Initial Mathematical Model Research Articles

Linear stability of a supersonic boundary layer on a plate under conditions of vibrational excitation and of viscous stratification

An asymptotic theory of the neutral stability curve for a supersonic boundary layer of a vibrationally excited molecular gas on a plate is developed. The initial mathematical model of flow consists of equations of two-temperature viscous heat-conducting gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the inviscid and viscous parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In this case, the critical Reynolds number increases with excitation enhancement of the internal degrees of freedom of molecules, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number.

PENGEMBANGAN MODUL AJAR BERBASIS MULTIMEDIA PADA MATA KULIAH STATISTIKA PENDIDIKAN

This type of research is development research using the initial two-stage analysis and formative final analysis. The first stage of this research is called the Stage of Early Preliminary Analysis (front-end analysis) which aims to determine the mathematics learning goals that must be approved by students. This activity is followed by the distribution of mathematical learning compiled based on aspects of the use of computers as multimedia. Through justification, analysis and evaluation of competent mathematical education experts, the initial mathematical learning model was developed. The data for the research that I obtained was obtained from various studies, such as field observations, documentation and interviews. Analysis of the content of competencies in the curriculum and adapted to data on regulations, materials that can be made in learning mathematics in the field are important aspects in developing teaching materials. Furthermore, as a Formative Analysis Phase that aims to validate, analyze, test, develop, analyze, and revise the initial concept. This will be tested on several students as a sample to see more about the readability of the material that has been designed. Data for this device was obtained from questionnaires and interviews. This stage will produce a model of testing mathematics learning in the form of multimedia computer-based teaching materials. Based on the results of the study, it can be concluded that the overall validity of the validator 81.14 means included in the very valid category. Based on the table of trial calculations, obtained a very practical category with an overall result of 86.93%. This means that the learning media developed is very easy to use by students in the learning process. Keywords: Multimedia Learning, Development of Teaching Modules

МЕТОДИКА МОДЕЛИРОВАНИЯ РЕГИОНАЛЬНО ОБОСОБЛЕННОГО ЭЛЕКТРОТЕХНИЧЕСКОГО КОМПЛЕКСА

Актуальность исследования обусловлена необходимостью устранения разрыва между существующими подходами к моделированию изолированных систем электроснабжения и необходимостью учета динамических процессов в их физически разнородных подсистемах, образующих совокупность, при наличии слабых связей и слабых взаимодействий между единичными системами. Цель исследования: сконструировать проблемно-ориентированный численный метод, непосредственно применимый к математическим моделям совокупности изолированных систем электроснабжения и существенно превосходящий по критерию «время счета – точность счета» универсальные численные методы. Объект: электротехнический комплекс, состоящий из совокупности изолированных систем электроснабжения, объединенных слабыми связями и слабыми взаимодействиями. Методы. При анализе формы и структуры исходной математической модели совокупности электротехнических комплексов, состоящих из изолированных систем электроснабжения, объединенных слабыми связями и слабыми взаимодействиями, и при конструировании проблемно-ориентированного численного метода использованы: энергетический подход к построению математических моделей электротехнических комплексов и систем, теория численных методов решения жестких систем дифференциальных уравнений, корректные допущения при составлении математических моделей и компьютерное моделирование. Результаты. Введено в рассмотрение понятие «Регионально обособленный электротехнический комплекс», и выявлены его характерные признаки. Показана возможность создания новых алгоритмов управления «Регионально обособленным электротехническим комплексом», в целях снижения возможного экологического ущерба и средней расчётной себестоимости производства электроэнергии электростанциями, входящими в «Регионально обособленный электротехнический комплекс». Выявлена исходная структура математической модели «Регионально обособленного электротехнического комплекса». Показано принципиальное отличие структуры данной модели от модели в нормальной форме Коши. Обосновано принципиальное наличие свойств жесткости и сверхжесткости у анализируемого класса моделей. Сконструирован и реализован в программе BKM-3 проблемно ориентированный трехшаговый численный метод, применимый к исходной математической модели «Регионально обособленного электротехнического комплекса». Проведен численный эксперимент, показавший, на идеализированных математических моделях «Регионально обособленного электротехнического комплекса», существенное преимущество программы BKM-3, по критерию «время счета – точность счета» в области применимости.

