Mathematical Modeling
Vol. 5 (2021), Issue 1

Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • Use of algorithms in semaphoric regulation. Tirana, Durrës case

      pg(s) 13-16

      In the design phase of transport systems, a significant step is also the traffic light regulation. In world practice, to evaluate the efficiency of the proposed theoretical methods, experiments on test transport systems and on real systems are carried out. The obtained results allow for the confrontation between different methods and the definition of those to be used in professional practice. For the semaphorical adjustment project, the algorithms proposed by the world literature were used in test networks with a non-large number of defining variables, so with as much semaphorized crossings in the project. This small number of variables makes it possible to find the optimal solution of the problem and evaluate how much the proposed approximation approaches this solution. While for the common topology project and traffic light regulation, algorithms were experimented in real transport systems. For this we chose two areas with about 60,000 inhabitants, respectively in Tirana and Durres. Since many of the half hypotheses used in the phase when acting on topology variables depend on one or several parameters, different values were used in order to reach their calibration . Next, the algorithms, with the calibrated parameters, will be used in another city. But this will be the subject of a future study.

    • On the question of the rational distribution of power between the hydrostatic and hydrodynamic branches of the complex steering mechanism for the tracked vehicle

      pg(s) 17-20

      The article presents a description of the mathematical model of the curvilinear movement of a tracked vehicle with a complex steering mechanism, which contains a control hydrostatic branch and an additional hydrodynamic branch for unloading the first. The adequacy of the presented mathematical model was verified by calculating the characteristics of the turn in place of the Leop ard-2 tank. The resulting tool can become the basis for parametric optimization of similar steering mechanisms for tracked vehicles.

    • Engine model for control concepts and e-fuel identification for recreational vehicles and hand-held tools

      pg(s) 21-26

      Mean value models are essential for developing control engineering methods, e.g., speed control concepts, failure monitoring features. This work briefly summarizes the main parts of such a second-order mean value model, suitable for control engineering purposes. The nonlinear model is linearized around one operating point, and a linear state controller is designed, both for single-input and multipleinput, without and with an integral component to eliminate steady-state deviations. Limitations of the proposed linear control concepts, potential advantages of nonlinear flatness-based control concepts, and possible extensions of the model for fuel identification are discussed in the outlook.

    • Optimal design of an integrated 1st generation biodiesel / diesel supply chain based on solid waste management for energy efficiency improvement

      pg(s) 27-30

      The transport sector is a major consumer of diesel fuel, which ranks it among the main greenhouse gas (GHG) emissions generators. They can be reduced by gradually introducing biofuels into transport fuels and their share is expected to increase over the years. However, full sustainability can only be achieved by simultaneously consideration of all stages of the product life cycle with a tendency to close it, by utilization of solid waste by-products to improve the energy efficiency of considered biofuel production.
      This study proposes an approach for optimal design of an Integrated Biodiesel/Diesel Supply Chain (IBDSC) based on 1st generation feedstock, taking into account the impact of the used feedstock for its energy efficiency improvement. It based on mathematical models of the environmental and economic impact of the considered IBDSC. The latter are included in an optimization problem for determination of optimal number, size and location of bio refineries and solid waste facilities; areas and quantities of raw materials needed for the production of biodiesel and mode of transport. Two optimization criteria are defined: environmental – minimum generated GHG emissions from IBDSC operation and economic – the total annual costs optimization criteria. The problem is solved if either at one of the two criteria, or at an integrated environmental and economic criterion. The approach involves an additional analysis of different feedstock as well as useful byproducts. Based on this analysis, the sunflower has been selected as the most appropriate feedstock which can be used as a generator of a useful by-product – sunflower husks. The obtained optimal amount of sunflower husks generated in the production of tons of biodiesel is 0.431(/.). They are used to produce the required amount of heat in biorefineries, where there are plants for burning flakes and is 0.215(/.). The remaining amount of sunflower husks is used for the production of pellets. When using an integrated environmental-economic optimization criterion, the following results are obtained – 33.4% of sunflower husks are used for the production of pellets, and 66.6% for the production of heat in biorefineries. This would have a positive impact on the formation of the final price of biodiesel.

