Comparison on Mathematical Models for Description of Flow Curves of Stable Austenitic Steels

The flow curves were measured for the stable austenitic steels 304L and 304LN by means of tensile test at room temperature,which are described by the models σ=K1εn1 + exp(K2 + n2ε), σ=Kεn1+n2lnε and σ=σ0+Kεn (where, K1, K2, n1 andn2; K, n1 and n2; σ0, K and n are constant). The comparison of the maximum deviations and the consideration of thevariation of the work hardening rate with true strain show that the flow curves for the austenitic steels 304L and 304LN canbe described by the model σ=Kεn1+n2 lnε at higher precision.The derivatives of the models σ=K1εn1 + exp(K2 + n2ε) and σ=Kεn1+n2lnε with respect to true strain, exhibit theextreme at low true strain. This inherent character indicates that both models are unsuitable to describe the part of the workhardening rate curve at low true strain.

Mathematical Modelling of Carbonitride Precipitation during Hot Working in Nb Microalloyed Steels

Based on thermodynamics and kinetics, precipitation behavior of microalloyed steels was analyzed. Deformation greatly promotes isothermal carbonitride precipitation and makes C-curve shift leftwards. The position and shape of C-curve also depend on the content of Nb and N. C-curve shifts leftwards a little when N content increases and the nose temperature is raised with increasing Nb content. Deformation shortened precipitation start time during continuous cooling, raised precipitation start temperature, accelerated precipitation kinetics of carbonitrides. With decreasing the finishing temperature and coiling temperature, the precipitates volume fraction increases and strength increment is raised during hot rolling. The simulated results are in agreement with experiment results.

A dynamic soil freezing characteristic curve model for frozen soil

The soil freezing characteristic curve(SFCC)plays a fundamental role in comprehending thermohydraulic behavior and numerical simulation of frozen soil.This study proposes a dynamic model to uniformly express SFCCs amidst varying total water contents throughout the freezing-thawing process.Firstly,a general model is proposed,wherein the unfrozen water content at arbitrary temperature is determined as the lesser of the current total water content and the reference value derived from saturated SFCC.The dynamic performance of this model is verified through test data.Subsequently,in accordance with electric double layer(EDL)theory,the theoretical residual and minimum temperatures in SFCC are calculated to be-14.5℃to-20℃for clay particles and-260℃,respectively.To ensure that the SFCC curve ends at minimum temperature,a correction function is introduced into the general model.Furthermore,a simplified dynamic model is proposed and investigated,necessitating only three parameters inherited from the general model.Additionally,both general and simplified models are evaluated based on a test database and proven to fit the test data exactly across the entire temperature range.Typical recommended parameter values for various types of soils are summarized.Overall,this study provides not only a theoretical basis for most empirical equations but also proposes a new and more general equation to describe the SFCC.

An improved model of partition curve based on accumulation normal distribution function

Extensive studies based on partition curve of gravity separation have been investigated. All created models are merely used to simulate density distribution at the same size fraction. However, they cannot be used to predictive distribution of materials depending on compound feature of density and size. According to this situation, an improved model of partition curve based on accumulation normal distribution, which was distinguished from conventional model of accumulation normal distribution for partition curve, was proposed in this paper. It could simulate density distribution at different size fractions by using the density-size compound index and conflating the partition curves at different size fractions as one partition curve. The feasibility of three compound indexes, including mass index, settlement index and transformation index, were investigated. Specific forms of the improved model were also proposed. It is found that transformation index leads to the best fitting results, while the fitting error is only 1.75 according to the fitting partition curve.

Mathematical model to predict COVID-19 mortality rate

Objective:Covid-19 is a highly contagious viral infection that has recently become a pandemic.Since the beginning of the pandemic,the disease has affected millions of people and taken many people's lives.The purpose of this paper is to predict and compare the number of cases and mortality rate due to Covid-19 every quarter in 2020 and 2021 in three countries:Iran,the United States,and South Korea.Materials and methods:The data of this study include the mortality rate of different countries of the world due to Covid-19,which has been approved by the World Health Organization(WHO).In this paper,to develop the mathematical model for mortality rate prediction,the data of the countries of Iran,the United States,and South Korea during the last two years from March 1,2020,to March 1,2022,have been used.In addition,the mortality trend was modeled using the MATLAB software toolbox version 2022b.During modeling,six methods including Fourier,Interpolant,Gaussian,Polynomial,Sum of Sine,and Smoothing Spline were implemented.Root Mean square error(RMSE)and final prediction error were used to evaluate the performance of these proposed methods.Results:As a result of the analysis,it was shown that the Smoothing Spline model with the lowest error rate was capable of accurately evaluating and predicting Covid-19 incidence and mortality rate.Using RMSE,a prediction of the Covid-19 mortality rate for three countries is 3.76498×10^(-5).The values of R-Square and Adj R-sq were 1 in all the experiments,which indicates the full compliance of the prediction model.Conclusion:Using the proposed method,the incidence rate and mortality rate can be properly assessed and compared with each other in three countries.This provides a better view of the progression of the coronavirus outbreak in spring,summer,autumn,and winter.By using the proposed method,governments will be able to prevent disease and alert people to follow health guidelines more closely,thereby reducing infection numbers and mortality rates.

