Optimization of coal tar gas chromatography conditions using probabilistic-deterministic design of experiment

The development of physicochemical methods for the analysis of objects of complex composition requires the application of methods of mathematical experiment design. This article investigates the possibility of using probabilistic-deterministic design of experiment (PDDoE) for obtaining a mathematical model of the chromatographic separation process of coal tar hydrogenation products on an Agilent 7890A device with an Rxi-5ms column. It is shown that the relationship between the column heating rate and the carrier gas pressure with the values averaged for the entire chromatogram can be established with a high accuracy. It is noted that the accuracy of modeling the individual characteristics of the mixture components’ peaks is less, but remains sufficient for many practical needs. Nonlinear multiple correlation coefficients (NMC) for the dependence of the average retention time and average intensity on the considered factors are more than 0.99; they are more than 0.98 for the average peak width. NMC for the dependence of the resolution with the relation to the peaks of naphthalene and 2-ethylphenol is more than 0.8 at a significant level that sufficient for practice. The quality of the mathematical model was checked by triple registration of the chromatogram at the values of the column heating rate and carrier gas pressure that were not used in the training experiment. The measurement results are excellent squared with those calculated using the obtained generalized equations. The PDDoE method can be recommended as a method for mathematical design of an optimization experiment in gas chromatography.

Mathematical experiment as a tool for modeling the freight transportation process

The process of multimodal freight transportation on a railway loop is investigated, for which a multicriteria optimization model with time indicators is created, which is a nonlinear integer programming problem. The developed approach is based on egalitarian and utilitarian principles in the welfare theory and allows (along with Pareto optimal transportation plans) to find other plans that can be considered rational from the point of view of maintaining the balance of interests of the transportation process participants. A mathematical experiment is an effective heuristic tool in research. The algorithm for solving the optimization problem is implemented in the environment of a computer algebra system and brought to numerical results.

Computational studies to optimize the geometry of the low-thrust rocket combustion chamber using gaseous propellants

Due to the tough requirements for the environmental safety of the space objects operation, the use of methane-based fuel together with oxygen is a promising direction in developing a new generation of rocket and space technology, including low-thrust rocket engines. When developing low-thrust rocket engines running on oxygen-methane fuel, a mathematical experiment helps to identify the determining factors that affect the quality of the working process in the combustion chamber and to make a calculated optimization of the parameters for supplying fuel components to the combustion chamber. This contributes to a better understanding of the physics of the ongoing processes and leads to recommendations for the design of individual components of the combustion chamber. The numerical simulation enables us to optimize the geometry of the combustion chamber in order to obtain the maximum value of the chamber coefficient, which for an isobaric combustion chamber can be equal to the coefficient of the flow complex. This approach can significantly reduce the number of expensive bench tests. The paper introduces a physical and mathematical model of the workflow in the combustion chamber of a low-thrust rocket engine and gives a comparative analysis of the calculation results for various modifications of the original geometry of the low thrust rocket chamber. Recommendations are given for changing the initial geometry of the combustion chamber in order to increase the coefficient of the flow complex while maintaining a satisfactory thermal state of this chamber.

Mathematical Modelling in Analytical Chromatography: Problems and Solutions

Based on an analysis of the results of original research performed in the Laboratory of Sorption Methods of the Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academy of Sciences within the project “Mathematical Chromatograph,” the review covers the aim and strategy of the imitation modeling of high-performance chromatography; associated problems of the theory of intermolecular interactions; classifications of polar stationary phases by their selectivity; descriptions of the kinetics and dynamics of sorption processes, choice of the composition of multicomponent mobile phases in HPLC and ion chromatography using the method of the dynamic map of a chromatographic system; and the development of alternating gradient modes using a mathematical experiment.

Profiling of sudden contraction of circular pipe by sharp-edged pipe insert

Measures to reduce energy losses in pipeline transport systems must be implemented already at the design stage. In particular, this also applies to local resistances of pipelines. For symmetrical sudden pipe contraction, one of such measure is profiling using insert. The paper considers a sharp-edged pipe insert, which in comparison with others has larger areas of flow separation. The diameter of the insert was calculated as the arithmetic mean between the diameters forming the sudden pipe contraction. Using the methodology described in the literature, the contraction length ratio as the areas of influence between two symmetrical sudden contractions of a circular pipe during the flow of a single-phase turbulent flow of Newtonian fluid was investigated. The coefficient of mutual influence of these local resistances was determined by formulae for direct-flowing and non-direct-flowing locking devices, which simulated symmetrical and asymmetrical fluid flow after the constriction plane, respectively. The contraction rate from 0.064 to 0.696 inclusive are considered. According to the results of calculations, no mutual influence of two sudden contractions of circular pipe was found. This indicates the unsuitability of using formulae for locking devices in this methodology for determining the contraction length ratio. Therefore, to study this problem on the sudden pipe contraction with different contraction rates, it is proposed to conduct a physical experiment. In a mathematical experiment, you can use formulae to determine the following values: upstream recirculation length and downstream recirculation length; inlet length of cylindrical pipes with turbulized the flow devices; length of the velocity profile stabilization after local resistances.

