New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model arei...New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.展开更多
Glass is the precious material evidence of the trade of the early Silk Road. The ancient glass was easily affected by the environmental impact and weathering, and the change of composition ratios affected the correct ...Glass is the precious material evidence of the trade of the early Silk Road. The ancient glass was easily affected by the environmental impact and weathering, and the change of composition ratios affected the correct judgment of its category. In this paper, mathematical models and methods such as Chi-square test, weighted average method, principal component analysis, cluster analysis, binary classification model and grey correlation analysis were used comprehensively to analyze the data of sample glass products combined with their categories. The results showed that the weathered high-potassium glass could be divided into 12, 9, 10 and 27, 7, 22 and so on.展开更多
Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived ...Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.展开更多
The effect of deformation conditions on dynamic recrystallization behavior of Nb,V,Ti microalloyed high-strength structural steel was investigated via high-temperature single pass reduction tests on a MMS-300 thermome...The effect of deformation conditions on dynamic recrystallization behavior of Nb,V,Ti microalloyed high-strength structural steel was investigated via high-temperature single pass reduction tests on a MMS-300 thermomechanical simulator,with mathematical models established for flow stress during hot deformation.The results show that the deformation resistance decreases with the increase of temperature and is in power function relationship with the temperature.Meanwhile,it increases with the increase of strain rate and is in log-log relationship with the strain rate.The dynamic recrystallization activation energy of tested steel was determined to be about 329.55 kJ/mol,295.31 kJ/mol at peak and steady states.The prediction models developed for flow stress indicated that they are in good agreement with experimental results.展开更多
With the interdisciplinary development of multiple disciplines,mathematical models play a role as a bridge in the research process of Chinese herbal compounds,which can make full use of the interrelationships of knowl...With the interdisciplinary development of multiple disciplines,mathematical models play a role as a bridge in the research process of Chinese herbal compounds,which can make full use of the interrelationships of knowledge,making the research and use of Chinese herbal compounds from complex and cumbersome to simple.This paper reviewed the research and application of mathematical models in the production and preparation,pharmacodynamics,pharmacokinetics and other aspects of Chinese herbal compound prescriptions,providing a theoretical basis for the development of the modern Chinese medicine industry.展开更多
This article focuses on the mathematical modelling of the extraction process of bioactive compounds from grape marc and berries (Aronia, rosehip, rowan, and hawthorn). The composition of the extraction medium (the con...This article focuses on the mathematical modelling of the extraction process of bioactive compounds from grape marc and berries (Aronia, rosehip, rowan, and hawthorn). The composition of the extraction medium (the concentration of the ethyl alcohol) served as a factor of influence. Furthermore, 8 experimental measured parameters were used as variables. The experimental results were processed using Hermite polynomials. In order to adapt the degree of the polynomial, the following conditions were imposed: high precision of the mathematical model by appealing to models on interval;obtaining a nominal model and two uncertain models (upper and lower);deduction of two predictive models, one superior and one inferior. It was found that the mathematical models based on Hermite polynomials do not provide explicit analytical expressions, although they allow the establishment of parameter values for any concentration of the extraction medium. In some cases, only high-grade polynomial models ensure the modelling error below 2%. Uncertain models (upper and lower 95%) include all experimental data. Predictive mathematical models (upper and lower) were established for a high prediction. The analytical expressions of the mathematical models on intervals are non-gaps, the coefficients having non-zero values. Dependencies between the measured parameters and the composition of the extraction solvent were analyzed, the results being presented through the calculation of a surface, with all the experimental values and their average values. Thus, it was found that polynomial mathematical models provide complete information for modelling the extraction processes of bioactive compounds of plant origin.展开更多
In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of...In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.展开更多
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous...Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.展开更多
