Mathematic model of rolling pressure during a semisolid shearing-rolling process

A mathematic model of rolling pressure during a novel semisolid shearing-rolling process was established. The rolling pressure in this process is higher than that in the conventional rolling. The increment of rolling pressure in the backward slip zone is higher than that in the forward slip zone, and the neutral plane moves toward to the roll gap entrance. The maximum and the average rolling pressures increase with the decrease of strip thickness, and the effects of strip thickness on the rolling pressure is more obvious in the forward slip zone than in the backward slip zone. Meanwhile, the neutral plane moves toward the roll gap exit with the decrease of strip thickness. The maximum and average rolling pressures increase with the decrease of strip width, and the strip width affects the pressure more obviously in the backward slip zone than in the forward slip zone. At the same time, the neutral plane moves toward the roll gap entrance with the decrease of strip width. The maximum and average rolling pressures increase with increasing roll radius, and the neutral plane moves toward the roll gap exit.

Mathematic modeling on flexible cooling system in hot strip mill

A novel cooling system combining ultra fast cooling rigs with laminar cooling devices was investigated.Based on the different cooling mechanisms,a serial of mathematic models were established to describe the relationship between water flow and spraying pressure and the relationship between water spraying heat flux and layout of nozzles installed on the top and bottom cooling headers.Model parameters were validated by measured data.Heat transfer models including air convection model,heat radiation model and water cooling capacity model were detailedly introduced.In addition,effects on cooling capacity by water temperature and different valve patterns were also presented.Finally,the comparison results from UFC used or not have been provided with respect to temperature evolution and mechanical properties of Q235B steel grade with thickness of 7.8 mm.Since online application of the sophisticated CTC process control system based on these models,run-out table cooling control system has been running stably and reliably to produce resource-saving,low-cost steels with smaller grain size.

Mathematic model and tooth contact analysis of a new spiral non-circular bevel gear

A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles of face-milling spiral bevel gears.Unlike straight non-circular bevel gears,spiral non-circular bevel gears have numerous advantages,such as a high contact ratio,high intensity,good dynamic performance,and an adjustable contact region.In addition,while manufacturing straight non-circular bevel gears is difficult,spiral non-circular bevel gears can be efficiently and precisely fabricated with a 6-axis bevel gear cutting machine.First,the generating principles of spiral non-circular bevel gears were introduced.Next,a mathematical model,including a generating tooth profile,tooth spiral,pressure angle,and generated tooth profile for this gear type was established.Then the precision of the model was verified by a tooth contact analysis using FEA,and the contact patterns and stress distributions of the spiral non-circular bevel gears were investigated.

Mathematic Model of Unsteady Penetration Mass Transfer in Randomly Packed Hollow Fiber Membrane Module

Based on the membrane-based absorption experiment of CO2 into water, shell-side flow distribution and mass transfer in a randomly packed hollow fiber module have been analyzed using subchannel model and unsteady penetration mass transfer theory. The cross section of module is subdivided into many small cells which contains only one hollow-fiber. The cross sectional area distribution of these cells is presented by the normal probability density distribution function. It has been obtained that there was a most serious non-ideal flow in shell side at moderate mean packing density, and the large amount of fluid flowed and transferred mass through a small number of large voids. Thus mass transfer process is dominated by the fluid through the larger void area. The mass transfer process in each cell is described by the unsteady penetration theory. The overall mass transfer coefficient equals to the probability addition of the mean mass transfer coefficient in each cell. The comparisons of the values calculated by the model established with the empirical correlations and the experimental data of this work have been done.The predicted overall mass transfer coefficients are in good agreement with experimental data.

The mathematic model of tension straightening process of magnesium alloy and experimental validation

The stress-strain curve of bending bar and the stress relax curve of AZ31 was obtained by a tension test using Gleeble-1500.The tension straightening process mainly consisted of the elastic loading-I and unloading stage,the elastic loading-II and unloading stage,and the elastic-plastic loading stage,which were based on the stretch force change during straightening.The circular bar straightening under one-dimensional bending was investigated and assumed to be linear strain-hardening elastic-plastic material.According to the elastic-plastic mechanics theory,the mathematical displacement-force model of a tension straightening process established,on which was based,the predicted displacement of tension straightening for various original deflection was calculated.The tension straightening experiment for AZ31 magnesium was conducted under the guidance of the predicted displacement.The experiment results present good straightness when there is a stress relaxation phenomenon or the temperature of tension straightening is 25℃.

MATHEMATIC MODEL FOR FORMABILITY CRITERIA OF SUPERPLASTIC AIR BULGING COMPONENTS

A proposal for two types of press close to die,including blank coming in die and Blank cov- ering die,and four criteria for formability is put forward in the study of the superplastic air bulge forming of the metallic thin wall components.A dimensionless weigh mathematic model for the criteria of superplastic air bulge forming is developed to be: Q_w=1.56(WS)/(HF)+2.37(0-(?)π/(180)-r/(r_0)+0.19 The superior formability of components is approaching,if Q_W≥1,and the worse,if Q_W<1.It was confirmed by practice that the above mentioned model is accurate sufficiently.

Research and Application of the Mathematic Model for the Washing Shrinkage of Woven Fabric

Having analyzed the relationships between washing shrinkage and weaving technique, parameters, material properties of woven fabrics and studied the shrinkage mechanism and its mathematical model of the plain fabric, researchers set up a shrinkage model of the twills and satins and proposed a method for calculating the washing shrinkage based on weaving technique and parameters of fabrics. Shrinkage experiments of silk habotai, silk twill and silk satin fabrics were performed. The results were compared with those of the theoretical computations, and theoretical method is reliable.

