Physical-mathematical Model Research Articles

Modern Physical-Mathematical Models and Methods for Design Surface Acoustic Wave Devices: COM Based P-Matrices and FEM in COMSOL

Comparative results of calculation and measurement of the frequency responses of the surface acoustic waves filter on a piezoelectric substrate of 64°YX-cut lithium niobate and delay line on a piezoelectric substrate of 128°YX-cut lithium niobate is presented. The calculation was performed on the basis of two approaches—the finite element method in the COMSOL Multiphysics software and using the model of coupling of modes based on P-matrices. A brief overview and features of each approach are presented. The calculation results based on the two approaches are in good agreement with each other and with the experimental results of measurements of the characteristics of the bandpass filter. The delay line operating with the use of the third harmonic frequency is calculated by FEM. The results showed a good match between numerical simulation and experiment. The considered approaches for designing SAW devices allow us to relatively quickly and accurately predict the frequency responses at the simulation stage, thereby reducing the number of experimental iterations and increasing the efficiency of development.

Response of two-temperature semiconductor model photomechanical and thermal waves during electrons-holes interaction processes

A novel mathematical-physical model is introduced in the context of the two-temperature thermoelasticity theory which describes the interaction between electrons and holes in semiconductors material. The response of the elasto-thermo- mechanical continuous waves is investigated during thermo-mass-diffusion transport processes. The photothermal (PT) technique is applied for the exciting medium. The one-dimensional (1D) Cartesian coordinate is used to describe the governing equations. Dimensionless quantity is used in the Laplace transform domain. To obtain the unknown variables, some conditions are applied at the free surface of the medium to get the main quantities analytically. The conversion of the Laplace transform technique has been employed with some numerical approximations to obtain the exact expressions of the main physical fields. The computational results have been introduced of silicon material to illustrate the impacts of the two temperature parameter and thermal memories on the wave propagation of the physical fields according to photo-thermoelasticity theory.

Numerical simulation and experimental verification of a small refrigerated warehouse with PCM plates

In this paper, phase change materials (PCM) plates are placed in cold store to use their latent heat to store cold and slow down the rise in temperature in the store, thus extending the shelf life of food products. Five kinds of PCM for cold storage were obtained by compounding several organic and inorganic solutions. The properties of phase change temperature, latent heat of phase change and subcooling were integrated, and a B composite solution consisting of 30% ammonium bromide, 10% ammonium chloride, 1% strontium dioxide, 5% xanthan gum and 54% water was recommended for -18 °C cold storage. Cold storage plates encapsulated B composite solution and placed on top of the storage. The temperature of the cold storage with PCM plates rose to -10 °C in 217 min, which was delayed near 2 h compared to the cold store without PCM plates. Meanwhile, a physical–mathematical model was developed and the temperature field of the cold store with PCM plates was simulated by computational fluid dynamics (CFD). The results showed that the temperature reached -10 °C in 215 min with an error of 2.2% compared to the experimental results, and the simulation results were reliable. It is shown that it is feasible to use numerical simulation to analysis the temperature field of the actual cold storage, and it provides a reference for the subsequent research of cold storage. For the PCM plates designed for 6 h of cold storage, the final storage time was 2 h. Subsequent research can be carried out on refrigerated warehouse with PCM plates with good insulation performance; the PCM plates will be cooled using the refrigeration unit to increase the heat transfer temperature difference. The use of a thinner thickness of the PCM plates, the fan of the refrigeration system is turned on to strengthen the heat exchange.

Analysis of gas thermal conductivity at low pressures using a mathematical-physical model

As part of the research in the field of pumping vacuum chambers in the Environmental Electron Microscope, research on supersonic flow through apertures is being carried out at the Department of Electrical and Electronic Technology of the Brno University of Technology in cooperation with the Institute of Scientific Instruments of the CAS. This paper deals with the effect of low pressures on the thermal conductivity of gases that occurs when observing samples in the Environmental Electron Microscope.