The aim of the study was to describe the drying kinetics of washed coffee (Coffea arabica L.) and evaluate the best mathematical model to fit the experimental drying data conducted with different air humidity (40%, 50...The aim of the study was to describe the drying kinetics of washed coffee (Coffea arabica L.) and evaluate the best mathematical model to fit the experimental drying data conducted with different air humidity (40%, 50% and 60%), temperatures (23, 40 and 60 °C) and the quality of the coffee. The cherries coffee were separated and standardized in the processes of washing, mechanical and manual separation. Then, approx. 85 kg of coffee cherries were pulped and taken directly to the yard. The washed coffee was completed dried in a mechanical dryer and yard. The results showed that the different conditions of the ambient air significantly influenced the processes of drying. The water content of the hygroscopic equilibrium of pulped coffee is directly proportional to the water activity and relative humidity (RH), decreasing with increasing temperature, for the same value of equilibrium. The Oswin model was best represented by the hygroscopicity of the pulped coffee, while the Midilli model shows the best fit to describe the drying curves of the washed coffee. The effective diffusion coefficient increases with increasing temperature of the drying air and reducing of RH, being described by the Arrhenius equation. Electrical conductivity, potassium leaching, total titratable acidity and grease acidity increase with increasing drying temperature regardless of the type of processing. Reducing sugars, total sugars and the sensorial quality was negatively affected with increasing drying temperature regardless of the type of processing. The drying at 60 °C/40% RH negatively affected the coffee quality.展开更多
Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fl...Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fluctuations may be significant when small populations of some reacting species are present and then a stochastic description of the cellular dynamics is required. Often, the biochemically reacting systems encountered in applications consist of many species interacting through many reaction channels. Also, the dynamics of such systems is typically non-linear and presents multiple time-scales. Consequently, the stochastic mathematical models of biochemical systems can be quite complex and their analysis challenging. In this paper, we present a method to reduce a stochastic continuous model of well-stirred biochemical systems, the Chemical Langevin Equation, while preserving the overall behavior of the system. Several tests of our method on models of practical interest gave excellent results.展开更多
Foam diversion can effectively solve the problem of uneven distribution of acid in layers of different permeabilities during matrix acidizing.Based on gas trapping theory and the mass conservation equation,mathematica...Foam diversion can effectively solve the problem of uneven distribution of acid in layers of different permeabilities during matrix acidizing.Based on gas trapping theory and the mass conservation equation,mathematical models were developed for foam-diverted acidizing,which can be achieved by a foam slug followed by acid injection or by continuous injection of foamed acid.The design method for foam-diverted acidizing was also given.The mathematical models were solved by a computer program.Computed results show that the total formation skin factor,wellhead pressure and bottomhole pressure increase with foam injection,but decrease with acid injection.Volume flow rate in a high-permeability layer decreases,while that in a low-permeability layer increases,thus diverting acid to the low-permeability layer from the high-permeability layer.Under the same formation conditions,for foamed acid treatment the operation was longer,and wellhead and bottomhole pressures are higher.Field application shows that foam slug can effectively block high permeability layers,and improve intake profile noticeably.展开更多
Thermoregulatory mathematical models have being developed for more than half a century and obtained more and more wide application. Among them, the "engineering-physiological" thermal models, which correlate...Thermoregulatory mathematical models have being developed for more than half a century and obtained more and more wide application. Among them, the "engineering-physiological" thermal models, which correlated closely to the man-machine-environment system, are the ones that developed most rapidly and have been widely accepted by thermal physiologists and environmental control engineers.This paper attempts to outline briefly the development and application of such kind of thermal models, discusses how to further develop and apply various combined thermal models in practice, and puts forward four respects of suggestions for establishment and modification of combined thermal models of man-clothing-cabin environment.展开更多
Through the analyses and researches on some related references of error separation techniques at home and abroad, this paper has built-up some mathematical models to measure and evaluate workpiece cylindricity error w...Through the analyses and researches on some related references of error separation techniques at home and abroad, this paper has built-up some mathematical models to measure and evaluate workpiece cylindricity error with multipoint method as well as unconstrained optimization methods. A few shortcomings of the technique to solve rotational error and cylindricity error are found, and some precise formulas are given. It is feasible by computer simulation tests.展开更多
Rotary kiln process for iron ore oxide pellet production is hard to detect and control.Construction of one-dimensional model of temperature field in rotary kiln was described.And the results lay a solid foundation for...Rotary kiln process for iron ore oxide pellet production is hard to detect and control.Construction of one-dimensional model of temperature field in rotary kiln was described.And the results lay a solid foundation for online control.Establishment of kiln process control expert system was presented,with maximum temperature of pellet and gas temperature at the feed end as control cores,and interval estimate as control strategy.Software was developed and put into application in a pellet plant.The results show that control guidance of this system is accurate and effective.After production application for nearly one year,the compressive strength and first grade rate of pellet are increased by 86 N and 2.54%,respectively,while FeO content is 0.05% lowered.This system can reveal detailed information of real time kiln process,and provide a powerful tool for online control of pellet production.展开更多