    • Features of modeling of ultralow power electric fields

      pg(s) 31-35

      The article presents the results of modeling quasi-stationary ultralow power electric fields (the order of tens of nanowatts) and establishes ranges of rational values of parameters (average density of electric voltage, specific potential) of these fields. As a result of mathematical modeling (based on a system of Gaussian equations) and subsequent numerical experiment, it is shown that an instantaneous increase in the average electric density of a quasi-static electric field in 2 times in one part of the field leads to an increase in charge redistribution time from 34 ns (at an initial density of electric tension of 17 nN/Ku.μm 3) to 189 ns (at a density of electric tension of 145 nN/Ku.μm3). This redistribution allows us to determine the range of rational values of the specific potential, which is 1.1… 9 nV/μm 2. In this case, the maximum specific power that can occur in such a field is 0.5… 0.77 nW/μm 2.

    • Contact heat transfer in the foundry – Tunnel effect

      pg(s) 36-39

      Mathematical methods of quantum mechanics are needed to describe the contact phenomena of the boundary casting/mold. Apart from the macro-level, the contact phenomena are part of the technological processes first order phase transition and second order phase transition. Need for professional software for mathematical simulation at macro- and micro-level in foundry. Education in basic mathematics and mathematical physics is also required for engineers. The branch machine-building infrastructure must develop a mechanism for inclusion in the computing infrastructure of the micro-foundries.

  • MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

    • Newtonian mechanics inertial conception of microeconomical systems

      pg(s) 40-45

      The study of the activities of microeconomic systems always remains a very important task of quantitative description of these systems. The proposal of new methods of study over time takes place in the emergence of new integrative scientific platforms such as econophysics which is a modern platform based on the description of economic phenomena by the application of classical and modern theories of physics. The microeconomic system of goods in general is characterized by the possession of some quantity of good s that is a potential for the revenues generating as the result of customer demands. The quantity of goods evolves over time as if it is a “trajectory” according to the theory of classical mechanics. This trajectory in economic terms is called the trend.
      The system “moves” on this trajectory and the movement takes place under the action of the forces acting on the system. This study delimits the following names of the forces acting on the microeconomic system. The first type of the force acting from the customers is called the driving force Fm .For the stable efficient continuation of the system over time, it is necessary both the permanent insurance with goods from the distributors and the payments in the form of salaries and other various taxes, all being expenses that are generally categorized in assets and liabilities. And they will be called in economic terms with a general term friction forces Ffr. These friction forces stop the numerical increase of the revenues in general.
      A special case belongs to the movement on a constant trend (case of uniform rectilinear movement). This case occurs when the driving force of customers is equal to all types of resistance force (all types of the payments in the form of various taxes and salaries). It should be noted that when all the free financial resources that come from the sale are all spent on new goods from distributors as well as other taxes and wages then it really seems that the system seems to be “in the rest state” (“does not move”) This is Newton’s first law, the respective speed and the acceleration is zero..
      The mechanical conception of the description of the activity of microeconomic systems allows understanding deeply the mechanisms of the generation of bankruptcy as well as the special conditions necessary for income generation by the application of the physics language of Newtonian mechanics movement.

    • Example of an accident reconstruction with Virtual Crash software and the mathematical simulation of this accident situation at intersection

      pg(s) 46-47

      The paper presents an example of an accident situation using Virtual Crash software in the reconstruction of a high-speed sideimpact accident of two vehicles at intersection. The simulation allowed estimating the velocity of the vehicles at the moment of collision and the determination of the location of the vehicles. We also focus on the result of the mathematical simulation of this accident situation at intersection when two vehicles and two pedestrians take part in this collision

  • MATHEMATICAL MODELLING OF MEDICAL-BIOLOGICAL PROCESSES AND SYSTEMS