Mathematical and computer simulation of semiconductor systems of various dimensions and the elements of device structures based on them

The article, in the form of a minireview, reflects the results of theoretical, and partly experimental investigations of the electrical, optical and magnetic phenomena in three-dimensional, two-dimensional, one-dimensional and zero-dimensional systems and elements of device structures made of germanium, silicon, carbon and other chemical elements carried out at the Faculty of Physics of Belarusian State University over the past 25 years.

Mathematical and Computer Simulation of Hex Head Screws for Implementation on a 3D Printer

In this paper, based on the R-functions theory, methods have been developed and equations have been constructed for the 3D printing of hex-head screws with Bristol, Pentalobe, Polydrive and other types of screw slots. Such screws are used both in personal computers and other high-end equipment. The Bristol slot has four or six radial grooved beams. The advantage of the design of this slot is the correct perpendicular, rather than tangential, vector of force application when the slot is rotated by a tool, which minimizes the risk of stripping out the slot. For this reason, the Bristol slot is used in soft metal screws. Compared to the internal hex, the Bristol slot allows a noticeably higher torque, only slightly higher than that of the Torx slot. This type of slot is used in aviation, high-end telecommunications equipment, cameras, air brakes, agricultural equipment, astronomical equipment, and foreign military equipment. Variations with a pin in the center are found in game consoles to prevent the use of a flat-blade screwdriver as an improvised key. The Pentalobe slot is a five-point slot designed by Apple and used in its products to limit unauthorized disassembly. It was first used in mid 2009 to mount MacBook Pro batteries. Its miniature version was used in the iPhone 4 and later models, in the MacBook Air (available since late 2010 models), and the MacBook Pro with Retina screens. The Polydrive slot is a starlike slot with rounded star points, used in the automotive industry for applications requiring high tightening torque. The Torq-set slot is a cross slot for fasteners requiring high tightening torque. The grooves are slightly offset, not intersecting at one point. Fasteners with this type of slot are used in military aviation, for example, in E-3, P-3, F-16, Airbus, Embraer, and Bombardier Inc. The Phillips Screw Company owns the trademark and manufactures fasteners with this type of slot. The slot design standards are National Aerospace Standard NASM 3781 and NASM 4191 for the ribbed version. The resulting equations for the surfaces of screws were checked during the modeling of the screws before 3D printing. The 3D printing technology allows us to reduce the cost and labor intensity of manufacturing products, including complex slot screws. The analytical recording of designed objects makes it possible to use alphabetic geometric parameters, complex superposition of functions, which, in turn, allows us to quickly change their design elements. The positivity property of the constructed functions at the internal points of an object is very convenient for the implementation of 3D printing.

Numerical methods for solving improper problems of filtration theory

This paper is devoted to the development and investigation of methods of mathematical and computer simulation of the process of fluid filtration in a porous medium. The methods of numerical solution of the problems of the filtration theory of build-up of conditions in the catchment and discharge areas boundaries, identification of filtration-capacitive parameters of the effective formation and determination of free (unknown) boundaries and creation of computational algorithms for analysis and forecast of technological indicators of oil and gas fields are considered. Methods and models of continuum mechanics, filtration theories, and methods for solving ill-defined problems, numerical modeling and computer programming were used. Approximate Numerical methods for solving direct and inverse problems of filtration theory, mathematical models for single-phase isothermal filtration of a gas mixture in a horizontal formation at small concentration gradients of components, studying the properties of self-similar solutions, as well as numerical solving the problem of identifying the capacitive parameters of the water-bearing stratum.

STUDY OF THE DYNAMIC LOADING OF THE LOAD-BEARING STRUCTURE OF A FLAT WAGON DURING TRANSPORTATION BY SEA

To increase the efficiency of combined transportation, the supporting structure of flat wagon has been created. A feature of the wagon is that the sections have a low center of gravity. This solution allows for the transportation of oversized cargo on a flat wagon within the established dimensions. The design of this flat wagon can be used for the carriage of goods not only by main lines, but also in rail and water traffic when transported by rail ferries. To ensure the safety of transportation of a flat wagon with containers on a railway ferry, their dynamic loading was determined. It is taken into account that a large-capacity container of 1AA standard size is placed on each section. The solution of the mathematical model was carried out in the MathCad software package. The resulting accelerations, as components of the dynamic load, were taken into account when determining the stability of a container on a flat wagon during transportation by a rail ferry. It was found that the stability of the container is ensured at tilt angles up to 25°. A computer simulation of the dynamic loading of the supporting structure of an articulated flat wagon with containers during transportation by a railway ferry has been carried out. The calculation is implemented in the CosmosWorks software package using the finite element method. The fields of distribution of accelerations relative to the supporting structure of the flat wagon and containers are determined. The maximum percentage of discrepancy between the results of mathematical and computer simulation does not exceed 11 %. The research carried out will contribute to the creation of innovative designs of flat wagons, as well as to increase the efficiency of the operation of combined transport in international traffic