Two related and under-studied components of modeling are: a) the process by which simplifying assumptions are derived;and b) the process by which tests of model validity are designed. This case study illustrates these...Two related and under-studied components of modeling are: a) the process by which simplifying assumptions are derived;and b) the process by which tests of model validity are designed. This case study illustrates these processes for two simple investment models: a) a version of the model supporting classical portfolio theory;and b) a version of a mean-reverting model consistent with some of the tenets of behavioral finance. We perform a simulation that demonstrates that the traditional method of empirically assessing the performance of value investment strategies is underpowered. Indeed, the simulation illustrates in a narrow technical sense how to make something out of nothing;namely, how to generate increased returns while reducing risk. Analyzing the mechanism underpinning this counter-intuitive result helps to illustrate the close and sometimes unexpected relationship between the substantial assumptions made about the systems being modeled, the mathematical assumptions used to build models of those systems, and the structure of the experiments used to assess the performance of those models.展开更多
Grate process is an important step in grate-kiln pellet production.However,as a relatively closed system,the process on grate is inaccessible to direct detection,therefore,it is hard to control.As a result,mathematica...Grate process is an important step in grate-kiln pellet production.However,as a relatively closed system,the process on grate is inaccessible to direct detection,therefore,it is hard to control.As a result,mathematical models of temperature distribution,moisture distribution and oxidation degree distribution in pellet bed,with good universality,computation speed and calculation accuracy,are presented based on analysis of heat transfer and physical-chemical reactions during grate process.And real-time visualization of temperature,moisture and oxidation degree distribution in pellet bed during grate process is realized.Model validation is displayed,and the similarity of 91% is proved.The results can reveal real time status on grate,and provide a solid foundation for the subsequent study of artificial intelligence control system of pellet production.展开更多
Intestinal infection has become a common disease in human and endoscopy can be a powerful means in diagnosis of intestinal illnesses. Mathematical models are developed for an inserted endoscope on the flow of chyme in...Intestinal infection has become a common disease in human and endoscopy can be a powerful means in diagnosis of intestinal illnesses. Mathematical models are developed for an inserted endoscope on the flow of chyme in the small intestine considering a Newtonian incompressible fluid flow, under an axisymmetric condition, in a cylindrical annulus between the small intestine and the endoscope. We obtain novel mathematical expressions for the pressure drop, forces exerted by the endoscope on the flow of chyme, and the force exerted by the chyme on the intestine for one wave length of the peristaltic rush wave. We also investigate and calculate the flow velocity and pressure for different flow rates and the wave lengths. The results are presented, and discussed for the cases and conditions under which pressure, pressure drop can be positive or negative and the forces can be acted either by the intestine or endoscope on the flow or vice-versa.展开更多
This paper presents a practical three-dimensional meathematical model of circulation and heat transfer in generator of glass melting furnaces.The model was based on the heat transfer between the smoke flow and the lat...This paper presents a practical three-dimensional meathematical model of circulation and heat transfer in generator of glass melting furnaces.The model was based on the heat transfer between the smoke flow and the lattice units,and between the air flow and the lattice units.This model not only bypassed the difficulty of complicated computation of the heat transfer process in the regenerator of glass furnaces,but also avoided the irrationality of fixing the temperature distribution on the surfaces.Use of the model yielded very important data and also the method for the design of the regenerator of glass furnaces in practical production.展开更多
Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived.The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notc...Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived.The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool,such as mass flow rates,flow coefficients,efflux angles and steady state flow forces under different operating conditions.At last,the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test.It is presented that the bottom arc of sloping U-shape notch(ABU) should not be omitted when it is required to accurately calculate the orifice area of ABU.Although the theoretical flow area of plain bottom sloping U-shape notch(PBU) is larger than that of ABU at the same opening,the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening,while the simulated flow force of PBU is larger than that of ABU at the same opening.Therefore,it should be prior to adapt the ABU when designing the spool with proportional character.展开更多
基金Lucian Blaga University of Sibiu&Hasso Plattner Foundation Research Grants LBUS-IRG-2020-06.
