Mathematical Model for Tempering Time Effect on Quenched Steel Based on Hollomon Parameter

Through the differentiating and integrating process, a mathematical model for tempering time effect on quenched steel was derived based on the attribute of state function and the general equation of Hollomon parameter, which correlates the tempering hardness with the tempering time at different tempering temperature. Using the established model, the linear relationship between the tempering hardness and the tempering time in logarithm was proved theoretically, and the tempering hardness for various tempering time was reduced to the measurement and calculation of a hardness experiment tempered for 1 h at different tempering temperatures. Moreover, the hardness of steel 42CrMo and T8Mn tempered for various times at 200-600℃ was calculated using this method. The predicted results are in good agreement with those of the available experiments.

The Importance of Mathematical Models to Explore the Effects of Marijuana and Other Plant Based Products on Learning and Memory

This article describes the use of the first order system transfer function for learning and memory studies involving consumption of marijuana and other plant based products. We provide detailed instructions on how the model can be used to analyze the performance of individual participants using a memory test developed by the senior authors. The importance of identifying possible learning and memory deficits of marijuana is paramount due to the growing number of states in the U.S. legalizing marijuana use for medicinal and recreational purposes. The model can also be extended to other plant based products purported to improve memory. While this article does not study the effect of marijuana, we provide details on how it can be used by illustrating its application on individuals consuming an amphetamine-like psychostimulant drug using our own memory test.

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.

Mathematical model for precursor gas residence time in isothermal CVD process of C/C composites

In the chemical vapor deposition（CVD） process of C/C composites,the dynamics and mechanism of precursor gas flowing behavior were analyzed mathematically,in which the precursor gas was infiltrated by the pressure difference of the gas flowing through felt.Differential equations were educed which characterized the relations among the pressure inside the felt,the pressure outside the felt of the precursor gas and the porosity of the felt as a function of CVD duration.The gas residence time during the infiltration process through the felt was obtained from the differential equations.The numerical verification is in good agreement with the practical process,indicating the good reliability of the current mathematical model.

Monitoring models for base flow effect and daily variation of dam seepage elements considering time lag effect

Affected by external environmental factors and evolution of dam performance, dam seepage behavior shows nonlinear time-varying characteristics. In this study, to predict and evaluate the long-term development trend and short-term fluctuation of the dam seepage behavior, two monitoring models were developed, one for the base flow effect and one for daily variation of dam seepage elements. In the first model, to avoid the influence of the time lag effect on the evaluation of seepage variation with the time effect component of seepage elements, the base values of the seepage element and the reservoir water level were extracted using the wavelet multi-resolution analysis method, and the time effect component was separated by the established base flow effect monitoring model. For the development of the daily variation monitoring model for dam seepage elements, all the previous factors, of which the measured time series prior to the dam seepage element monitoring time may have certain influence on the monitored results, were considered. Those factors that were positively correlated with the analyzed seepage element were initially considered to be the support vector machine(SVM) model input factors, and then the SVM kernel function-based sensitivity analysis was performed to optimize the input factor set and establish the optimized daily variation SVM model. The efficiency and rationality of the two models were verified by case studies of the water level of two piezometric tubes buried under the slope of a concrete gravity dam.Sensitivity analysis of the optimized SVM model shows that the influences of the daily variation of the upstream reservoir water level and rainfall on the daily variation of piezometric tube water level are processes subject to normal distribution.

Modeling of Carrier-based Aircraft Ski Jump Take-off Based on Tensor

A general mathematical model of carrier-based aircraft ski jump take-off is derived based on tensor. The carrier, the aircraft body and the movable parts of the landing gears are treated as independent entities. These entities are assembled into a multi-rigid-body system with flexible links. Dynamical equations of each entity are derived on the basis of the Newton law and the Euler transformation. Using the invariance property of the tensor, the dynamical and kinematical equations are converted to tensor forms which are invariant under time-dependent coordinate transformations. Then the tensor-formed equations are expressed by the matrix operation. Differential equation group of the matrix form is formulated for the programming. The closure of the model is discussed, and the simulation results are given.

