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Mathematical Models of Tire-Lateral Road Adhesion for Use in Road Vehicle Dynamics Studies 被引量:1
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作者 刘昭度 《Journal of Beijing Institute of Technology》 EI CAS 1997年第1期92-99,共8页
Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad... Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle. 展开更多
关键词 mathematical model tire-lateral road adhesion coefficient vehicle dynamics
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MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE
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作者 包康博 梁桂珍 +1 位作者 田天海 张兴安 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期1165-1188,共24页
Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory ca... Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes. 展开更多
关键词 mathematical model drug resistance cancer heterogeneity immune system targeted therapy
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Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling
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作者 Fatma Nese Efil Sania Qureshi +3 位作者 Nezihal Gokbulut Kamyar Hosseini Evren Hincal Amanullah Soomro 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第7期485-512,共28页
The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal... The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness. 展开更多
关键词 COVID-19 mathematical modeling CANCER DIABETES heart diseases sensitivity analysis
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A Mathematical Modeling of 3D Cubical Geometry Hypothetical Reservoir under the Effect of Nanoparticles Flow Rate,Porosity,and Relative Permeability
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作者 Mudasar Zafar Hamzah Sakidin +6 位作者 Abida Hussain Loshini Thiruchelvam Mikhail Sheremet Iskandar Dzulkarnain Roslinda Nazar Abdullah Al-Yaari Rizwan Safdar 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第11期1193-1211,共19页
This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O... This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3),in unconventional oil reservoirs.The simulation is conducted for different parameters of volume fractions,porosities,and mass flow rates to determine the optimal oil recovery.The impact of nanoparticles on relative permeability(kr)and water is also investigated.The simulation process utilizes the finite volume ANSYS Fluent.The study results showed that when the mass flow rate at the inlet is low,oil recovery goes up.In addition,they indicated that silicon nanoparticles are better at getting oil out of the ground(i.e.,oil reservoir)than Al_(2)O_(3)and Fe_(2)O_(3).Most oil can be extracted from SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3)at a rate of 97.8%,96.5%,and 88%,respectively. 展开更多
关键词 Unconventional reservoir cubical cavity oil recovery rate reservoir engineering mathematical modeling
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Mathematical Modeling of Cell Polarity Establishment of Budding Yeast
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作者 Yue Liu Jun Xie +1 位作者 Hay-Oak Park Wing-Cheong Lo 《Communications on Applied Mathematics and Computation》 EI 2024年第1期218-235,共18页
The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in t... The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously.Polarization of these signaling molecules involves complex regulation,so the mathematical models become a useful tool to investigate the mechanism behind the process.In this review,we discuss how mathematical modeling has shed light on different regulations in the cell polarization.We also propose future applications for the mathematical modeling of cell polarization and morphogenesis. 展开更多
关键词 Budding yeast CDC42 MORPHOGENESIS SEPTIN mathematical models
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Practical Use of the Subjective Mathematical Model of Bayes and Its External Validation in Dental Medicine & Dentistry
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作者 Muyembi Muinaminayi Pierre Kayembe Mwimbi David +9 位作者 Nyimi Boshabu Fidèle Panoumvita Kapamona Junior Nsudila Mpoyi Monique Tubanza Mulongo Simplot Sekele Issouradi-Bourley Jean-Paul Mantshumba Milolo Augustin Kalala Kazadi Em Mabela Rosti Munyanga Mukongo Sylvain Dan Wang 《Open Journal of Statistics》 2024年第5期553-575,共23页
Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of a... Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established. 展开更多
关键词 External Validation-MSB-MRL mathematical model
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Analysis and Evaluation of Housing Price Factors Using Mathematical Modeling
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作者 Xing Lyu 《Proceedings of Business and Economic Studies》 2024年第6期17-23,共7页
In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to... In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to challenges,particularly concerning housing prices,which have drawn widespread societal attention.This article explores the theories of housing prices,analyzes factors influencing them,and conducts an empirical investigation of the impact of representative factors on ordinary residential prices.Using regression analysis and the entropy weight method,a mathematical model was developed to examine how various factors affect housing prices. 展开更多