A Mathematic Model of Gas-diffusion Electrodes in Contact with Liquid Electrolytes

A mathematic model is developed which is applied to analyze the main factors that affect electrode performance and to account for the process of reaction and mass transfer in gas-diffusion electrodes in contact with liquid electrolytes. Electrochemical Thiele modulus φ^2 and electrochemical effectiveness factor η are introduced to elucidate the effects of diffusion on electrochemical reaction and utilization of the gas-diffusion electrode. Profile of the reactant along axial direction is discussed, dependence of electrode potential V on current density J, are predicated by means of the newly developed mathematical model.

Multi-analysis with mathematic model of 3125 non-thyrogenous masses of the neck

Objective： To systematically analyze and summarize non-thyrogenous masses of the neck （NTMN） by consideration of new areas, a large sample size and multiple-aspect analysis. Methods： Our research involved 3125 NTMN cases. We summarized the proportion of various NTMN and the distribution of the neck diseases based on the new international classification. The clinical traits such as sexual proportion and age, etc, were analyzed along with the unknown primary cervical metastatic carcinomas （UPCMC）, and built up a mathematical model based on the data above. Results： There were 68 different diseases identified. Among all the NTMN, the percentage of metastatic carcinomas was 63.3%. The neck masses with a focus above the clavicle comprised 62.3% of the metastatic carcinomas whose focuses were clear. Moreover, other results almost supported the ＂rule of 80%＂. There was an obvious distribution of traits at every sub level. For example, there were 23 different diseases in level Ⅲ, of which the most common was lymphoma. UPCMC made up 12.3% of all metastatic carcinomas. The clinic cases could be analyzed by our model even to form a primary diagnosis which showed a high coincident rate with clinic diagnosis. Conclusion： NTMN are complex and various, with a definite distribution in each neck level. Data relating component character, sex ratio and UPCMC et al to the clinical traits of NTMN will provide vigorous support for clinical applications. The mathematical model could be an efficient method to synthetically analyze complicate data of NTMN.

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

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.

Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling

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.

Mathematical Modeling of Cell Polarity Establishment of Budding Yeast

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.

Practical Use of the Subjective Mathematical Model of Bayes and Its External Validation in Dental Medicine & Dentistry

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.

Mathematical Modeling of the Co-Infection Dynamics of HIV and Tuberculosis Incorporating Inconsistency in HIV Treatment

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.

Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment

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.

MATHEMATICAL MODEL OF ~4He QUANTUM INTERFEROMETER GYROSCOPE

The mathematical model of 4He quantum interferometer gyroscope is presented. The model includes the driven equation, the current equation and the position equation. Therefore, it can sufficiently describe the gyro- scope system. The driven equation shows the thermally driven gyroscope can work for a long time but the pres- sure driven one cannot. From the current equation, the superfluid currents passing through the weak link contain the AC currents which show the rotation flux, and other currents caused by drive. As shown in the position equa- tion, the displacement of diaphragm is the only detectable parameter in the gyroscope system. The model is tested by the simulations based on experimental parameters, and can be used to research performance of the gyroscope and analyse the gyroscope error.

Application of the Sediment Mathematical Modelling on Planned Project of Lingdingyang Bay

Based on the combined hydraulic calculation for the eastern network region at the Pearl River estuary and several outlets to the Lingdingyang Bay, the sediment calculation modelling was introduced in the establishment of the sediment mathematical model for Lingdingyang Bay and the eastern region with one and two dimensional flow calculation. Model adjustment and verification were performed in conjunction with field data. The simulated results coincide well with measured data.In addition the model is applied to predict the shore-line planning scheme of Lingdingyang Bay.The theoretical criterion is provided for the shore line plan in the model.And a new mathematical simulated method is put out to research the planning engineering concerned with one-dimensional net rivers and two-dimensional estuary.

MATHEMATICAL MODEL OF SELF-REPAIRING FLIGHT CONTROL

The most prospective method for certain structural failures and damages that cannot employ redundancy is self-repairing techniques, to ensure especially the maximum flight safety. Based on the characters of self-repairing aircraft, this paper states some basic assumptions of the self-repairing aircraft, and puts forward some special new conceptions concerning the self-repairing aircraft: control input, operating input, command input, repair input and operating and control factor as well as their relationships. Thus it provides a simple and reliable mathematical model structure for the research on the self-repairing control of the aircraft.

Mathematic model of solid fraction during rheo-casting by the cooling sloping plate process

A mathematic model of the solid fraction during rheo-casting by the cooling sloping plate process was established, and the effects of the process parameters on the solid fraction were analyzed. The calculation results show that the experimental result is approximately agreed with the calculation value. The effect of the casting temperature on the change rate of the solid fraction is not obvious. But the beginning solidification length is greatly influenced by the casting temperature. The beginning solidification length increases with the increment of the casting temperature. The effect of the sloping angle on the solid fraction becomes obvious with the increment of the sloping plate length. The solid fraction increases sharply with the decrease of the initial thickness of the melt. The melt initial thickness between 15 and 20 mm is suggested.

Mathematic Model of SEN Clogging During Continuous Casting of Steel

The SEN clogging is a serious problem for continuous casting operation and steel quality.The kinetics mathematic model of SEN clogging during steel continuous casting is discussed.The fluid flow and inclusions motion are calculated by means of mathematic model.Effects of diameters of inclusions,roughness of nozzle,diameter of nozzle and casting speed on the entrapment probability are calculated and evaluated.The result shows that inclusions are more easily to attach to the nozzle by the following condition：smaller inclusion size,larger roughness of the wall and the smaller bulk velocity in the nozzle.