Preliminary Mathematical Modeling Research Articles

APPLICATION OF HYDROGELS FOR WATER SHUTOFF TREATMENTS. Message No. 2

The article analyzes the use of hydrogels with nanoparticle additives for well water shutoff, as well as the development of a mathematical apparatus for hydrodynamic modeling of water shutoff operations. One of the most significant trends in the development of gel forming compounds for well water shutoff in the last 10 years has been the use of nanocomposites. The base polymers for nanocomposites used for water shutoff operations are either synthetic or biopolymer origin. The article highlights the novelty and prospects of using nanoparticles in sealing compositions. Various nanocomponent additives are used to increase the success of the use of hydrogel polymer systems in order to limit water inflow and expand the scope of their application in complicated reservoir conditions. These include carbon and mineral nanoparticles, which increase the stability and strength of crosslinked gels in formation conditions.In this paper, we consider the optimization of the repair and insulation operations design using gels for well water shutoff using mathematical modeling, which helps to justify the volume of hydrogel injection and calculate the necessary pressure gradients at which the sealing screen remains stable. The paramount importance of determining the source of well flooding is emphasized, depending on which the processing design is already being built, and appropriate materials are selected; trends in the development of repair and insulation operations at the present stage are traced. Based on the results of the implementation of the proposed model by numerical methods, the authors constructed diagrams of the stability of the waterproofing screen depending on the fracture width, screen size, gel injection rate and reservoir permeability. The technique proposed in the work allows to correctly select and optimize the technological parameters of the operation to maintain the stability of the screen in specific geological conditions.Mathematical modeling allows us to strictly justify the volume of injection of the gel screen, increase the technological and economic efficiency of the process, and in large fields — to rank wells according to the priority of processing. Oilfield practice in various regions of the country fully confirms the main conclusions made in this review article. Preliminary mathematical modeling and the introduction of microdispersions into gel formulations can significantly increase the efficiency of water shutoff operations. The next step in the development of water insulation technologies is the use of nanodispersions, which look very promising in laboratory modeling and are no longer exotic materials with unrealistic cost.

Physiology of the weight-loss plateau in response to diet restriction, GLP-1 receptor agonism, and bariatric surgery.

The objective of this study was to investigate why different weight-loss interventions result in varying durations of weight loss prior to approaching plateaus. A validated mathematical model of energy metabolism and body composition dynamics was used to simulate mean weight- and fat-loss trajectories in response to diet restriction, semaglutide 2.4 mg, tirzepatide 10 mg, and Roux-en-Y gastric bypass (RYGB) surgery interventions. Each intervention was simulated by adjusting two model parameters affecting energy intake to fit the mean weight-loss data. One parameter represented the persistent shift of the system from baseline equilibrium, and the other parameter represented the strength of the feedback control circuit relating weight loss to increased appetite. RYGB surgery resulted in a persistent intervention magnitude more than threefold greater than diet restriction and about double that of tirzepatide and semaglutide. All interventions except diet restriction substantially weakened the appetite feedback control circuit, resulting in an extended period of weight loss prior to the plateau. These preliminary mathematical modeling results suggest that both glucagon-like peptide 1 (GLP-1) receptor agonism and RYGB surgery interventions act to weaken the appetite feedback control circuit that regulates body weight and induce greater persistent effects to shift the body weight equilibrium compared with diet restriction.

ГРАФО-АНАЛИТИЧЕСКИЙ МЕТОД ОПРЕДЕЛЕНИЯ НАПРЯЖЕНИЙ В ПОЧВЕННОМ СЛОЕ ПОД ДЕЙСТВИЕМ ДВУГРАННОГО КЛИНА

The study of the stress distribution process in the soil layer is an important stage in the design of tillage machines, particularly tillage working elements. The experimental identification of patterns between the stress distribution zone in the soil layer and the parameters of tillage working elements is a time-consuming process. Therefore, it is recommended to conduct preliminary mathematical modeling of this process to minimize the overall number of experiments. The research purpose: development of a grapho-analytical method that can determine the pattern between the stress distribution zone in front of the dihedral wedge and its parameters. The concepts of classical and agricultural mechanics were used in the research. The methodology is based on scientific methods of cognition such as mathematical modeling, abstraction, analysis, and synthesis. Using the equation proposed by J. Boussinesq, a grapho-analytical method was developed to determine the stresses arising in the soil layer under the influence of the dihedral wedge. This method takes into account the influence of the dihedral wedge parameters and the physical and mechanical characteristics of the soil. The proposed method can be used in the design of tillage working elements. Specifically, to justify the chisel outreach of the blade working element at the stage of theoretical research. It was found that there is a direct proportion between the length of the dihedral wedge and the total area of deformed soil. Thus, as the length of the wedge increased by 83 percent (from 0.05 to 0.30 meters), the area of deformed soil increased by 80 percent (from 0.02 to 0.10 square meters).