Усредненная модель распространения малых возмущений в конфигурации упругое тело – пороупругая среда для двухскоростного континуума

The article continues the series of the authors’ papers devoted to averaging of mathematical models describing the isothermal acoustic processes in a heterogeneous medium with two components separated by a common boundary. One of these components is an elastic body, and the other is a poroelastic continuum. Poroelastic medium is understood to mean an elastic body permeated with a system of pores filled with liquid. The exact mathematical model constructed proceeding from the classical laws of continuum mechanics is used as the initial model. The model’s differential equations contain rapidly oscillating coefficients that appear in making transition to dimensionless variables. It is assumed that there are finite or infinite limits of these coefficients as the small parameter “epsilon” tends to zero. The small parameter “epsilon” is taken equal to the ratio of the average pore size to the characteristic size of the region under consideration. It should be noted that the coefficients of differential equations and the geometry of the considered region both depend on these parameters. Various averaged (limit) models that do not contain rapidly oscillating coefficients have been derived. For the possibility of using the averaging theory and the known averaging results, simplifying geometric assumptions about the periodicity and connectivity of the pore space and elastic skeleton are added. Averaged models are understood to mean such boundary value problems for equations or systems with relatively slowly changing characteristics that the solutions of boundary value problems for the initial models converge (in a sense) to the solution of the corresponding equations for the averaged model when the period e of the considered periodic structure tends to zero. Depending on the characteristics of the continuum (whether the fluid is viscous, low-viscous, compressible, or incompressible; whether the skeleton is highly deformable, elastic, perfectly rigid, etc.), different limit modes are obtained. One of cases involving weakly compressible and low viscous liquid and a weakly deformable elastic skeleton in one region and an elastic body in the other region is investigated. The original mathematical model reflects the real physical process in a fairly accurate manner, but is so complex that the standard averaging scheme does not work for it. Therefore, the two-scale convergence method is used as the main tool. On the one hand, it is often impossible to calculate the model’s limit modes even in terms of weak convergence, but it is possible to do so in terms of two-scale convergence. On the other hand, the sequence of solutions is usually bounded but not compact, and in this case the sequence weak limit is not a satisfactory approximation to the solution of the initial mathematical model, and it is more preferable to use a two-scale limit. The results for an individually taken poroelastic region or for a region occupied by an elastic body were presented in the authors’ previous papers. In the case considered, the joint motion of an elastic body and porous elastic medium is studied, and the main problem lies in deriving the conditions at the common boundary of the elastic and poroelastic regions.

Towards a Model-Based Experimental Design of the Maturation Process of Biohybrid Heart Valves

Model-based experimental designs minimize the experimental effort while maximizing the amount of analyzable experimental data. In this paper, an initial mathematical model of the spatially distributed maturation process of tissue engineered heart valves is developed for a model-based experimental design. The model contains the state variables cell amount, collagen concentration and elastin concentration. Based on the developed model, a variance-based sensitivity analysis using Sobol’s method is performed. The results indicate that all model parameters influence the model solution, while the variance of the parameters related to cell diffusion comprises an exceeding influence. Consequently, corresponding experiments should especially focus on those parameters.

DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems

BackgroundModels of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed.ResultsIn this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics.ConclusionThe presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future.

A spectral method for approximate solving a second-order linear differential equation

We suggest an approximate method for the linear differential equation x″(t) + 2αx′ (t) + Ax(t) = f(t), where A is an unbounded self-adjoint operator, α is a given scalar and the operator A − α21 is positive semidefinite. A priori estimates of the approximation error are obtained. The results of numerical experiments for the hyperbolic equation are presented. The suggested approach can be used in the remodeling problems for complicated objects and systems if the initial mathematical model is such an equation.