THEORETICAL FLOATABILITY CURVE OF COAL AND ITS MODEL

On the basis of the float-and-sink analysis and the timed-release analysis, a new theoretical floatability curve of coal has been advanced. By means of fitting to a lot of data, a model of theoretical floatability curve has been set up. The characteristics of curve and how to achieve standardization were discussed.

Mathematical modeling of microwave-assisted convective heating and drying of grapes

This research studied the processing performance and product quality of Thompson seedless grapes dried using microwave-assisted convective hot air drying as well as the effect of blanching and dipping pretreatments.Two pretreatment methods were compared,dipping into 2%ethyl oleate(V/V)and 5%potassium carbonate solution(m/V)at 40℃for 3 minutes and steam blanching at 90℃for 140 s,to accelerate drying rate and inactivate PPO aiming to improve drying rate and product color.Pretreated grapes were dried in a microwave-assisted convective dryer at 0.25 W/g specific power and 60℃air temperature.In this study dielectric and physical properties of grapes were calculated using descriptive equations for fruits and vegetables.Semi-theoretical models were used to describe the drying curves of both pretreated and untreated grapes.Center and near surface temperature profile of grapes was obtained using fiber optic probes.Experimental center temperature was modeled using one dimensional heat equation and was simulated using Partial Differential Equation toolbox of Matlab.The results showed that the maximum difference between experimental and predicted values were 4℃which occurred at the initial heating up period.It has been observed that dipping into solution had no effect on drying rate whereas steam blanching significantly reduced the drying time and produced product with desirable color.

Cutting edge curve models for equal pitch cutters and their applications

A mathematic model is established using infinitesimal geometry for the cutting edge design of special milling cutters which use equal lead helix as cutting edges; equations are given for front-end and proclitic surface of revolution of ball pillar milling cutters, ball taper milling cutters and angularly conical milling cutters; and corresponding models are established for the continuity cutting edge curves of milling cutters. Typical examples are given to illustrate the applications of mathematic models, which prove the correctness and applicability of these geometric models.

Modeling and Simulations in Symmetrical Supercapacitors Using Time Domain Mathematical Expressions

This study presents the deduction of time domain mathematical equations to simulate the curve of the charging process of a symmetrical electrochemical supercapacitor with activated carbon electrodes fed by a source of constant electric potential in time ε and the curve of the discharge process through two fixed resistors. The first resistor RCo is a control that aims to prevent sudden variations in the intensity of the electric current i1(t) present at the terminals of the electrochemical supercapacitor at the beginning of the charging process. The second resistor is the internal resistance RA of the ammeter used in the calculation of the intensity of the electric current i1(t) over time in the charging and discharging processes. The mathematical equations generated were based on a 2R(C + kUC(t)) electrical circuit model and allowed to simulate the effects of the potential-dependent capacitance (kUC(t)) on the charge and discharge curves and hence on the calculated values of the fixed capacitance C, the equivalent series resistance (ESR), the equivalent parallel resistance (EPR) and the electrical potential dependent capacitance index k.

Research on cubic polynomial acceleration and deceleration control model for high speed NC machining

To satisfy the need of high speed NC (numerical control) machining, an acceleration and deceleration (acc/dec) control model is proposed, and the speed curve is also constructed by the cubic polynomial. The proposed control model provides continuity of acceleration, which avoids the intense vibration in high speed NC machining. Based on the discrete characteristic of the data sampling interpolation, the acc/dec control discrete mathematical model is also set up and the discrete expression of the theoretical deceleration length is obtained furthermore. Aiming at the question of hardly predetermining the deceleration point in acc/dec control before interpolation, the adaptive acc/dec control algorithm is deduced from the expressions of the theoretical deceleration length. The experimental result proves that the acc/dec control model has the characteristic of easy implementation, stable movement and low impact. The model has been applied in multi-axes high speed micro fabrication machining successfully.

The universal applicability of logistic curve in simulating ecosystem carbon dynamic

As an S-shaped curve,the logistic curve has both high and low limit,which provides advantages in modelling the influences of environmental factors on biogeological processes.However,although the logistic curve and its transformations have drawn much attention in theoretical modelling,it is often used as a classification method to determine a true or false condition,and is less often applied in simulating the real data set.Starting from the basic theory of the logistic curve,with observed data sets,this paper explored the new application scenarios such as modelling the time series of environmental factors,modelling the influence of environmental factors on biogeological processes and modelling the theoretical curve in ecology area.By comparing the performance of traditional model and the logistic model,the results indicated that logistic modelling worked as well as traditional equations.Under certain conditions,such as modelling the influence of temperature on ecosystem respiration,the logistic model is more realistic than the widely applied Lloyd-Taylor formulation under extreme conditions.These cases confirmed that the logistic curve was capable of simulating nonlinear influences of multiple factors on biogeological processes such as carbon dynamic.