DETERMINATION OF DEFECTS SIZES AND THEIR POSITION DURING ULTRASONIC CONTROL BY METHODS OF MATHEMATICAL AND COMPUTER SIMULATION

The use of sound waves to study the integrity of various metal structures is the most relevant method. The relevance is traced, in particular, in the ease of conducting such experiments, as well as its cheapness. The design of various parts requires the use of modern computer technology, which, using a mathematical apparatus that describes the process, allows you to determine the actual characteristics of the material to determine durability. This approach makes it possible to effectively create design solutions in order to create new parts and upgrade existing materials to extend their service life. The purpose of this work is to build mathematical models of homogeneous wave processes and their analysis in the form of computational experiments to control the passage of sound signals through the surface of the studied materials of objects. This approach is used to determine the influence of geometric parameters of defects in the form of cracks through which the signal passes, on its characteristics, which it describes after passing through these defects to the signal receiver, in particular, is the amplitude and frequency. For computational experiments, a point exciter of harmonic oscillations and a point receiver were chosen, which are located on different sides relative to the defect of a simple geometric shape. It should be noted that even minor defects affect the amplitude of the received signal, which passed through such defects. When a signal passes through defects of a simple geometric shape, the amplitude of such a signal decreases by 5–8 times and the average frequency decreases by 2–3 times.

Role of Surface Roughness in the Interlayer Boundary Formation during Manufacturing of Clad Metal Composites

In the present research work, the role of surface roughness in the interlayer boundary formation during manufacturing of clad metal composites was analyzed. Process of interlayer boundary formation was described through mathematical and computer simulation. The importance of taking into account not only arithmetical mean roughness Ra or ten-point mean roughness Rz, but also Rz/S ratio (where S – mean spacing of adjacent peaks) is shown, because this relation affects the length of actual contact between dissimilar materials. As the result of mathematical and computer simulation, dependence of the length of actual contact between dissimilar materials on Rz/S ratio and semi-angle of the ridge vertex was obtained.

SIMULATION MODELING OF PARAMETERS OF FUNCTIONING OF RAILWAY PROJECTS

The speed of communication on any route, directly and indirectly through the function of redistribution of traffic volumes, causes an increase in the number of movements, traffic volumes, transport work, in the network of the appropriate type, at the same time the values of the medium system coefficient of passenger capacity use and the number of vehicles may vary both in the direction of the increase and vice versa. The results of the calculations of the basic parameters of the functioning of intercity passenger route systems for various values of the speed of communication on intercity railway routes established the appropriate mathematical model for determining the parameters of this passenger communication. The conducted analysis of simulation methods has determined the possibility of using for the determination of quantitative parameters for changing the basic indicators of the operation of the system of intercity passenger route methods of mathematical and computer simulation. The results of the work determined the basic indicators of the functioning of the system of intercity passenger route transportation. These indicators include: the number of movements in the network; volume of transportation; transfer ratio; transport work; average distance of the route; average distance of the network ride; medium coefficient of passenger capacity use; required number of buses / cars. According to the analysis of the methods and models of calculations of the basic indicators of the functioning of the system of intercity passenger traffic, it was assumed that the change in the quantitative characteristics of the parameters entering into the system or the quantitative characteristics of its elements may lead to a change in the quantitative indicators of the functioning of the system itself or its individual elements. Keywords: transport system, intercity passenger transport route, basic parameters of transportation, efficien-cy, model.

PHENOMENON OF COMPLEX SYSTEMS – A MATTER FOR SCIENTIFIC ENQUIRY

Complex systems is the subject of some mathematical studies in a series of fundamental and applied scientific areas. At present complex systems become the subject of interdisciplinary study and the increasing attention of researchers who seek more effective solutions of ”traditional” tasks as well as develop generalized theories and methods which offer a clearer view of new problems that come under the heading of stubborn problems. The paper discusses the phenomenon of complex systems in the form of retrospective historical analysis and is aimed at promoting a better understanding of the mentioned phenomenon as a problem of mathematical and computer simulation.