A Custom Manipulator for Dental Implantation Through Model-Based Design

This paper presents a Model-Based Design(MBD)approach for the design and control of a customized manipulator intended for drilling and position-ing of dental implants accurately with minimal human intervention.While performing an intra-oral surgery for a prolonged duration within a limited oral cavity,the tremor of dentist's hand is inevitable.As a result,wielding the drilling tool and inserting the dental implants safely in accurate position and orientation is highly challenging even for experienced dentists.Therefore,we introduce a customized manipulator that is designed ergonomically by taking in to account the dental chair specifications and anthropomorphic data such that it can be readily mounted onto the existing dental chair.The manipulator can be used to drill holes for dental inserts and position them with improved accuracy and safety.Further-more,a thorough multi-body motion analysis of the manipulator was carried out by creating a virtual prototype of the manipulator and simulating its controlled movements in various scenarios.The overall design was prepared and validated in simulation using Solid works,MATLAB and Simulink through Model Based Design(MBD)approach.The motion simulation results indicate that the manipulator could be built as a prototype readily.

Modeling and Control of Time-pressure Dispensing for Semiconductor Manufacturing

To improve the consistency of the adhesive amount dispensed by the time-pressure dispenser for semiconductor manufacturing, a non-Newtonian fluid flow rate model is developed to represent and estimate the adhesive amount dispensed in each cycle. Taking account of gas compressibility, an intelligent model-based control strategy is proposed to compensate the deviation of adhesive amount dispensed from the desired one. Both simulations and experiments show that the dispensing consistency is greatly improved by using the model-based control strategy developed in this paper.

Computer-based Creativity Enhanced Conceptual Design Model for Non-routine Design of Mechanical Systems

Computer-based conceptual design for routine design has made great strides, yet non-routine design has not been given due attention, and it is still poorly automated. Considering that the function-behavior-structure（FBS） model is widely used for modeling the conceptual design process, a computer-based creativity enhanced conceptual design model（CECD） for non-routine design of mechanical systems is presented. In the model, the leaf functions in the FBS model are decomposed into and represented with fine-grain basic operation actions（BOA）, and the corresponding BOA set in the function domain is then constructed. Choosing building blocks from the database, and expressing their multiple functions with BOAs, the BOA set in the structure domain is formed. Through rule-based dynamic partition of the BOA set in the function domain, many variants of regenerated functional schemes are generated. For enhancing the capability to introduce new design variables into the conceptual design process, and dig out more innovative physical structure schemes, the indirect function-structure matching strategy based on reconstructing the combined structure schemes is adopted. By adjusting the tightness of the partition rules and the granularity of the divided BOA subsets, and making full use of the main function and secondary functions of each basic structure in the process of reconstructing of the physical structures, new design variables and variants are introduced into the physical structure scheme reconstructing process, and a great number of simpler physical structure schemes to accomplish the overall function organically are figured out. The creativity enhanced conceptual design model presented has a dominant capability in introducing new deign variables in function domain and digging out simpler physical structures to accomplish the overall function, therefore it can be utilized to solve non-routine conceptual design problem.

Mathematical model of flow characteristic in multi-strand continuous casting tundishes

In this paper, the subject of mathematical model is a series of math expressions, which is used to calculate different regions＇ volume fraction and analyze flow characterization in multi-strand tundish. But research about mathematical model for multi-strand tundish is few, and so far, there has been no acknowledged math model for multi- strand tundish to describe its flow characteristic. If Sahai＇s model, which is originally proposed for the case of single-strand tundish （proposed in reference, and this model is widely used in the world）, is applied to describe flow feature in multi-strand tundish, the calculation results would be unreasonable. Based on the data of watermodel experiment results, the sum of each strand＇s dead region＇s volume fraction is bigger than 100%, and this obviously doesn＇T agree with reality; and the value of dead region＇s volume fraction is calculated to be minus according to mathematical simulation results data in another case. What＇s more, Sahai＇s model does not propose the standard of plotting the RTD-curve, and this makes scholars around the world can＇t achieve consensus of views about plotting RTD-curve. And the model doesn＇t consider the bypass flow and can＇t calculate its volume fraction, but bypass flow is critical to tundish metallurgy. And through Sahai＇s model, the calculation result of plug flow region＇s volume fraction is also not reasonable, because the model doesn＇t well describe the essence of plug flow. So these suggest that it is not reliable to apply Sahai＇s single-strand tundish model to multi-strand tundish case. Then a new model is attempted to propose in this paper for your discussion. In the new model, the standard of plotting RTD curve is definitely proposed, and relative calculation method is also proposed; and the feature of dead region is carefully studied and the model proposes a new method to calculate its volume fraction, and the calculation formula about its volume fraction can be adjustable according the actual demand; what＇s more, the new model considers the bypass flow and proposes a method to calculate its volume fraction for the first time, and then volume fraction of plug flow region, backmix flow region, dead region and bypass flow can be calculated and obtained at the same time; and this new model can better capture the deviation of reality flow pattern from ideal plug flow pattern, and reflects the feature of plug flow.