Structural optimization design and heat transfer characteristics of air-to-air cooled high voltage motor heat exchanger

In order to improve the heat transfer efficiency of air cooled high voltage motor heat exchanger, this paper takes 500 kW high voltage motor heat exchanger as the research object, and establishes the mathematical model and physical model of the heat exchanger based on hydrodynamics and numerical heat transfer theory. The flow field and temperature field of the model are solved by finite element method. The temperature distribution and fluid flow characteristics in the heat exchanger are clarified and compared with the experimental data. The experimental results verify the reasonableness of the model and the accuracy of the calculation results. Finally, based on the flow distribution and the interaction of cooling factors, the structure of the heat exchanger is optimised to address the shortcomings of the original design, and an effective solution is obtained to improve the heat transfer capacity of the heat exchanger.

Parent’s experience in remote learning during COVID-19 with digital and physical mathematical modelling

In reaction to the COVID-19 pandemic, the government of Luxembourg suspended in-school teaching and learning towards remote teaching. A survey conducted by the Ministry of Education after three weeks of confinement, showed that more than half of the parents faced difficulties when using remote teaching with their students. To tackle this new challenge, we adapted our research to the use of augmented reality, digital and physical mathematical modelling in remote mathematics education for elementary schools. The elementary school students (aged 5 to 12) created cultural artifacts (i.e., Easter egg cups) during the confinement. In this paper, we will describe mathematical modelling in remote teaching and further concentrate on parents’ perspectives, who played an essential role in assisting their children. Moreover, we will discuss different didactical principles that emerged from the task design during the study through parents’ eyes. Thus, understanding parents’ perspectives became highly important in enabling us to improve task designs and related pedagogical approaches in remote teaching. The data collected in this study included semi-structured interviews with students, parents, and teachers as well as questionnaires and field notes. We followed an exploratory stance with our data analyses, primarily utilizing grounded theory (Corbin & Strauss, 1990, 2014) approaches. Through the insights we gained from our findings, we aim to explain how the parents perceived teaching and learning mathematical modelling in our experiments, how they scaffolded the given tasks, and what support they required and would need in future remote teaching.

A Novel Photo Elasto-Thermodiffusion Waves with Electron-Holes in Semiconductor Materials with Hyperbolic Two Temperature

In this paper, a novel mathematical—physical model of the generalized elasto-thermodiffusion (hole/electron interaction) waves in semiconductor materials is studied when the hyperbolic two-temperature theory in the two-dimensional (2D) deformation is taken into account. Shear (purely transverse) waves are dissociated from the remainder of the motion and remain unaffected by external fields. The coupled system of partial differential equations of the main interacting fields has been solved. Using the Laplace transform method, the governing equations of motion and heat conduction can be formulated in 2D. The hole charge carrier, displacement, thermal, and plasma boundary conditions are applied on the interface adjacent to the vacuum to obtain the basic physical quantities in the Laplace domain. The inversion of the Laplace transform with the numerical method is applied to obtain the complete solutions in the time domain for the main physical fields under investigation. The effects of thermoelastic, the phase-lag of the temperature gradient and the phase-lag of the heat flux, the hyperbolic two-temperature parameter, and comparing between silicon and germanium materials on the displacement component, carrier density, hole charge carrier, and temperature distribution have been discussed and obtained graphically.

NATURAL CONVECTION ON CORRUGATED PLATES: A NUMERICAL CASE STUDY ABOUT MESHES, BOUNDARY CONDITIONS AND PHYSICAL DOMAIN DETERMINATION

The transfer of heat and mass by natural convection is present in the most diverse physical and chemical phenomena of nature and engineering equipment. In the last decades, the number of research on natural convection has grown dramatically, highlighting studies in physical-mathematical modeling and numerical solutions, experimental analysis and design and optimization techniques for fluid-thermal systems. This case study analyzed the influence of several numerical parameters in physical-mathematical modeling and numerical solution of natural convection heat transfer problems on isothermal plates with square waves in turbulent conditions of high Rayleigh number. The numerical parameters analyzed were the mesh refinement degree, wall boundary conditions (with or without wall functions implemented in the turbulent parameters) and computational physical domain influence. Free and open-source computational numerical tools were exclusively used in the construction of this work. Meshes with wall functions implemented in turbulent parameters presented greater accuracy and required less computational effort and simulation time, besides enabling the use of a lower degree of mesh refinement. The best numerical configuration of the physical model for the situation problem studied were defined from the criteria of accuracy, computational effort demanded, and stability and numerical convergence of the solution.

