Mathematical Modeling
Vol. 9 (2025), Issue 2

Table of Contents

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • Field-free calculation of heat and mass transfer flows with short-term contact of phases

      pg(s) 45-46

      Calculation of thermal diffusion and filtration fluxes at the interface by “traditional” methods requires preliminary determination of the potential values (concentration, moisture content, temperature, pressure) in the four-dimensional space of events. Such methods for solving boundary value problems, which provide “extra” information for technical calculations, are usually very laborous and require the use of numerical methods that are not always convenient in engineering practice. The proposed fieldless calculation method allows one to determine on the boundary of the region the gradients from the transfer potentials and, consequently, energy and material flows in the form of a known functional of the potentials at the interface at their short-term contact directly on the matrix of transfer coefficients of the formalized boundary value problem. This method uses the fractional index differentiation operation (fractional differentiation) and is convenient for solving limiting boundary value problems, i.e. when the characteristic size of the contacting phases in the boundary conditions of boundary value problems tends to infinity or the time of their interaction tends to zero.

    • Study on the effectiveness of integrated methodologies for determining thermophysical properties of building envelope structures

      pg(s) 47-51

      To design energy-efficient buildings, it is essential to accurately calculate, monitor, and analyze their energy consumption at all stages: from conceptual (sketch) development and design to construction and operation. However, current regulatory documentation lacks methodologies that fully account for the interrelated processes occurring in building envelopes—such as heat transfer, moisture accumulation, and air infiltration—evaluate the effectiveness of specific energy-saving measures, or perform energy consumption data analysis to determine a building’s actual energy performance indicators.This highlights the relevance of calculating and analyzing building energy consumption while accounting for heat and mass transfer processes in envelope structures and the presence of various architectural and construction elements. A methodology has been developed for processing data obtained from building thermal energy metering systems. This methodology allows, during the operational phase, to determine buildings’ energy characteristics, evaluate the efficiency of thermal energy use, and assess the effectiveness of energy-saving measures.

    • Study on the dynamics of truck loader crane during cargo unloading using modeling and simulations

      pg(s) 52-58

      This article is a study on the work operation of a hydraulic crane installed on a heavy truck known as Truck Loader Crane. The crane is used to carry loads from the truck to the ground and vice versa. It usually is an integral part of the truck mounted behind the cabin or behind the cargo body, and there are cases when it is additionally mounted on the truck. The crane has several mechanical and hydraulic parts. It is controlled from the command panel attached to the crane or by using the remote panel. The work operation analyzed is cargo unloading from the truck body on the ground. It is a complex process consisting of attaching the cargo (load) to the boom, lifting the cargo from the truck body, transferring the cargo several meters, and lowering it on the ground. During this process, the crane undergoes heavy oscillations due to the motion and swinging of the load it carries. The type of analysis is dynamic analysis, and the methodology consists of 3D modeling of the crane and implementing simulations with SimWise4D software. Through this study, the aim is to identify the nature and extent of forces and stresses on the crane and its parts, the intensity of the swinging and oscillations of the cargo, and their effect on crane operation. High oscillations can cause parts failure and raise concerns about safety. Results will be shown in graphical form for the main influential parameters. Conclusions from this paper will be useful regarding the strength of crane materials, motion dynamics and motion control of crane and cargo, design of crane parts and safety during work. The Truck Loader Crane model is designed based on the data from the standard manufacturer.

    • Mathematical modeling of the hydrogen supply chain — an integrated approach for sustainable transport

      pg(s) 58-61

      This study proposes a mathematical model for design and optimization of a hydrogen supply chain, covering all stages of the life cycle – feedstocks, production, storage, distribution, end-use in the transport sector. The developed methodology integrates different hydrogen production technologies and takes into account environmental, economic and social impacts in order to identify the most efficient and sustainable configuration. The focus in this work falls on hydrogen production by steam reforming of methane and hydrogen production by electrolysis of water in hydrogen refueling stations. The mathematical model is formulated in terms of MILP programming and can be solved using the GAMS software product. The aim is to find an optimal balance between economic efficiency, environmental sustainability and social impact by using weighted coefficients (weights). The proposed concept provides a decision-making tool for planning hydrogen infrastructure in line with European decarbonization and sustainable transport goals.

    • FEA-Driven Design of Nonwoven Winder Drums: Stress Minimization and Rigidity Assessment for Structural Integrity

      pg(s) 62-66

      Nonwoven winding machines are critical equipment where the structural integrity of the main drum directly impacts the quality and stability of the final product. This study presents the mechanical analysis and braking system design for a main winding drum (Diameter 400 mm) in a high-speed nonwoven application, driven by Finite Element Analysis (FEA) for stress minimization. The load analysis, based on the Principles of Static Equilibrium, determined the total maximum load on the drum supports, considering a maximum spool weight of 1500 kg and a nip force of 1962 N. The resultant total load applied on the supports was calculated as approximately 11.5 kN. The FEA, utilizing ST37 steel, revealed a maximum Von Mises Stress of 1.754 MPa and an extremely low maximum deflection of 0.005 mm. This confirms an optimal factor of safety (FS approx 134) and high rigidity. Furthermore, the paper addresses the safety requirement for emergency stopping from a maximum speed (omega = 50 rad/s). The minimum required braking torque was calculated as 235 Nm, while the selected COREMO PNEUMATIC CALIPER BRAKE B-2N system provides 306.8 Nm, ensuring reliable and controlled deceleration. The results validate the structural and functional design, contributing to enhanced machine performance and operational safety.