Feedback Scheduling of Model-based Networked Control Systems with Flexible Workload

In this paper,a novel control structure called feedback scheduling of model-based networked control systems is proposed to cope with a flexible network load and resource constraints.The state update time is adjusted according to the real-time network congestion situation.State observer is used under the situation where the state of the controlled plant could not be acquired.The stability criterion of the proposed structure is proved with time-varying state update time.On the basis of the stability of the novel system structure,the compromise between the control performance and the network utilization is realized by using feedback scheduler. Examples are provided to show the advantage of the proposed control structure.

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.

Surging footprints of mathematical modeling for prediction of transdermal permeability

In vivo skin permeation studies are considered gold standard but are difficult to perform and evaluate due to ethical issues and complexity of process involved. In recent past, a useful tool has been developed by combining the computational modeling and experimental data for expounding biological complexity. Modeling of percutaneous permeation studies provides an ethical and viable alternative to laboratory experimentation. Scientists are exploring complex models in magnificent details with advancement in computational power and technology. Mathematical models of skin permeability are highly relevant with respect to transdermal drug delivery, assessment of dermal exposure to industrial and environmental hazards as well as in developing fundamental understanding of biotransport processes.Present review focuses on various mathematical models developed till now for the transdermal drug delivery along with their applications.

Dose prediction of lopinavir/ritonavir for 2019-novel coronavirus (2019-nCoV) infection based on mathematic modeling

Wuhan novel coronavirus or 2019-novel coronavirus(2019-nCoV)infection is a rapidly emerging respiratory viral disease[1].2019-nCoV infection is characterized as febrile illness with possible severe lung complication[1].The disease was firstly reported in China in December 2019 and then spread to many countries(such as Thailand,Japan and Singapore)[2,3].As a new disease,there is a limited knowledge of treatment for the infection.Lu recently proposed that some drug might be useful in treatment of 2019-nCoV infection[3].

Variation in Thermal time model Parameters Between Two Contrasting Chickpea (<i>Cicer arietinum</i>) cultivars

A laboratory experiment was carried out to determine the effect of different constant temperatures on germination and early seedling establishment and to study the variation among parameters of thermal time model parameters for two contrasting chickpea cultivars . Seeds were subjected to six constant temperatures from 10 o C to 35 o C . A complete randomized design was used with four replication. Analysis of variance showed significant differences among treatments for all characters studied. The final germination percentage significantly increased with increasing temperature up to 25 ° C, and thereafter there was a sharp decrease in final germination at 30 ° and 35 ° C. Desi type cultivar (small seeded) “Jabel Marra” significantly exhibited higher final germination percentage and lower germination rate compared with the kabui type cultivar “Shendi” at all temperatures. The median (θ T(50) ) of the thermal time was significantly differ between the two chickpea cultivars. The large seeded cultivars (shendi) recorded significantly higher median thermal time than the small seeded cultivars (Jabel Marra). The results also revealed a significant differences between the two cultivars in all thermal time model parameters. The small seeded cultivar (Jabel Marra) scored lower total dry matter and temperature tolerance index (TTI) compared to the large seeded cultivar (Shendi) at all temperatures studied.

