mathematical model of blob matching is developed in this paper. Based on the model, the matching performance of Bhattacharyya coefficient is analyzed and evaluated. The numerical critical conditions of biased matching and mistaken matching for Bhattacharyya coefficient are given. According to the model analysis, a modified version of Bhattacharyya coefficient is proposed, which improves the matching performance relative to the original one. The numerical analysis based on the new model and visual experiments both demonstrate the superior performance of the modified Bhattacharyya coefficient. [Copyright &y& Elsevier]

This paper presents a mathematical model based on a three-phase theory, which is used to describe the mass and heat transfer between the gas and solids phases in a batch fluidised bed dryer. In the model, it is assumed that the dilute phase (i.e., bubble) is plug flow while the interstitial gas and the solid particles are considered as being perfectly mixed. The thermal conductivity of wet particles is modelled using a serial and parallel circuit. The moisture diffusion in wet particles was simulated using a numerical finite volume method. Applying a simplified lumped model to a single solid particle, the heat and mass transfer between the interstitial gas and solid phase is taken into account during the whole drying process as three drying rate periods: warming-up, constant rate and falling-rate. The effects of the process parameters, such as particle size, gas velocity, inlet gas temperature and relative humidity, on the moisture content of solids in the bed have been studied by numerical computation using this model. The results are in good agreement with experimental data of heat and mass transfer in fluidised bed dryers. The model will be employed for online simulation of a fluidised bed dryer and for online control. [Copyright &y& Elsevier]

Abstract: The vertebrate adaptive immune system, with its learning and memory capabilities, is a particularly rich example of the complexity of biological systems. The most difficult challenge in immunological research is the understanding of lymphocyte repertoires—the generation of their diversity and the forces that shape the ever-changing dynamics of lymphocyte clones. The explosively growing quantities of immunological information, which are rapidly becoming available from experimental and clinical studies, necessitate the use of theoretical tools, namely, mathematical and computational modeling and bioinformatical methods of analysis. In this paper, I review several examples of problems in lymphocyte repertoire modeling and analysis, demonstrate the types of solutions employed, and highlight the contribution of these theoretical studies to immunological research. [Copyright &y& Elsevier]