Dimensioned Algebra: Mathematics with Physical Quantities

A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has shaped current mathematical models of theoretical physics, which generally lack any explicit reference to units of measurement, and we propose a novel mathematical framework to alleviate this. Our proposal is a generalization of the usual categories of algebraic structures used to formulate physical theories (groups, rings, vector spaces...), herein dubbed dimensioned, that can naturally articulate the structure of physical dimension. Our goal in the present work is not so much to define an algebraic theory of physical quantities—this has already been done—but to define a theory of algebra informed by how physical quantities are used in practice. We conclude by studying the dimensioned analogue of Poisson algebras in some detail due to their relevance in Jacobi geometry and classical mechanics.

Physical model test and parametric optimization of a hydroelectric generating system with a coaxial shaft surge tank

The novel structure of the surge tank is often designed in hydropower stations, for example, the Coaxial Shaft Surge Tank (CSST). Reasonable mathematical modeling and physical model verification are effective methods in dealing with novel structure tanks. This study aims to analyze the influence of geometric and hydraulic parameters on the hydraulic characteristics of the Hydroelectric Generating Systems (HGS) with CSST in the transient process. First, the mathematical model of CSST and the physical model of HGS with a geometric scale of 42.33 are established. The correctness of the mathematical model is verified by the physical model test. Second, an evaluation method is proposed to optimize the specific transient parameters of HGS. The results show that the sensitivity coefficient of the diversion tunnel diameter to the highest surge in CSST is 6.09, and the impedance hole coefficient φ of CSST to the maximum water hammer pressure of the spiral casing reaches 13.47. The results also indicate that changing the diameter of the penstock can adjust the maximum water hammer pressure while keeping the surge wave in CSST unchanged. This research provides design guidance and a theoretical basis to design HGS and improve its operational safety.

Physical Mathematical Modeling and Simulation Based on Hyperbolic Heat Transfer for High Heating Rate Processes in Biomass Pyrolysis

Abstract This paper explores the hyperbolic heat transfer effects in processes involving high heating rates. The behavior of the model is analyzed in detail under different boundary conditions and the circumstances under which a non-Fourier law could be used to describe thermal conduction processes established from physical mathematical analysis. Finally, the model developed here is coupled to a previous population balance framework to predict the bubbling phenomenon that occurs during the fast pyrolysis of biomass. We found that a transient overheating occurs in the central zone of the generated liquid phase due to the high heating rates that take place during that process.

ЕЛЕМЕНТИ ТЕОРІЇ ПОДОЛАННЯ РУХЛИВОЇ ПЕРЕШКОДИ ВІЙСЬКОВИМ АВТОМОБІЛЕМ

The working process of the car is accompanied by the loading of the wheel drive by gravitational force, which leads to compression and stretching of the tire during its deformation, as well as hitting various obstacles and moving through them. The article considers the study of the mechanical system "car" using the theorem on the change of kinetic energy of this system, the general equation of dynamics. The aim of the study is to improve the technological scheme of loading the wheel drive when moving the movable support, converting the energy supplied to the wheel drive into controlled relative to the obstacle movement with the addition of traction of the car with transmission force, which is an auxiliary factor to innovative technology. The scientific and practical direction of work is that for the first time the technology is considered in which the law of change of mechanical energy is applied when rotating the wheel drive on a moving obstacle, and this allows a more appropriate approach to the implementation of torque on the wheel drive. The methodology of the study was to establish a mathematical relationship between the speed of the car wheel from the moving obstacle and the parameter of the obstacle it creates, as well as the dynamic mobility of the car itself. The result of the study is the development of elements of the theory of overcoming a moving obstacle that works with "physical discomfort of the support surface." In disclosing the concept of "physical discomfort of the support surface" differential equations were used, which mathematically confirm the overcoming of such an obstacle and such a support surface in certain operating conditions of the car. The value of the study, the results of this work will contribute to the automotive industry. The proposed car model is suitable for use in order to increase the ability to overcome obstacles by vehicles. Keywords: physical-mathematical model, force, reaction, wheel, moving obstacle.