文摘New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.
文摘Glass is the precious material evidence of the trade of the early Silk Road. The ancient glass was easily affected by the environmental impact and weathering, and the change of composition ratios affected the correct judgment of its category. In this paper, mathematical models and methods such as Chi-square test, weighted average method, principal component analysis, cluster analysis, binary classification model and grey correlation analysis were used comprehensively to analyze the data of sample glass products combined with their categories. The results showed that the weathered high-potassium glass could be divided into 12, 9, 10 and 27, 7, 22 and so on.
文摘Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.
文摘The effect of deformation conditions on dynamic recrystallization behavior of Nb,V,Ti microalloyed high-strength structural steel was investigated via high-temperature single pass reduction tests on a MMS-300 thermomechanical simulator,with mathematical models established for flow stress during hot deformation.The results show that the deformation resistance decreases with the increase of temperature and is in power function relationship with the temperature.Meanwhile,it increases with the increase of strain rate and is in log-log relationship with the strain rate.The dynamic recrystallization activation energy of tested steel was determined to be about 329.55 kJ/mol,295.31 kJ/mol at peak and steady states.The prediction models developed for flow stress indicated that they are in good agreement with experimental results.
文摘With the interdisciplinary development of multiple disciplines,mathematical models play a role as a bridge in the research process of Chinese herbal compounds,which can make full use of the interrelationships of knowledge,making the research and use of Chinese herbal compounds from complex and cumbersome to simple.This paper reviewed the research and application of mathematical models in the production and preparation,pharmacodynamics,pharmacokinetics and other aspects of Chinese herbal compound prescriptions,providing a theoretical basis for the development of the modern Chinese medicine industry.
文摘This article focuses on the mathematical modelling of the extraction process of bioactive compounds from grape marc and berries (Aronia, rosehip, rowan, and hawthorn). The composition of the extraction medium (the concentration of the ethyl alcohol) served as a factor of influence. Furthermore, 8 experimental measured parameters were used as variables. The experimental results were processed using Hermite polynomials. In order to adapt the degree of the polynomial, the following conditions were imposed: high precision of the mathematical model by appealing to models on interval;obtaining a nominal model and two uncertain models (upper and lower);deduction of two predictive models, one superior and one inferior. It was found that the mathematical models based on Hermite polynomials do not provide explicit analytical expressions, although they allow the establishment of parameter values for any concentration of the extraction medium. In some cases, only high-grade polynomial models ensure the modelling error below 2%. Uncertain models (upper and lower 95%) include all experimental data. Predictive mathematical models (upper and lower) were established for a high prediction. The analytical expressions of the mathematical models on intervals are non-gaps, the coefficients having non-zero values. Dependencies between the measured parameters and the composition of the extraction solvent were analyzed, the results being presented through the calculation of a surface, with all the experimental values and their average values. Thus, it was found that polynomial mathematical models provide complete information for modelling the extraction processes of bioactive compounds of plant origin.
