• ## A MATHEMATICAL MODEL OF OIL SPILL DIFFUSION IN NEAR-SHORE ZONE OF GEORGIA

The oil products remain the main contaminant of the Black Sea, as well as of the entire world’s oceans. A main amount of oil is transported by tankers and reloaded in port terminals. 12 per cent of overall marine pollution is the share of transportation, oil congestion and accidents losses. At the Caspian-Black Sea-Mediterranean area there are actively used the Black Sea ports of Batumi, Poti and Kulevi.
A huge damage to the nature is doing by oil spills on the surface of the oceans and seas owing to transportation oil by tankers. These spills are associated with loading and unloading operations as well as with tankers accidents. In this case, the oil spreads as a spot on the surface of the sea.

Problems associated with environmental pollution from the oil spill in the sea, made necessity to develop mathematical models that describe the transportation and transformation processes of oil spills. The proposed mathematical model can be used for prediction of the spread of an oil spill during the process of spreading of oil products on the water surface, and it also enables to take into account the reduction of the area of spill due to the action of sea-surface winds and turbulence of the water surface.

• ## SIMULATION MODEL OF THE CATERPILLAR DRIVE OF THE TRACTOR

The aim of this work is to develop a simulation model of the caterpillar drive, in order to determine at the development stage output characteristics during movement under varying input parameters. This is achieved by developing a dynamic model, a mathematical model and a simulation model of a caterpillar drive.

• ## TEST PLATFORM, DATA COLLECTION, SYSTEM IDENTIFICATION OF MULTICOPTER VEHICLE

Multicopters are widely used in a professional manner today in film industry, military applications etc. These vehicles are easy to build which have mechanical and electrical parts. Also autopilots are being sold to control these vehicles. However, mostly these vehicles are being built and used with little knowladge about the system dynamics, performance and stability. Mostly wrong propeller motor battery combinations are used. And mostly these vehicles are being used by different payloads. Every change in payload changes dynamics and stability of the vehicle. Very little of users are eligible at PID tuning and increasing the stability of multirotor vehicles. We aim to provide a test platform and methodoly for system identification and increasing stability of Multirotor Vehicles.

• ## ON A PHYSICO-MATHEMATICAL MODEL FOR CONTROLLED FORMATION OF PERIODIC NANOSTRUCTURES AT SOLID SURFACES IRRADIATED BY FEMTOSECOND LASER PULSES

In this paper, we propose a physico- mathematical 3D model to study some of the basic features of the interaction of radiation with solid materials (metals, semiconductors , insulators) under the action of femtosecond laser pulses. The constructed model is a parametric model that, in particular, takes into account the dependence of the physical and chemical characteristics of the periodic nano-surface structures controlled laser irradiation parameters the polarization, angle of incidence, the energy density, wavelength, etc. The developed model is meant for the excitation of periodic nano-surface structures by electric waves which are in the process of irradiation and periodically amplified and attenuated, i.e. it holds periodic interference.

## SIMPLIFIED ANALYTIC SOLUTION OF THE PROBLEM OF AUTOMATED MOTION CONTROL OF AN AUTONOMOUS RIGID BODY WITHOUT ITS OWN PROPULSION SYSTEM IN INCOMPRESSIBLE STRATIFIED VISCOUS FLUID

Industry 4.0, Vol. 2 (2017), Issue 3, pg(s) 108-110

This paper results are based on the mathematical model of the motion control of an autonomous solid body moving in incompressible stratified viscous fluid which was presented by the authors at and XIII MTM Congress held in March 2016 and XIII MTM Congress held in September 2016. It is assumed that the body does not have its own propulsion system, but is equipped with controlled rudders – wings of finite span. It is moved by the influence of the buoyancy force and wings lift effect. The control is produced by the angle of attack of the wing change for reaching to a neighborhood of the given point by this solid body. This body motion is considered to be planeparallel motion. At this paper authors present a simplification of this mathematical model in order to find an analytical solution of the differential equation describing the object motion and a necessity and acceptability analysis of the simplification.

## THEORETICAL INVESTIGATION AND DEVELOPMENT OF A DESIGN OF A NEW HAULM TOPPING MACHINE

Theoretical investigations have been conducted of the technological process of a sugar beet haulm topping machine with a rotary cutter mechanism, as a result of which there is developed a refined mathematical model of interaction of the cutting blade with a bundle of leaves, the blade being pivotally fixed on the horizontal drive shaft of the arcuate cutting blade. Basic analytical dependencies have been obtained, application of which in designing and constructing of a haulm topping machine will ensure guaranteed quality removal of the bundles of leaves without extracting the sugar beet roots from the soil. The numerical calculations of the obtained analytical expressions performed on the PC, using a prearranged program, made it possible to determine the design parameters of the rotary haulm topping apparatus.