Thermoelectric properties determination of multilayered semiconductor materials at harmonic single-frequency excitation of temperature field

During several decades, interest in thermal electricity has rose rapidly [1,2]. Thermoelectric devices provide unique abilities and, therefore, are used in assemblies where any other way of direct or invert conversion of heat into electricity is difficult. For example, they are used for thermovisors cooling or combustion engines efficiency increasing [3,4]. The amount of thermal electricity application would significantly increase if thermoelectric converters efficiency will be increased up to 20-30%. The most promising variant of solution for the issue is the search for new materials with maximum possible thermoelectric figure of merit Z [5]. To achieve the high values of the parameter, it is necessary to ensure the lowest thermal conductivity of the material at the highest specific electrical conductivity and thermal electromotive force coefficient of a material. The materials with high Z are constantly searched for, at that, some new pages of material science and thermal electricity are discovered.When new materials are invented, the most important part of that process is produced samples performance tests. Most traditional measuring procedures show intrinsic shortcomings preventing valid data acquisition. Thereupon, we set the goal to develop the technology of accurate and quick measurements for integrated study of thermal and electrophysical qualities of thermoelectric materials. At that, it is supposed that all necessary characteristics of material will be measured simultaneously, the procedure shall be applicable for measurements within the range 100 - 450oK, moreover, for both homogeneous, and segmented branches of thermoelectric generators (TEG).This method is a kind of transient method and one of the easiest. Such methods were introduced as a class by Maldonado [6] for measuring both thermal conductivity and thermoelectric power of bulk materials. The advantages of these technics are good noise immunity, high information content, the ability to conduct experiments with small amplitude of electrical heating current, the independence of the measurement results from the initial temperature distribution and multiple process repeatability [7].At this stage, the initial mathematical model of our method is composed, its verification by means of numerical simulation is conducted, stand model for its experimental check is manufactured, and the first measurements performed.In this work, the principle of operation of the procedure in respect to the measurement of homogeneous sample thermal conductivity.

Holobionts as Units of Selection and a Model of Their Population Dynamics and Evolution

Holobionts, consisting of a host and diverse microbial symbionts, function as distinct biological entities anatomically, metabolically, immunologically, and developmentally. Symbionts can be transmitted from parent to offspring by a variety of vertical and horizontal methods. Holobionts can be considered levels of selection in evolution because they are well-defined interactors, replicators/reproducers, and manifestors of adaptation. An initial mathematical model is presented to help understand how holobionts evolve. The model offered combines the processes of horizontal symbiont transfer, within-host symbiont proliferation, vertical symbiont transmission, and holobiont selection. The model offers equations for the population dynamics and evolution of holobionts whose hologenomes differ in gene copy number, not in allelic or loci identity. The model may readily be extended to include variation among holobionts in the gene identities of both symbionts and host.

Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the “inviscid” and “viscous” parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

Mining routinely collected acute data to reveal non-linear relationships between nurse staffing levels and outcomes

ObjectivesNursing is a safety critical activity but not easily quantified. This makes the building of predictive staffing models a challenge. The aim of this study was to determine if relationships...

Modelling Characteristics Turning Processing for Want of Management by an Elastic Deformed Condition

For an accepted physical model with allowance of cutting “on a trace” phenomena, the initial mathematical model for want of processing non-rigid shafts is considered. In this model the improper rigidities of an elastic system are taken into account. In particular, pliability of a technological system on coordinate X in relation to cutting forces component on Y coordinate. Considered the individual models of dynamic system of turning machines for want of small rigidity shafts processing with management on the channel of additional managing force effects, which with a sufficient degree of an exactitude can be used in engineering accounts.

Assessment of stochastically updated finite element models using reliability indicator

Finite element (FE) model updating techniques have been a viable approach to correcting an initial mathematical model based on test data. Validation of the updated FE models is usually conducted by comparing model predictions with independent test data that have not been used for model updating. This approach of model validation cannot be readily applied in the case of a stochastically updated FE model. In recognizing that structural reliability is a major decision factor throughout the lifecycle of a structure, this study investigates the use of structural reliability as a measure for assessing the quality of stochastically updated FE models. A recently developed perturbation method for stochastic FE model updating is first applied to attain the stochastically updated models by using the measured modal parameters with uncertainty. The reliability index and failure probability for predefined limit states are computed for the initial and the stochastically updated models, respectively, and are compared with those obtained from the ‘true’ model to assess the quality of the two models. Numerical simulation of a truss bridge is provided as an example. The simulated modal parameters involving different uncertainty magnitudes are used to update an initial model of the bridge. It is shown that the reliability index obtained from the updated model is much closer to true reliability index than that obtained from the initial model in the case of small uncertainty magnitude; in the case of large uncertainty magnitude, the reliability index computed from the initial model rather than from the updated model is closer to the true value. The present study confirms the usefulness of measurement-calibrated FE models and at the same time also highlights the importance of the uncertainty reduction in test data for reliable model updating and reliability evaluation.