Quantitative evaluation of lateral sealing of extensional fault by an integral mathematical-geological model

To evaluate the lateral sealing mechanism of extensional fault based on the pressure difference between fault and reservoir, an integral mathematical-geological model of diagenetic time on diagenetic pressure considering the influence of diagenetic time on the diagenetic pressure and diagenetic degree of fault rock has been established to quantitatively calculate the lateral sealing ability of extensional fault. By calculating the time integral of the vertical stress and horizontal in-situ stress on the fault rock and surrounding rock, the burial depth of the surrounding rock with the same clay content and diagenesis degree as the target fault rock was worked out. In combination with the statistical correlation of clay content, burial depth and displacement pressure of rock in the study area, the displacement pressure of target fault rock was calculated quantitatively. The calculated displacement pressure was compared with that of the target reservoir to quantitatively evaluate lateral sealing state and ability of the extensional fault. The method presented in this work was used to evaluate the sealing of F_(1), F_(2) and F_(3) faults in No.1 structure of Nanpu Sag, and the results were compared with those from fault-reservoir displacement pressure differential methods without considering the diagenetic time and simple considering the diagenetic time. It is found that the results calculated by the integral mathematical-geological model are the closest to the actual underground situation, the errors between the hydrocarbon column height predicted by this method and the actual column height were 0–8 m only, proving that this model is more feasible and credible.

A New Activity-Based Cost (ABC) Mathematical Model

Along with the product price competition growing intensely, it is apparently important for reasonably distributing and counting cost. But, in sharing indirect cost, traditional cost accounting unveils the limitations increasingly, especially in authenticity of cost information. And the accounting theory circles and industry circles begin seeking one kind of new accurate cost calculation method, and the activity based cost (ABC) method emerges as the times require. In this paper, we will build its mathematical model by the basic principle of ABC, and will improve its mathematical model further. We will establish its comparison mathematical model and make the ABC method go a step further to its practical application.

A Theoretical Model of pH-Based Potentiometric Biosensor Based on Immobilized Enzyme Membrane

A theoretical model for the non steady-state response of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase (OPH) is discussed. The model is based on a system of five coupled nonlinear reaction-diffusion equations under non steady-state conditions for enzyme reactions occurring in potentiometric biosensor that describes the concentration of substrate and hydrolysis products within the membrane. New approximate analytical expressions for the concentration of the substrate (organophosphorus pesticides (OPs)) and products are derived for all values of Thiele modulus and buffer concentration using new approach of homotopy perturbation method. The analytical results are also compared with numerical ones and a good agreement is obtained. The obtained results are valid for the whole solution domain.

Mathematical Model for Electroslag Remelting Process

A mathematical model, including electromagnetic field equation, fluid flow equation, and temperature field equation, was established for the simulation of the electroslag remelting process. The distribution of temperature field was obtained by solving this model. The relationship between the local solidification time and the interdendritic spacing during the ingot solidification process was established, which has been regarded as a criterion for the evaluation of the quality of crystallization. For a crucible of 950 mm in diameter, the local solidification time is more than 1 h at the center of the ingot with the longest interdendritic spacing, whereas it is the shortest at the edge of the ingot according to the calculated results. The model can be used to understand the ESR process and to predict the ingot quality.

Equivalent series system to model a multiple friction pendulum system with numerous sliding interfaces for seismic analyses

Current structural analysis software programs offer few if any applicable device-specifi c hysteresis rules or nonlinear elements to simulate the precise mechanical behavior of a multiple friction pendulum system(MFPS) with numerous sliding interfaces.Based on the concept of subsystems,an equivalent series system that adopts existing nonlinear elements with parameters systematically calculated and mathematically proven through rigorous derivations is proposed.The aim is to simulate the characteristics of sliding motions for an MFPS isolation system with numerous concave sliding interfaces without prior knowledge of detailed information on the mobilized forces at various sliding stages.An MFPS with numerous concave sliding interfaces and one articulated or rigid slider located between these interfaces is divided into two subsystems: the fi rst represents the concave sliding interfaces above the slider,and the second represents those below the slider.The equivalent series system for the entire system is then obtained by connecting those for each subsystem in series.The equivalent series system is validated by comparing numerical results for an MFPS with four sliding interfaces obtained from the proposed method with those from a previous study by Fenz and Constantinou.Furthermore,these numerical results demonstrate that an MFPS isolator with numerous concave sliding interfaces,which may have any number of sliding interfaces,is a good isolation device to protect structures from earthquake damage through appropriate designs with controllable mechanisms.