## BIOTROPIC PARAMETERS OF ELECTROMAGNETIC RADIATION FOR REGENERATION OF ANIMAL DAMAGED BONE TISSUE

The development of effective medication-free treatment and means of animal injuries treatment is urgent task. The optimal parameters of electromagnetic field of ultra-high frequency range interacting with the bone tissues of animals have been determined. The aim of the work is to identify the high-frequency range of the electromagnetic field parameters in interaction with animal tissues using the developed mathematical model. The dependence of electric component amplitude of magnetic frequency field was investigated. It has been proved that the dimensions of the limbs and internal tissues significantly affect the internal distribution of the electromagnetic fields. The results of experimental studies have made it possible to determine the optimal frequency, power and radiation source arrangement for the injury treatment of different animal species. The application of electromagnetic radiation with optimal parameters intensifies metabolism on the diseased cells membrane level and assists more rapid recovery of the injured bone tissue.

## THEORETICAL RESEARCH AND DEVELOPMENT OF NEW DESIGN OF BEET TOPS HARVESTING MACHINERY

Beet tops harvesting machines designs working out is actual scientific and technical task for beet industry. Development of beet tops harvesting machine with technical and operational indicators of work on the level of the best world analogs is research objective. In the research used the methods of design and construction of agricultural machinery, methods of creation calculation mathematical models based on higher mathematics, theoretical mechanics, as well as programming and numerical calculations on the PC. Theoretical researches of technological process sugar beet tops cutting by the rotor mechanism are conducted. The mathematical model of interaction beet tops bunch with arc-shaped blade of knife which pivotally mounted on a power horizontal shaft is constructed. New analytical dependence of full cutting beet tops bunch of a given diameter on constructive, kinematic and power parameters of this design of beet tops harvesting machines is obtained. The dependence for speed definition of beet tops cutting device which providing effective cutting of tops bunches from sugar beet root crops which are in the soil is found. Carried out on the PC, numerical calculations, made it possible to determine the design parameters of the new rotary beet tops harvesting device. Tests of the beet tops harvesting machine in different zones of sugar beet cultivation showed that technical and operational indicators of its work correspond to the level of the best world analogs.

## DETERMINING THE LEVEL OF RELIABILITY OF SELF-PROPELLED AGRICULTURAL MACHINERY USING THE METHOD OF INSTANTANEOUS OBSERVATIONS

To solve the tasks related to the operational management of the technical condition of self-propelled agricultural equipment the method of momentary observations to quickly assess the level of reliability of self-propelled agricultural equipment was improved.
A comparative study of the reliability of the self-propelled agricultural machinery / harvesters / classic method and the method of current observation, and it has been found that the accuracy of the results obtained by the method of current observation satisfy the requirements for practical usage.

## MODELING OF MACHINE-TRACTOR UNITS WORKFLOW ON THE USE OF BIOFUELS

It is considered in the work integrated mathematical model of the machine-tractor units (MTU) that takes into account the physic-chemical properties of biofuel. The novelty of this model is that it takes into account the impact of the working processes in the structural elements of the MTU, one by one influencing each other. This scientific approach to the calculation of the MTU provides the opportunity to evaluate objectively the impact of biofuel on the operational and technological indicators, taking into account the weather conditions, the physical and mechanical properties of the soil and other conditions that may diminish the impact of biofuel on the operation of the unit and distort the final results. In addition the model is adapted to use computer applications, which makes it possible to reduce significantly the complexity of the calculations and reduce the influence of the human factor.

• ## THEORETICAL SUBSTANTIATION OF TOPPING PARAMETERS WITHOUT SUGAR BEET HEAD COPYING

Nowadays topper machines which cut beet tops without copying root heads via rotary topper and only after this heads are cuts individually by passive knife widely used in the world. However, with using this topping method significantly increases sugar-bearing plant material losses. Taking into account that sugar beet tops is effective raw material for receiving biogas, its collecting without loss is actual beet industry problem. However, when cutting tops from sugar beet heads with individual copying and collecting tops from each root crop head the topper productivity is significantly reduced, the design of the topping device becomes complicated, operational expenses considerably increase. Methods of mathematical modeling, programming and calculations on PC are used in the course of research. As a result of the conducted research the mathematical model of a cut without individual copying of root crop heads as well as algorithm are developed. This algorithm enables to determine the rational height of installation of the cutting device over the level of soil surface that in this turn provides minimum losses of beet tops. Dependence of sugar-bearing plant material losses and residues of beet tops on cut height without individual copying of root crops heads was experimentally defined. Comparison with theoretical calculations showed that in the range of working heights of a cut of 20-60 mm deviation does not exceed 1%.

• ## THEORY FOR ATTACHMENT OF TRACTOR-DRIVEN SUGAR BEET HARVESTING MACHINES

An analytical study is related to giving proof and selection of the optimal parameters for the units, consisting of a tractor and a tractor-driven sugar beet harvesting machine. A mathematical model is built on the basis of this study and describes the conditions for effective attachment and give opportunity for determination of the working speed and productivity. The calculations allow finding the optimal parameters of the mentioned above aggregates in relation to productivity and energy consumption.