文摘In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.
文摘Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.
文摘The aim of the study was to describe the drying kinetics of washed coffee (Coffea arabica L.) and evaluate the best mathematical model to fit the experimental drying data conducted with different air humidity (40%, 50% and 60%), temperatures (23, 40 and 60 °C) and the quality of the coffee. The cherries coffee were separated and standardized in the processes of washing, mechanical and manual separation. Then, approx. 85 kg of coffee cherries were pulped and taken directly to the yard. The washed coffee was completed dried in a mechanical dryer and yard. The results showed that the different conditions of the ambient air significantly influenced the processes of drying. The water content of the hygroscopic equilibrium of pulped coffee is directly proportional to the water activity and relative humidity (RH), decreasing with increasing temperature, for the same value of equilibrium. The Oswin model was best represented by the hygroscopicity of the pulped coffee, while the Midilli model shows the best fit to describe the drying curves of the washed coffee. The effective diffusion coefficient increases with increasing temperature of the drying air and reducing of RH, being described by the Arrhenius equation. Electrical conductivity, potassium leaching, total titratable acidity and grease acidity increase with increasing drying temperature regardless of the type of processing. Reducing sugars, total sugars and the sensorial quality was negatively affected with increasing drying temperature regardless of the type of processing. The drying at 60 °C/40% RH negatively affected the coffee quality.
文摘Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fluctuations may be significant when small populations of some reacting species are present and then a stochastic description of the cellular dynamics is required. Often, the biochemically reacting systems encountered in applications consist of many species interacting through many reaction channels. Also, the dynamics of such systems is typically non-linear and presents multiple time-scales. Consequently, the stochastic mathematical models of biochemical systems can be quite complex and their analysis challenging. In this paper, we present a method to reduce a stochastic continuous model of well-stirred biochemical systems, the Chemical Langevin Equation, while preserving the overall behavior of the system. Several tests of our method on models of practical interest gave excellent results.
文摘Foam diversion can effectively solve the problem of uneven distribution of acid in layers of different permeabilities during matrix acidizing.Based on gas trapping theory and the mass conservation equation,mathematical models were developed for foam-diverted acidizing,which can be achieved by a foam slug followed by acid injection or by continuous injection of foamed acid.The design method for foam-diverted acidizing was also given.The mathematical models were solved by a computer program.Computed results show that the total formation skin factor,wellhead pressure and bottomhole pressure increase with foam injection,but decrease with acid injection.Volume flow rate in a high-permeability layer decreases,while that in a low-permeability layer increases,thus diverting acid to the low-permeability layer from the high-permeability layer.Under the same formation conditions,for foamed acid treatment the operation was longer,and wellhead and bottomhole pressures are higher.Field application shows that foam slug can effectively block high permeability layers,and improve intake profile noticeably.
文摘Thermoregulatory mathematical models have being developed for more than half a century and obtained more and more wide application. Among them, the "engineering-physiological" thermal models, which correlated closely to the man-machine-environment system, are the ones that developed most rapidly and have been widely accepted by thermal physiologists and environmental control engineers.This paper attempts to outline briefly the development and application of such kind of thermal models, discusses how to further develop and apply various combined thermal models in practice, and puts forward four respects of suggestions for establishment and modification of combined thermal models of man-clothing-cabin environment.
文摘Through the analyses and researches on some related references of error separation techniques at home and abroad, this paper has built-up some mathematical models to measure and evaluate workpiece cylindricity error with multipoint method as well as unconstrained optimization methods. A few shortcomings of the technique to solve rotational error and cylindricity error are found, and some precise formulas are given. It is feasible by computer simulation tests.