Modeling of analytical, preparative and industrial scale counter-current chromatography separations

Analytical, preparative and industrial scale counter-current chromatography (CCC) processes differ in the volumes of the loaded solution of components to be separated and in the design of the equipment. Preliminary mathematical modeling is necessary for selection of the optimal design and operation mode of these CCC separations. This study aims to compare simulations of CCC separations at different scales, using an exact description based on the model of equilibrium cells and a much simpler approximate solution based on the Gaussian distribution. Equations for modeling CCC separations of different scales and examples of simulation these separations are presented. It is shown that the discrepancy between the two simulations increases with an increase in the volume of the loaded solution of the components and a decrease in the number of equilibrium cells of a CCC device. In analytical and preparative separations, which are based on complex centrifugal devices, and relatively small sample volumes are injected, approximate equations can be used to simulate various options of CCC separation. In industrial-scale CCC separations, large volumes of the solution of components may be loaded, and as we have proposed previously, these separations can be based on a cascade of mixer-settler extractors. In this case, a more accurate mathematical description based on the cell model equations should be used for modeling.

ADAPTIVE SPATIAL-FREQUENCY, SPATIAL-TEMPORAL AND SPATIAL-CODE SIGNAL SEPARATION SYSTEMS

The basis of systems considered in this article is a self-focusing antenna array, consisting of bars with 2 * m receiving antenna elements located equidistantly in each of them. The description and results of preliminary mathematical modeling of an adaptive antenna lattice with a possibility of realization of functions are provided in her spatially-frequency or spatially-code allocation and tracking of signals. The results of modeling of a linear lattice which have confirmed a possibility of reliable allocation of one of two the coded signals influencing her are given in rather wide dynamic range of their entrance levels. Similar systems can find application in satellite and land systems of a radio communication. The use of such systems increases the energy potential of radio links and reduces interference between signals.

Experimental substantiation of the rational parameters for a reaping machine of the comb type for harvesting oil flax seeds

This paper reports the results of the experimental study to substantiate the rational structural and regime parameters of a two-drum reaping machine for harvesting flax oilseeds by the method of combing plants on the root. We have confirmed the results of the preliminary mathematical modeling of the process of separating a combed heap in the reaping machine with a predefined curved shape of the casing. An experimental study of the heap separation process in a reaping machine has established the dependence of the mass fraction of the discharge of husk and stem particles from its region δ h , the proportion of the release of seeds and capsules with seeds δ h, and the consumed power P, on the rotation frequency of the beater-reflector n 1 , and the combing drum n 2 , the position of the air grate L and its width B. The following structural-mode parameters of the comb-type reaping machine for harvesting oil flax seeds have been defined as the most significant ones: the rotation frequency of the beater-reflector, n 1 =892 rpm; the rotation frequency of the comb drum, n 2 =652 rpm; the position of the air grate, L=0.62 m, and its width, B=0.56 m. In this case, the mass fraction of the discharge of husk and stem particles is δ h =47.5 %, the share of the loss of seeds and capsules with seeds from the reaping machine is, respectively, δ h =2.1 %, and the power consumed to perform the process is P=2.7 kW. The statistical analysis has demonstrated that the correlation coefficient between the theoretical and experimental data is 0.88‒0.95; a relative error in the optimal values is 4.6 %. The actual and statistical comparison of the theoretical and experimental data has confirmed the adequacy of the mathematical models built as a result of the theoretical research. Based on the results of our experimental research, one can argue about the usefulness of their application for engineering calculations when designing new technical means for harvesting crops by the method of combing plants on the root

Digitalization of Legal Practices: New Opportunities

Fragmentary digital models of society and its legal life have already been created and used, including the ones used unconsciously and haphazardly. Improving the efficiency and reducing the level of budget, corporate and personal costs associated with the implementation of legal should be one of the goals of the "digital" legal policy. The authors investigate some applied aspects of developing digital models of law enforcement (in particular, the rules of forming the forecast of social and legal reality indicators). Successful digitalization of legal regulation, according to the authors, is impossible without building correct quantitative mathematical models using methods of both theoretical and empirical modeling. The article formulate recommendations for building stochastic models that allow to use the mathematical apparatus of the probability theory. It substantiates the expediency of using probabilistic values as quantitative indicators of such models. It identifiers the main directions of practical implementation of the proposed approaches. Such directions, in particular, include ensuring transition of rule-making practice from an intuitive assessment of the effectiveness of the projected legislation to a computational assessment based on preliminary mathematical modeling of the projected norms and their applications.