关键词 mathematical modeling Regression analysis Housing price Formation factors Multiple linear regression H ypothesis testing Multiple decision coefficients
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Mathematical Modeling of the Co-Infection Dynamics of HIV and Tuberculosis Incorporating Inconsistency in HIV Treatment
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作者 Sr Mary Nyambura Mwangi Virginia M. Kitetu Isaac O. Okwany 《Journal of Applied Mathematics and Physics》 2024年第5期1744-1768,共25页
A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was ... A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection. 展开更多
关键词 Co-Infection modeling HIV-TB Co-Infection mathematical modeling Reproduction Number Inconsistent Treatment
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Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment
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作者 Sr Mary Nyambura Mwangi Virginia M. Kitetu Isaac O. Okwany 《Journal of Applied Mathematics and Physics》 2024年第4期1063-1078,共16页
HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not... HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease. 展开更多
关键词 HIV modeling mathematical modeling Reproduction Number Inconsistent Treatment
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Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods 被引量:10
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作者 王兆强 顾临怡 +2 位作者 冀宏 陈家旺 李林 《Journal of Central South University》 SCIE EI CAS 2014年第1期140-150,共11页
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 not... 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, effiux 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
关键词 spool valve flow field simulation flow area steady state flow force mathematical model sloping U-shape notch
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Mathematical models and expert system for grate-kiln process of iron ore oxide pellet production.Part Ⅱ:Rotary kiln process control 被引量:7
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作者 范晓慧 王祎 陈许玲 《Journal of Central South University》 SCIE EI CAS 2012年第6期1724-1727,共4页
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
关键词 mathematical model expert system one-dimensional temperature field rotary kiln iron ore oxide pellet
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Mathematical models and expert system for grate-kiln process of iron ore oxide pellet production(Part Ⅰ):Mathematical models of grate process 被引量:4
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作者 王祎 范晓慧 陈许玲 《Journal of Central South University》 SCIE EI CAS 2012年第4期1092-1097,共6页
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
关键词 mathematical model temperature distribution moisture distribution oxidation degree distribution iron ore oxide pellet
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Mathematical models for foam-diverted acidizing and their applications 被引量:3
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作者 Li Songyan Li Zhaomin Lin Riyi 《Petroleum Science》 SCIE CAS CSCD 2008年第2期145-152,共8页
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, mathemati... 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 highpermeability 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
关键词 Foam slug foamed acid DIVERSION ACIDIZING nonhomogenous mathematical model
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Mathematical models for properties of mortars with admixtures and recycled fine aggregates from demolished concretes 被引量:1
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作者 Mi Renjie Pan Ganghua +1 位作者 Li Yang Lu Xiaojun 《Journal of Southeast University(English Edition)》 EI CAS 2018年第3期371-376,共6页
In order to expand the engineering application of recycle aggregate mortars (RAM) with aggregates from demolished concretes, the models for the properties of RAM and the replacement rate of these recycled fine aggre... In order to expand the engineering application of recycle aggregate mortars (RAM) with aggregates from demolished concretes, the models for the properties of RAM and the replacement rate of these recycled fine aggregates were proposed. First, different kinds of mathematical models for the basic properties (compressive strength, water retention rate, and consistency loss) of RAM with two kinds of admixtures, thickening powders (TP) and self-made powdery admixtures (SSCT) designed for RAM, and the replacement rates were established, while the average relative errors and relative standard errors of these models were calculated. Additionally, the models and their error analyses for the curves of drying shrinkage and curing time of RAM + SSCT at different replacement rates were put forward. The results show that polynomial functions should be used to calculate the basic properties of RAM + TP and RAM + SSCT at different replacement rates. In addition, polynonfial functions are the most optimal models for the sharp shrinkage sections in the curves of drying shrinkage-curing time of RAM + SSCT, while exponential functions should be used as the models for the slow shrinkage sections and steady shrinkage sections. 展开更多
