Application of new method in quantum-mechanical calculations of the structural properties and the formation energy of the ordered Mu - phase in the Fe - Mo system

A new technique of finding the minimum total energy, calculated by quantum mechanical calculations, for hexagonal Mu- (μ-) phases of stoichiometric compositions taking into account relaxation, as well as optimized crystal lattice parameters for different compositions in the Fe-Mo system, has been applied. The convergence of the total energy is investigated as a function of the number of plane waves (k) in the range 2000 ÷ 105. Differences in the structural energies between bcc, C14 Laves and μ- phases of pure components, as well as the formation energies of μ- phases of stoichiometric compositions Fe9Mo4, Fe7Mo6 and Fe6Mo7 are calculated.

Energy Justification of the Number of Tractors for Agricultural Operations

The relevance of the problem under study is due to the need to substantiate the sufficient number of tractors used for various technological operations, depending on the volume of works performed, and taking into account their influence on the crop yield. The purpose is to develop the mathematical model of machine and tractor units used in technological operations by formalizing the vague concept of optimal agrotechnical timing of technological operations and calculating the optimal number of tractors to perform works by the total energy costs. The main research method is mathematical modeling of operations performed by machine-tractor units based on the system analysis and computational experiments and using the energy mathematical model. The article describes a criterion for optimizing the tractor parameters, dependences of the energy mathematical model of the unit. The results of computational experiments showed that for each operation there is an optimal number of tractors and tractor units minimizing the minimum total energy costs. Calculations were carried out when treating 1000 hectares with various tractors. It was revealed that the total energy consumption differs by 2 or more times. The required number of tractors depends on their main parameters, propeller parameters and other factors. It was revealed that with an increase in the volume of works, the required optimal number of tractors increases. The method for substantiating the required optimal number of tractors in technological operations will improve operations of tractors used by large agricultural producers, reduce the total energy costs for cultivating up to 12–16 thousand MJ/ha.

Improving the energy method for calculating beams with a narrow rectangular section on the side buckling

We propose an improved version of the energy method in calculating rectangular beams for the stability of a flat bending shape. The essence of this variant of the method is to use the principle of the minimum total energy instead of the condition for the equality of the potential strain energy and the work of external forces. This version of the method makes it easy to obtain a numerical-analytical solution for any number of members of series. The solution of the problem for a pivotally supported beam is presented taking into account the vertical displacement of the load relative to the center of gravity.

Development of Effective Arable Units for Dump Plowing

This article presents the results of the development of a mathematical model and a flowchart for optimizing the workflow of dump plowing with the simultaneous application of mineral fertilizers, as well as additional crumbling and leveling of the soil proposed by the authors of a machine-tractor unit. The optimal power of the tractor engine, its mass, the width of the implement and its mass, the operating speed and the optimization criterion value - the minimum total energy costs for the process of plowing with related works (fertilizing, leveling the soil) were obtained. The technical and operational indicators of modern dump plows are analyzed and the most effective ones are selected. New directions of increasing the efficiency of arable units on dump plowing are presented.

Insights from Mathematical Modelling into Energy Requirement and Process Design of Continuous and Batch Stirred Tank Aerobic Bioreactors

Bioreaction kinetics, oxygen transfer and energy modelling were applied to stirred tank aerobic bioreactors. This was done to investigate how key input design variables influence bioreactor size, feed and wasted substrate, and electrical energy requirements for aeration and cooling, and to compare batch and continuous modes of operation. Oxygen concentration in the liquid is a key input design variable, but its selection is challenging as it can result in design trade-offs. Reducing its value caused a decrease in electrical energy requirement, however this tended to increase the working volume of the bioreactor. The minimum or near-to-minimum total energy requirement for oxygen transfer occurred when operating at the onset of flooding throughout the bioreaction time. For typical KS values, continuous mode of operation required a much smaller bioreactor volume, due to higher operating cell concentration, and this is a major advantage of continuous over batch.

Application of Mathematical Modelling to Reducing and Minimising Energy Requirement for Oxygen Transfer in Batch Stirred Tank Bioreactors

In this study, microbial kinetic and oxygen transfer modelling coupled with energy analysis was applied to investigate how manipulation and control of agitator power input and air flowrate can reduce and minimise the total energy requirement in a batch aerobic bioprocess subject to constraints. The study showed that major energy savings can be made by appropriate selection of these variables and how they are controlled throughout a bioprocess. In many bioprocesses, the oxygen concentration in the liquid is controlled at a constant value. This may be achieved by maintaining the agitator power at a constant value and varying the air flowrate or vice versa, or by continuously varying both. The modelling showed that the minimum or near-minimum total energy requirement occurred when operating at the onset of impeller flooding throughout the bioprocess by continuously varying both impeller power and air flowrate over the bioprocess time. Operating at the onset of flooding may not be practical to implement in practice. However, the minimum energy can be approached by dividing the bioprocess time into a small number of time segments with appropriately chosen constant agitator powers and varying the air flowrate within each segment. This is much more practical to implement.

Fundamental principles of vascular network topology

The vascular system is arguably the most important biological system in many organisms. Although the general principles of its architecture are simple, the growth of blood vessels occurs under extreme physical conditions. Optimization is an important aspect of the development of computational models of the vascular branching structures. This review surveys the approaches used to optimize the topology and estimate different geometrical parameters of the vascular system. The review is focused on optimizations using complex cost functions based on the minimum total energy principle and the relationship between the laws of growth and precise vascular network topology. Experimental studies of vascular networks in different species are also discussed.

Asymptotically Stabilizing Potential Control for the Eye Movement Dynamics

In this paper, we analyze the problem of stabilizing a rotating eye movement control system satisfying the Listing’s constraint. The control system is described using a suitably defined Lagrangian and written in the corresponding Hamiltonian form. We introduce a damping control and show that this choice of control asymptotically stabilizes the equilibrium point of the dynamics, while driving the state to a point of minimum total energy. The equilibrium point can be placed by appropriately locating the minimum of a potential function. The damping controller has been shown to be optimal with respect to a suitable cost function. We choose alternate forms of this cost function, by adding a term proportional to the potential energy, and synthesize stabilizing control, using numerical solution to the the well known Hamilton Jacobi Bellman equation. Using Chebyshev collocation method, the newly synthesized controller is compared with the damping control.