НЕВИЯВЛЕНІ ТЕОРЕТИЧНІ МОЖЛИВОСТІ ПОДОЛАННЯ ОПОРУ КОЧЕННЯ КОЛІСНОГО РУШІЯ ВІЙСЬКОВИМ АВТОМОБІЛЕМ

The purpose of the study is to improve the technological scheme of the internal load of the wheel drive of the car when it is loaded with additional peripheral torque, the transformation of the energy supplied to the technological wheel of the wheel drive into a rotational movement controlled relative to the hub with the addition of the rotational movement of the car wheel to the rotational movement of the technological wheel of the car, which is an auxiliary factor to innovative technology of its movement. The scientific and practical direction of the work consists in the fact that for the first time the considered technology in which, during the rotation of the wheel drive, it is loaded with an additional peripheral torque, the law of change of mechanical energy is applied, and this makes it more expedient to approach the consideration of the influence of the peripheral torque on increasing the angular speed of the wheel drive . The research methodology was to establish a mathematical relationship between the rolling speed of the wheel drive and the peripheral torque. The result of the study is the identification of the undiscovered possibilities of the working process of the wheel drive when it is loaded with a peripheral torque and thereby create prospects for increasing the efficiency of the wheel drive. When revealing the concept of the undisclosed load possibilities of the wheel drive, the theorem of the increase of the vector of the kinetic moment of the system with respect to the fixed center for a finite time is equal to the momentum of the moments of external forces with respect to the same center for the same timе, which mathematically confirms the influence of the peripheral moment on the improvement of the quality of the work process, which is created by the wheel drive in certain conditions of operation of the car. Keywords: physical-mathematical model, force, reaction, wheel, moment, wheel drive.

Investigation of Nonlinear Piezoelectric Energy Harvester for Low-Frequency and Wideband Applications.

This paper proposes a monostable nonlinear Piezoelectric Energy Harvester (PEH). The harvester is based on an unconventional exsect-tapered fixed-guided spring design, which introduces nonlinearity into the system due to the bending and stretching of the spring. The physical–mathematical model and finite element simulations were performed to analyze the effects of the stretching-induced nonlinearity on the performance of the energy harvester. The proposed exsect-tapered nonlinear PEH shows a bandwidth and power enhancement of 15.38 and 44.4%, respectively, compared to conventional rectangular nonlinear PEHs. It shows a bandwidth and power enhancement of 11.11 and 26.83%, respectively, compared to a simple, linearly tapered and nonlinear PEH. The exsect-tapered nonlinear PEH improves the power output and operational bandwidth for harvesting low-frequency ambient vibrations.

The mathematical model of thermoelastic stresses in the Carpathian region

The two-dimensional thermoelastic model of the Carpathian region is constructed using the finite element method. The physical-mathematical model is as close as possible to the real environment. A~high-precision detailed distribution of temperatures, heat flow, thermoelastic stresses and displacements is obtained. It is shown that inhomogeneous heating of rocks and structural heterogeneities lead to significant changes in stress and displacement fields in the Carpathian region.

Leading-Edge Vortex Lift (LEVL) Sample Probe for Venusian Atmosphere

Can a small, lightweight, free-falling sample probe be slowed enough in the Venusian atmosphere to run a 10 min microelectromechanical systems (MEMS) ion gas micro spectrometer, without adding a propulsion systems or explosives and parachutes to the probe mass? To meet this requirement a leading-edge vortex lift (LEVL) autorotating probe design (i.e., maple or sycamore seed shape) has been proposed and evaluated. It has been found that a probe with a total mass of less than 1 kg would allow prolonged flight longer than 15 min. Mathematical modelling and physical scale model testing has been performed to show that this flight time is achievable, allowing MEMS ion gas micro-spectrometer sampling of the Venusian atmosphere.

Physical-mathematical model to predict the kinetic coagulation process by clotting activity of bacterial endopeptidases

A physical-mathematical model was used to evaluate the capability of an enzymatic pool of Bacillus sp. P7 (isolated from Piaractus mesopotamicus) to promote the bovine casein micelles coagulation. Experiments were designed to assess the effects of temperature, pH, and enzyme activity/mass of substrate ratio on the kinetic parameters of the coagulation process and the microstructure of the obtained clots. Descriptive and predictive equations indicate that the temperature and the pH modified these parameters significantly. In optimal conditions, the clot’s mean pore size was 3.6 times smaller using chymosin. On the other hand, rheological measurements evidence a moderate elasticity of clot, which indicates the usefulness of P7 protease preparation as a clotting agent in spreadable or soft cheese manufacture. Also, the hydrolysis products, which are in the whey after casein micelles coagulation, demonstrated antioxidant activities. Equations to model and predict the process kinetics were combined with rheological and microstructure analyses of the obtained clots, and whey bioactivities were evaluated. Nevertheless, the use of P7PP requires further investigation concerning the stability of the enzyme preparation during storage, its performance, and how these variables could be related to the proposed models.