关键词 demolished concrete recycled fine aggregates ADMIXTURES recycled aggregate mortars mathematical model
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Foundation of three—dimensional mathematical models for glass furnace regenerator 被引量:1
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作者 沈锦林 宋晨路 《Journal of Zhejiang University Science》 CSCD 2002年第5期570-573,共4页
This paper presents a practical three dimensional mathematical 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 la... This paper presents a practical three dimensional mathematical 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
关键词 REGENERATOR mathematical model Gas flow Temperature field
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Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation 被引量:3
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作者 Karan S. Surana Sri Sai Charan Mathi 《American Journal of Computational Mathematics》 2020年第2期167-220,共54页
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
关键词 Plate and Shell mathematical models Energy Functional Thermodynamic Consistency Classical Continuum Mechanics Non-Classical Continuum Mechanics Internal Rotations Cosserat Rotations Principle of Virtual Work
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Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua 被引量:1
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作者 Karan S. Surana Emilio N. Alverio 《Applied Mathematics》 2020年第7期546-578,共33页
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
关键词 Energy Methods Principle of Virtual Work Calculus of Variations Euler’s Equation mathematical model Classical and Non-Classical Continuum Mechanics
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Mathematical Models for Vacuum Drying Characteristics of Pomegranate Aril 被引量:1
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作者 K. Pongtong R. Assawarachan A. Noomhorm 《Journal of Food Science and Engineering》 2011年第1期11-19,共9页
The aim of this study was to investigate and determine the best mathematical models in describing vacuum drying characteristic of pomegranate arils in the range of 55-75 ℃. The vacuum batch dryer used in the evaluati... The aim of this study was to investigate and determine the best mathematical models in describing vacuum drying characteristic of pomegranate arils in the range of 55-75 ℃. The vacuum batch dryer used in the evaluation was successful in drying a thin layer of pomegranate arils from the initial moisture content of 464.02% (d.b.) to 6.18% (d.b.) within 6.5 to 13.5 hr of continuous drying at the above mentioned temperature range. The drying rates increased with an increase in temperature and drying time. Five of the well known semi-theoretical and empirical models were fitted to the vacuum drying of pomegranate arils. The semi-empirical Midilli model has shown an excellent fit to predict drying behavior of the pomegranate arils because this model gave the highest coefficient of determination (RE), the least chi-square (X2), and the lowest root mean square error (RMSE). The total drying occurs during falling period, signifying the influence of moisture diffusion during the drying. The effective diffusivity varied from 1.25× 10^10 to 2.91 × 10^10 m^2/s over the temperature range. Temperature dependence of the diffusivity was well documented by Arrhenius models. The activation energy of moisture diffusion during drying was found to be 40.46 kJ/mol. 展开更多
关键词 mathematical models vacuum drying POMEGRANATE
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Mathematical Models for a Social Partitioning Problem 被引量:1
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作者 Vardges Melkonian 《American Journal of Computational Mathematics》 2021年第1期1-22,共22页
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
关键词 Health Care Operations Research mathematical models for Pandemics Graph Partitioning Integer Linear Programming Heuristic Algorithms
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MATHEMATICAL MODELS ARISING FROM A SURVEY OF FERROMAGNETIC MATERIALS UNDER MAGNETISATION
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作者 顾晓安 曾进 沈荣瀛 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第9期1065-1074,共10页
This paper focuses on mathematical models describing the mechanical behavior of ferromagnetic materials under magnetization. Through combination of the electromagnetic field theory with the theory of elastic mechanics... This paper focuses on mathematical models describing the mechanical behavior of ferromagnetic materials under magnetization. Through combination of the electromagnetic field theory with the theory of elastic mechanics, several nonlinear systems of fourth order partial differential equations were deduced. By making further assumption, the first-order approximation of the above equations was established, of which the solutions are good enough for engineering application. 展开更多
关键词 sinusoidal magnetic field ferromagnetic material mechanical behavior mathematical model
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