A dai-liao hybrid conjugate gradient method for unconstrained optimization

One of todays’ best-performing CG methods is Dai-Liao (DL) method which depends on non-negative parameter and conjugacy conditions for its computation. Although numerous optimal selections for the parameter were suggested, the best choice of remains a subject of consideration. The pure conjugacy condition adopts an exact line search for numerical experiments and convergence analysis. Though, a practical mathematical experiment implies using an inexact line search to find the step size. To avoid such drawbacks, Dai and Liao substituted the earlier conjugacy condition with an extended conjugacy condition. Therefore, this paper suggests a new hybrid CG that combines the strength of Liu and Storey and Conjugate Descent CG methods by retaining a choice of Dai-Liao parameterthat is optimal. The theoretical analysis indicated that the search direction of the new CG scheme is descent and satisfies sufficient descent condition when the iterates jam under strong Wolfe line search. The algorithm is shown to converge globally using standard assumptions. The numerical experimentation of the scheme demonstrated that the proposed method is robust and promising than some known methods applying the performance profile Dolan and Mor´e on 250 unrestricted problems. Numerical assessment of the tested CG algorithms with sparse signal reconstruction and image restoration in compressive sensing problems, file restoration, image video coding and other applications. The result shows that these CG schemes are comparable and can be applied in different fields such as temperature, fire, seismic sensors, and humidity detectors in forests, using wireless sensor network techniques.

Structure and operation algorithm of the data collection module of the Super c-τ factory electromagnetic calorimeter

The study is devoted to the development of a data collection module of the electromagnetic calorimeter of the Super c-τ factory collider. The data collection module is one of the main parts of the data acquisition system of the electromagnetic calorimeter. It is designed for analog and digital signal processing of scintillation counters, calculating its main characteristics (amplitude, time of occurrence and quality of fitting), and participates in the launch of the detector data acquisition system. A prototype of the module on which the module will be debugged and the algorithm of the device will be checked is being developed. The algorithm of the module includes the calculation of signal characteristics and the formation of packets for data transmission. Signal characteristics are calculated by approximating a function defined either by the least squares method or by the method of χ2 function minimization. In the course of a mathematical experiment, it was found that the method of χ2 function minimization gave more accurate calculation values than the least squares method. However, it requires an experiment with scintillation counters to determine the necessary coefficients. Therefore, the coefficients of the approximating curve are determined by the least squares method in the proto-type and the method of χ2 function minimization is used in the module. Based on the results obtained, an algorithm of the module operation was compiled, which was then implemented in the field-programmable gate array Altera Cyclone 10GX.

Development of methods for parameters of long-term contracts optimization for operational road maintenance

The object of research is the processes of cost, duration and quality management in long-term contracts for the maintenance of roads. The presented work is based on the use of project management theory. The main hypothesis of the study is the application of methods for optimizing the parameters of long-term contracts for the maintenance of roads. Features, advantages and problematic issues concerning the use of long-term contracts based on quality indicators in the road sector are considered. The world and domestic experience of introduction of long-term maintenance of highways is analyzed. The main approaches to optimization of parameters are defined and the mathematical model of management of processes of cost, duration and quality in long-term contracts is developed. Based on the model, two methods of mathematical solution of the optimization problem of the proposed parameters have been developed. A mathematical experiment based on the example of the project of long-term maintenance of roads on the final quality indicators, the results of which showed that the adaptive capacity of projects by the second method is less flexible than the first. But the second method achieved better performance to minimize time parameters with averaging at 5 %. Optimization of parameters of long-term contracts for maintenance of roads has a multiplier effect, which is expressed in reducing administrative costs of the customer, reducing the responsibility of road services, creating conditions for stable financing of road works, satisfaction of road users, building strong partnerships between the customer and the contract. The results of calculations have practical value and can serve as a tool for making sound management decisions to determine the basic parameters of long-term contracts for the maintenance of roads based on quality.

The mathematical model of engagement and analytical description of tooth profile of waveform edge kinematic reducer

The problem of creating a waveform edge kinematical reducer with multi-pair gearing brings to the fore a range of issues in the field of geometric-kinematic gearing theory, which are considered in this work. The synthesis of multi-pair gearing for a waveform edge kinematical reducer, which ensures the constancy of their transfer function, provides for: development of a mathematical model of gearing taking into account the peculiarities of the interaction of teeth during special-spherical motion; description of the profile of the teeth by a system of equations for a spherical surface and for a normal section of teeth for internal gearing; identification with the help of the MathCAD 2010 Professional program of a mathematical experiment and determination of the area of existence of 100 % multi-pair mating of teeth by comparing the shape of their profile with the nature of the analytical function of multi-pair engagement