Predicting the Tensile Curve of Polyester Twisted Ply Yarn under Large Deformation

Considering the changes of ply yarn 's structure parameters during the axial extension,a new model has been proposed for predicting the tensile curve of polyester twisted ply yarn under large deformation without the tensile strength tests.The relationships between the structural parameters and tensile properties under large deformation were considered.The feasibility and accuracy of the model were studied by comparing the predictive results and the experimental ones.The structural parameters in the model were acquired under every strain before rupture.The radial dimension and twist angle of the yarn were obtained by an observation platform and image processing technique.The true modulus of the yarn was obtained indirectly from the tensile data of the single yarn and the mathematical equations.The tensile curves of the yarns at different twist levels for predicting were plotted.The results demonstrated that the predicted curve tendency and the values were quite close to the experimental ones.The model exhibited a good applicability to predict the tensile curves for low and medium twist yarns.

A fast commonly-used algorithm of P-III distribution curve and its application

Based on theoretical analysis and studying other methods, P-III curve is transformed into an incomplete G function by means of mathematical expression transformation, thus the mathematical model of the fast commonly-used algorithm is drawn out. Algorithm comparison and practices demonstrate that the mathematical model has an easy algorithm, agile resolution process, very good commonality, faster convergence rate and better calculation accuracy, and can be applied to other respects.

Application of Tracer Model in the Remaining Oil Distribution of 95 Block Oilfields of Central Plains

With the development and utilization of oil and gas fields, oil mining become more and more difficult. The remaining re- serves of oil in the oil distribution is difficult to confirm, in order to understand and grasp the distribution of the remaining oil in the reser-voir, calculated using tracer concentration methods used mathematical models to calculate the residual oil saturation in the reservoir, from the theoretical analysis of tracer migration process, you can more accurately determine the distribution of the remaining oil, this method has good prospects for development.

Recognition Methods of Geometrical Images of Automata Models of Systems in Control Problem

The laws of functioning of discrete deterministic dynamical systems are investigated,presented in the form of automata models defined by geometric images.Due to the use of the apparatus of geometric images of automata,developed by V.A.Tverdokhlebov,the analysis of automata models is carried out on the basis of the analysis of mathematical structures represented by geometric curves and numerical sequences.The purpose of present research is to further develop the mathematical apparatus of geometric images of automaton models of systems,including the development of new methods for recognizing automata by their geometric images,given both geometric curves and numerical sequences.

Sauna Technique, Drying Kinetic Modeling and Effectiveness on Solar Drying Compared with Direct Drying in Drying Process of <i>Kappaphycus striatum</i>in Selakan Island Malaysia

A sauna drying technique—the solar drier was designed and imposed, constructed and tested for drying of seaweed. The seaweed moisture content was decreased around 50% in 2-day sauna. Kinetic curves of drying of seaweed were known to be used in this system. The non-linear regression procedure was used to fit three different drying models. The models were compared with experimental data of red seaweed being dried on the daily average of air temperature about 40℃. The fit quality of the models was evaluated using the coefficient of determination (R2), Mean Bias Error (MBE) and Root Mean Square Error (RMSE). The highest values of R2 (0.99027), the lowest MBE (0.00044) and RMSE (0.03039) indicated that the Page model was the best mathematical model to describe the drying behavior of sauna dried seaweed. The percentage of the saved time using this technique was calculated at 57.9% on the average solar radiation of about 500 W/m2 and air flow rate of 0.056 kg/s.

Applications of Chapman-Richards model to geotechnical engineering

In this paper,the Chapman-Richards model is adapted to best fit three types of nonlinear curves that are generally encountered in geotechnical engineering practices,i.e.the degree of consolidation versus time factor curves in one-dimensional consolidation and plane strain consolidation under strip loading,the compressibility and permeability curves of soft clay,and the geometry parameters of geosynthetic tube versus pumping pressure curves.The methods of determining unknown parameters using the Chapman-Richards model are fully demonstrated.It is found that the Chapman-Richards model has its range of applications in geotechnical engineering and may provide unique insights into the complexity of geotechnical problems.

A NEW APPROACH TO THE CURVE FITTING OF IN VITRO RADIOASSAYS BASED ON THE MASS ACTION LOW

A new curve fitting method with its mathematical models derived from the mass action law is presented which is applicable to several in vitro radioassays including RIA and RBA. Experiments revealed that the robustness of this method is better than the conventional methods like Woolf plot in RBA and 4- parameter logistic plot in RIA. However, the robustness of this method is only relative: in some cases of RIA and RBA, the bias of the results may still be too large to be acceptable. Further improvement is expected to be studied.

Application of Curved Surface of Ball Movement in Hydraulic Engineering

The curved surface of ball movement is a connecting bent pipe commonly used in hydraulic engineering. The curved surface poses a complicated problem with computation. The mathematic model of the circular curved surface of ball movement in engineering is set up by adopting the concept of envelope curved surface.