Design and experiments of ultra-precision aerostatic turning machine tool

Ultra-precision turning is one of the commonly machining methods to obtain high-quality optical components. Ultra-precision turning machine tools are the industrial equipment that realize ultra-precision turning process. In this paper, a combined design, performance analysis and experimental verification are carried out to build an ultra-precision aerostatic turning machine tool (UPATMT), which adopts aerostatic support systems for the spindle system and the feed system. Firstly, the mathematical model and physical model of UPATMT are established, and the dynamic performance of UPATMT model is carried out and analyzed by finite element method. In addition, the electromechanical control system is simulated and analyzed to obtain better dynamic performance. Finally, the modal tests and turning experiments are carried out on a homemade UPATMT platform. The machined workpiece surface roughness is measured, the arithmetical mean deviation of the workplace surface roughness is Ra 7.4 nm, and the maximum peak valley height of workplace surface roughness Rz 34.4 nm. The results show that electromechanical coupling analysis can obtain high machining performance of UPATMT.

The Hall current effect of magnetic-optical-elastic-thermal-diffusive semiconductor model during electrons-holes excitation processes

In this work, a theoretical electrons and holes interaction model in semiconductors is studied. This mathematical-physical model is described during an optical-elastic-thermal-diffusion (OETD) process when the medium is excited by photo-energy due to high temperatures. The effect of the Hall current associated with the fall of a strong magnetic field on the outer surface of the semiconductor medium is studied. The density of magnetic flux due to the magnetic field causes a Hall effect. The governing equations are taken into one dimensional (1D) in the context of electronics-thermal-elastic deformation. To illustrate that the Laplace transform with initial conditions of the dimensionless main physical fields is used. The general linear solutions for the charge carrier holes and electrons, strain, and thermal distributions are obtained mathematically in the Laplace domain. Some thermal, mechanical, and optical conditions are taken at the free surface of the semiconductor with the Laplace inverse approximate technique numerically to obtain the complete solutions of the main physical fields in the time domain. The Hall current effect and influence of thermal relaxation times according to photo-thermoelasticity theory are presented graphically and discussed for silicon material.

Multiplicative random seismic noise caused by small-scale near-surface scattering and its transformation during stacking

Even after sophisticated processing, land seismic data in complex areas exhibit weak and distorted prestack reflections with low coherency. Usually, the local stacking methods reveal clear reflections. However, the absolute level of amplitude spectra after such stacking experiences a substantial decline across the entire frequency band, reaching −10 to −25 dB. In addition, stacking leads to a significant and progressive loss of higher frequencies. We describe mathematical and intuitive physical models for multiplicative random noise that could consistently explain these field observations at least semiquantitatively. Multiplicative noise is represented by random timeshifts (residual statics) and random phase perturbations different for each frequency. Residual statics explain the progressive loss of higher frequencies. On the other hand, phase perturbations lead to a severe loss of coherency on prestack gathers and produce a strong downward bias or loss of broadband amplitudes after stacking. We find that both types of multiplicative noise can be physically generated by near-surface scattering layers with small-to-medium-scale geologic heterogeneities. We speculate that such multiplicative distortions can be referred to as seismic speckle noise well established in optics and ultrasonics. Furthermore, we derive the fundamental properties of how random multiplicative noise transforms while stacking. The first essential finding reveals that stacking produces an unbiased estimate of the clean signal phase. The second finding finds the mathematical relationship between the frequency-dependent loss of stacked amplitude and the standard deviation of residual statics and phase perturbations. These findings serve as a theoretical justification for the previously proposed methods of phase substitution and phase corrections and open the way to efficiently address random multiplicative noise in seismic processing.