基金Project(NCET-05-0630) supported by Program for New Century Excellent Talents in University of China
文摘Rotary kiln process for iron ore oxide pellet production is hard to detect and control.Construction of one-dimensional model of temperature field in rotary kiln was described.And the results lay a solid foundation for online control.Establishment of kiln process control expert system was presented,with maximum temperature of pellet and gas temperature at the feed end as control cores,and interval estimate as control strategy.Software was developed and put into application in a pellet plant.The results show that control guidance of this system is accurate and effective.After production application for nearly one year,the compressive strength and first grade rate of pellet are increased by 86 N and 2.54%,respectively,while FeO content is 0.05% lowered.This system can reveal detailed information of real time kiln process,and provide a powerful tool for online control of pellet production.
文摘Two related and under-studied components of modeling are: a) the process by which simplifying assumptions are derived;and b) the process by which tests of model validity are designed. This case study illustrates these processes for two simple investment models: a) a version of the model supporting classical portfolio theory;and b) a version of a mean-reverting model consistent with some of the tenets of behavioral finance. We perform a simulation that demonstrates that the traditional method of empirically assessing the performance of value investment strategies is underpowered. Indeed, the simulation illustrates in a narrow technical sense how to make something out of nothing;namely, how to generate increased returns while reducing risk. Analyzing the mechanism underpinning this counter-intuitive result helps to illustrate the close and sometimes unexpected relationship between the substantial assumptions made about the systems being modeled, the mathematical assumptions used to build models of those systems, and the structure of the experiments used to assess the performance of those models.
基金Project(NCET050630) supported by Program for New Century Excellent Talents in University,China
文摘Grate process is an important step in grate-kiln pellet production.However,as a relatively closed system,the process on grate is inaccessible to direct detection,therefore,it is hard to control.As a result,mathematical models of temperature distribution,moisture distribution and oxidation degree distribution in pellet bed,with good universality,computation speed and calculation accuracy,are presented based on analysis of heat transfer and physical-chemical reactions during grate process.And real-time visualization of temperature,moisture and oxidation degree distribution in pellet bed during grate process is realized.Model validation is displayed,and the similarity of 91% is proved.The results can reveal real time status on grate,and provide a solid foundation for the subsequent study of artificial intelligence control system of pellet production.
文摘Intestinal infection has become a common disease in human and endoscopy can be a powerful means in diagnosis of intestinal illnesses. Mathematical models are developed for an inserted endoscope on the flow of chyme in the small intestine considering a Newtonian incompressible fluid flow, under an axisymmetric condition, in a cylindrical annulus between the small intestine and the endoscope. We obtain novel mathematical expressions for the pressure drop, forces exerted by the endoscope on the flow of chyme, and the force exerted by the chyme on the intestine for one wave length of the peristaltic rush wave. We also investigate and calculate the flow velocity and pressure for different flow rates and the wave lengths. The results are presented, and discussed for the cases and conditions under which pressure, pressure drop can be positive or negative and the forces can be acted either by the intestine or endoscope on the flow or vice-versa.
文摘This paper presents a practical three-dimensional meathematical model of circulation and heat transfer in generator of glass melting furnaces.The model was based on the heat transfer between the smoke flow and the lattice units,and between the air flow and the lattice units.This model not only bypassed the difficulty of complicated computation of the heat transfer process in the regenerator of glass furnaces,but also avoided the irrationality of fixing the temperature distribution on the surfaces.Use of the model yielded very important data and also the method for the design of the regenerator of glass furnaces in practical production.
基金Project(51004085)supported by the National Natural Science Foundation of China
文摘Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived.The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool,such as mass flow rates,flow coefficients,efflux angles and steady state flow forces under different operating conditions.At last,the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test.It is presented that the bottom arc of sloping U-shape notch(ABU) should not be omitted when it is required to accurately calculate the orifice area of ABU.Although the theoretical flow area of plain bottom sloping U-shape notch(PBU) is larger than that of ABU at the same opening,the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening,while the simulated flow force of PBU is larger than that of ABU at the same opening.Therefore,it should be prior to adapt the ABU when designing the spool with proportional character.