    • Reliability Criteria for the Working Elements of Robotic Systems

      pg(s) 66-67

      The article presents the rationale for an algorithm describing the interaction of random peak load parameters and strength parameters used in defining the reliability criteria for the working elements of robotic systems. The assessment method is founded upon finding the probability of attaining a dangerous state during the realization of an extreme random process within the calculated operational time interval. To facilitate this analysis, the random parameters of the load and the strength of the machine’s working element are represented as functional dependencies of the generalized load and generalized strength on time.

    • Development of numerical model for buoyancy-driven heat transfer between parallel plates

      pg(s) 68-71

      The main objective of this study is to develop and experimentally validate a finite volume numerical model for buoyancy-driven (natural convective) heat transfer between parallel plates representative of plate fin passive heat sinks. The validation employs a calorimetry-based setup: a vertical aluminum plate fin heat sink is mounted to the only uninsulated wall of an otherwise well-insulated, water-filled rectangular vessel that serves as a controllable heat source. The total heat transfer rate and convective heat transfer coefficients are inferred from the time evolution of the calorimetric water temperature, and fin surface temperatures are measured at several characteristic locations. The model resolves conjugate heat transfer between the solid heat sink and the surrounding air. Numerical predictions of heat transfer rate, fin surface temperatures, and convective heat transfer coefficients show good agreement with measurements and with established literature correlations, confirming the validity of the mathematical model and numerical procedure. The developed numerical model can be used for further analyses and optimization processes.

  • MATHEMATICAL MODELLING OF MEDICAL-BIOLOGICAL PROCESSES AND SYSTEMS

    • Modeling quantum correlations in donor-acceptor transport processes of biomolecules

      pg(s) 72-73

      A quantum model of excitation transfer from a donor molecule to an acceptor molecule through a biomolecule represented by a quasi-one-dimensional molecular chain is proposed. The sites of the chain correspond to the structural elements of biomolecules, such as amino acid residues linked into the chain by peptide bonds in proteins or nucleotides in RNA and DNA. Particular attention is paid to the emergence of quantum entanglement between the donor and acceptor molecules as the specific type of quantum correlations, which provides an intramolecular quantum channel for information transmission.

    • Finite Elements Modelling for Calculation of Magnetic Fields in Magnetoencephalography

      pg(s) 74-77

      The present study concerns the simulation, in two dimensions, by the finite element method, of the behaviour of the magnetic field created by sources of equivalent neuronal currents by considering a simplified model of a diagnostic device used in MEG (Magnetoencephalography). The simplified geometric model is composed of the head, the magnetic field sensors and the sources of equivalent currents representing the neurons. The geometric model of the head is represented by 3 layers which are brain, bone and skin. The sensors placed above the part of the skin make it possible to calculate the electric voltage induced by the magnetic field resulting from the sources of equivalent currents produced by the neurons. Neurons are represented by equidistant point current sourcesThe Maxwell-multi physics software has been used.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • Heuristic optimization of moving-average trading rules on stock data

      pg(s) 77-79

      This paper investigates the optimization of a Moving-Average (MA) crossover trading strategy using derivative-free methods. The strategy, defined on daily prices of the S&P 500, Apple (AAPL), and Alphabet (GOOGL) (1995–2024), is characterized by two integer parameters: short-term and long-term window lengths. We treat the in-sample annualized Sharpe ratio as a black-box objective function. We propose a multi-start coordinate pattern search algorithm that iteratively probes neighboring parameters and adaptively shrinks step sizes. Results from 1000 Monte Carlo runs per asset demonstrate that the method reliably converges to near-optimal solutions comparable to expensive brute-force grid searches. The optimizer identifies distinct optimal regimes: medium-term windows for GOOGL, a fixed long-term trend (approx. 220 days) for the S&P 500, and a specific fast-slow combination (2 and 240 days) for AAPL.

    • Topology as a lens for semantic organization in transformer embeddings

      pg(s) 80-83

      This paper examines the geometric structure of sentence embeddings through the lens of persistent homology. The goal is to determine whether semantic similarity produces distinctive topological patterns in a controlled embedding environment. To isolate semantic effects, a single sentence template was combined with different target words, forming two point clouds in a transformer embedding space: one derived from semantically similar words and one from dissimilar words. A Vietoris–Rips filtration was applied to both clouds, and the resulting persistence diagrams were summarized by average lifetime, entropy of birth–death intervals, and the area under the Betti curve. The results show a coherent difference across topological dimensions: similar words generate stable connected components with lower variability, while dissimilar words produce a richer set of cycle features that persist across a broader range of scales. These findings indicate that persistent homology can capture multi-scale structural differences in embedding spaces that are not visible through standard distance-based comparisons. Although the experiment is intentionally simple, it highlights the potential of topological methods for studying how semantic structure is distributed across levels of a neural embedding space.