혼합정수계획법을 이용한 요격미사일의 할당 및 교전 일정계획에 관한 연구

This paper considers the allocation and engagement scheduling of air defense missiles by using MIP (mixed integer programming). Specifically, it focuses on developing a realistic MIP model for a real battle situation where multiple enemy missiles are headed toward valuable defended assets and there exist multiple air defense missiles to counteract the threats. In addition to the conventional objective such as the minimization of surviving target value, the maximization of total intercept altitude is introduced as a new objective. The intercept altitude of incoming missiles is important in order to minimize damages from debris of the intercepted missiles and moreover it can be critical if the enemy warhead contains an atomic or chemical bomb. The concept of so called the time window is used to model the engagement situation and a continuous time is assumed for flying times of the both missiles. Lastly, the model is extended to simulate the situation where the guidance radar, which guides a defense missile to its target, has the maximum guidance capacity. The initial mathematical model developed contains several non-linear constraints and a non-linear objective function. Hence, the linearization of those terms is performed before it is solved by a commercially available software. Then to thoroughly examine the MIP model, the model is empirically evaluated with several test problems. Specifically, the models with different objective functions are compared and several battle scenarios are generated to evaluate performance of the models including the extended one. The results indicate that the new model consistently presents better and more realistic results than the compared models.

Modelling of Dynamic System Characteristics of Deep Hole Drilling Process with Tools about Flexible Stifness

For an accepted physical model with allowance of cutting "on a trace" phenomena, the initial mathematical model for want of processing deep hole is considered. In the work has been presented principal assumption to modeling of vibrating process of deep hole drilling. To implement the process were used specially developed construction of waveguide transducer to generate the self-excited vibrations. The use of the transducer was aimed at increasing the efficiency of the process and improve the quality of performed hole. Performed model was used to process numerical researches to obtain the amplitude-phase characteristics of the drilling parameters. Then they were compared with the appropriate characteristics obtained from experimental studies.

Force control of semi‐active valve lag dampers for vibration reduction in helicopters

This study considers the design of a closed-loop force-tracking system for a semi-active damper, designed to be used to reduce in-plane vibrations caused by helicopter rotor blades during steady-state forward flight conditions. The study describes the development of the control law and includes details of (i) how the initial mathematical model of the system is adapted for controller design; (ii) how a non-linear dynamic inversion (NDI) control law is modified into a form suitable for implementation; and (iii) how the free parameters in the NDI controller can be optimised for various different operational modes. The success of the approach is demonstrated through both force-tracking simulations and also more comprehensive tests in which the controller is incorporated into a large-scale vibration simulation of the AgustaWestland 101 helicopter. The results show that the NDI-based controller can provide a satisfactory level of performance and hence greatly assist in the reduction of unwanted vibrations.

Dynamic modeling of behavior change

We consider a conceptual and quantitative modeling approach for investigating dynamic behavior change. While the approach is applicable to behavior change in eating disorders, smoking, substance abuse and other behavioral disorders, here we present our novel dynamical systems modeling approach to understand the processes governing an individual’s behavior in the context of problem drinking. Recent advances in technology have resulted in large intensive longitudinal data sets which are particularly well suited for study within such frameworks. However, the lack of previous work in this area (specifically, on the interand intra-personal factors governing drinking behavior of individuals) renders this a daunting and unique challenge. As a result, issues which are typically routine in mathematical modeling require considerable effort such as the determination of key quantities of interest, and the timescale on which to represent them. We discuss the construction of an initial mathematical model for two starkly distinct individuals and make a case for the potential for such efforts to help in understanding the underlying mechanisms responsible for behavior change in problem drinkers. AMS Subject Classification: 91E10, 34K29, 62G10.

A mathematical programming approach for walking-worker assembly systems

Purpose – It has become increasingly critical to design and maintain flexible and rapid assembly systems due to unpredictable and varying market conditions. The first stage of developing such systems is to restructure the existing assembly system. After designing the manufacturing system, efforts should be made for capacity adjustments to meet the demand in terms of allocating tasks to workers. Walking-worker assembly systems can be regarded as an effective method to achieve flexibility and agility via rabbit chase (RC) approach in which workers follow each other around the assembly cell or line and perform each task in sequence. In this paper, a novel mathematical programming approach is developed with the aim of integrating RC in assembly processes. Therefore, this study is thought to add value to industrial assembly systems in terms of effectively raising engineering control for task allocation activities. Design/methodology/approach – Two consecutive mathematical models are developed, since such a hierarchical approach provides computational convenience for the problem. The initial mathematical programming model determines the number of workers in each RC loop for each segment. In addition, the number of stations and the distribution of station times in the segments is essential. Therefore, the succeeding mathematical programming model generates stations in each segment and provides convenience for the workflow in RC loops. The output of mathematical programming models are the parameters of simulation model for performance assessment. Findings – The effectiveness of the proposed approach was validated by an application in a real-life chair production system. The application resulted in performance improvements for labour requirement (12.5 per cent) and production lead time (9.6 per cent) when compared to a classical assembly system design (CASD) where one stationary worker exists in each station. In addition, it is worth to note that RC leads to a reduced number of workers for a considerable number (39.4 per cent) of test problems. What is more, input as well as output factors have been determined via discriminant analysis and their impacts to the utilization of RC were analyzed for different levels. Practical implications – This study is thought to add value to the industry in terms of effectively providing convenience during production planning and task allocation in assembly lines and cells. Originality/value – To the best knowledge of the author, optimization models for RC considering a real industrial application have not yet been developed. In this context, this paper presents an approach which models RC by the use of mathematical programming in manual assembly processes to address this research gap. The contribution of the paper to the relevant literature is the development of hierarchical mixed integer linear programming models to solve RC problem for the first time.

Modeling and model predictive control of a nonlinear hydraulic system

This paper deals with modeling and control of a hydraulic three-tank system. A process of creating a computer model in the MATLAB/Simulink environment is described, and optimal PID (proportional–integral–derivative) and model predictive controllers are proposed. The modeling starts with the creation of an initial mathematical model based on a first-principles approach. Then, the initial model is enhanced to obtain better correspondence with a real-time system, and parameters of the modified system are identified from measurements. The real-time system contains nonlinearities which cannot be neglected, and therefore are identified and included in the final mathematical model. The resulting model is used for a control design. As the real-time system has long time constants, usage of the Simulink model dramatically speeds up the design process. Optimal PID and model predictive controllers (MPC) are proposed and compared. Model predictive controllers for both a linearized model and the nonlinear system are proposed. The techniques described are not limited to one particular modeling problem, but can be used as an illustrative example for the modeling of many technological processes.

Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla

Recent studies of three-dimensional architecture of rat renal inner medulla (IM) and expression of membrane proteins associated with fluid and solute transport in nephrons and vasculature have revealed structural and transport properties that likely impact the IM urine concentrating mechanism. These studies have shown that 1) IM descending thin limbs (DTLs) have at least two or three functionally distinct subsegments; 2) most ascending thin limbs (ATLs) and about half the ascending vasa recta (AVR) are arranged among clusters of collecting ducts (CDs), which form the organizing motif through the first 3-3.5 mm of the IM, whereas other ATLs and AVR, along with aquaporin-1-positive DTLs and urea transporter B-positive descending vasa recta (DVR), are external to the CD clusters; 3) ATLs, AVR, CDs, and interstitial cells delimit interstitial microdomains within the CD clusters; and 4) many of the longest loops of Henle form bends that include subsegments that run transversely along CDs that lie in the terminal 500 microm of the papilla tip. Based on a more comprehensive understanding of three-dimensional IM architecture, we distinguish two distinct countercurrent systems in the first 3-3.5 mm of the IM (an intra-CD cluster system and an inter-CD cluster system) and a third countercurrent system in the final 1.5-2 mm. Spatial arrangements of loop of Henle subsegments and multiple countercurrent systems throughout four distinct axial IM zones, as well as our initial mathematical model, are consistent with a solute-separation, solute-mixing mechanism for concentrating urine in the IM.