DEVELOPMENT OF VIBRATION-PROOF METAMATERIALS TO REDUCE THE NEGATIVE IMPACT ON OIL AND GAS FACILITIES

Background The article is devoted to the concept of new vibration-proof metamaterials with quasizero stiffness to reduce the negative impact on humans, machines and equipment. At oil and gas facilities, vibration can occur from a variety of sources. For protection, it is proposed to use modern approaches in vibration isolation. From the point of view of mechanics, the most promising direction is the use of special elastic mechanical systems, known as systems with quasi-zero stiffness. Modern advances in the field of additive technologies, three-dimensional printing, provide ample opportunities in the field of creating metamaterials. In particular, this approach can be used to create special elastic structures in elastic constructions, in other words, to create new means of protection against vibration and shock. By creating various internal structures of elastic metamaterials, one can impart to them various force characteristics, including those with quasi-zero rigidity. Aims and Objectives To study the vibration-proof metamaterial with an internal structure that provides quasizero stiffness during its compression. The proposed vibroprotection metamaterial consists of two external elastic layers, as well as an internal layer, which is an elastic undulating structure that, when deformed, provides quasi-zero rigidity. Methods A preliminary mathematical modeling of a single cell of the proposed metamaterial has been carried out. Possible cell sizes are estimated. To verify the data results, computer simulation of a single cell was performed using the ANSYS software package. Results The results of analytical and computer calculations showed that this vibration-proof material with the adopted parameters will have an optimal load equal to 8154 kg. To test the feasibility of manufacturing these metamaterials, demo samples were published using printing on a Picaso Designer 3D printer. The thickness of the layers was 0.3 mm. The analysis of the obtained samples showed that using 3D printing it is possible to create the developed vibration-proof metamaterials, which potentially can have high operational properties. The proposed structure of metamaterials makes it possible to effectively and smoothly damp oscillations of objects, in other words, to have high vibration-proofing and shock-proof properties, and to be effective at various objects of the oil and gas industry.

Properties of B-pillar made of aluminium 7075 in warm forming process

Abstract This paper presents the properties of warm forming of a B-pillar from 7075 aluminum alloy in state T6. Based on preliminary mathematical modeling, it was determined that the greatest strains and risk of aluminum cracking occur in the foot of B-pillar, therefore the forming process was simplified and conducted only for this part. The most important issue was to select the proper forming temperature and heating time, so as to preserve state T6 of the aluminum. Conducted tests demonstrated that the best mechanical properties without cracking were obtained for component place in a chamber furnace preheated to temperature 350°C. After approx. 5-6.5 minutes, it reached a temperature of 240°C.

COMPLEX APPROACH FOR PORTABLE CRYOPRESERVATION OF SEGMENTS OF BLOOD VESSELS WITH POLYDIMETHYLSILOXANE

Aim.To develop a safe protocol for cryopreservation of segments of iliac arteries straight after their retrieval from post-mortem donor with the use of polydimethylsiloxane as a coolant and cryoprotectant.Materials and methods.Eleven segments of iliac arteries were retrieved from post-mortem donor and divided into four groups including control. Based on preliminary heat and cold transfer mathematical modeling and tests with tissueequivalent phantom arterial segments were placed on plastic mounts and cryopreserved by following protocol: groups 1 and 2 were immersed in polydimethylsiloxane and cooled rapidly at 180 °С/min to –75 °С. Group 3 segments were cryopreserved at 1,6 °С/min in PDMS – fi lled cryo-container placed in the freezer at –80 °С. All segments were defrosted by immersion in PDMS at +24 °С and then examined for morphology changes by histological methods and SEM. EDS analysis with the use of AzTech software also was performed for Si – content evaluation. Restricted biomechanical tests were conducted for group 2 segments.Results.There were no signifi cant morphological differences between segments of the control and cryopreserved groups except for the segment with slow cooling.Conclusion.Mobile cryopreservation may allow increasing the effi ciency of retrieval of a large number of donor tissues for possible later use in the processing of bioprostheses of blood vessels; or, after decellularization, as well as tissue-specifi c matrices for tissue-engineering blood vessels.

Metallic Composites Strengthened with Intermetallic Reinforcing Elements

An efficient method which uses explosion welding to obtain titanium-based composites with isotropic mechanical properties is examined. A new scheme has been devised for strengthening a composite on the basis of preliminary mathematical modeling in the program Cosmos Works. The relationship of the material’s thermal loading regime to its phase composition and volumetric content of reinforcing intermetallic elements is studied.

Experimental advances and preliminary mathematical modeling of the Swiss-roll mixed-reactant direct borohydride fuel cell

The Swiss-roll single-cell mixed reactant (SR-MRFC) borohydride – oxygen fuel cell equipped with Pt/carbon cloth 3D anode and either MnO2 or Ag gas-diffusion cathodes is investigated by a combination of experimental studies and preliminary mathematical modeling of the polarization curve. We investigate the effects of four variables: cathode side metallic mesh fluid distributor, separator type (Nafion 112® vs. Viledon®), cathode catalyst (MnO2 vs. Ag), and the hydrophilic pore volume fraction of the gas-diffusion cathode. Using a two-phase feed of alkaline borohydride solution (1 M NaBH4 – 2 M NaOH) and O2 gas in an SR-MRFC equipped with Pt/C 3D anode, MnO2 gas diffusion cathode, Viledon® porous diaphragm, expanded mesh cathode-side fluid distributor, the maximum superficial power density is 2230 W m−2 at 323 K and 105 kPa(abs). The latter superficial power density is almost 3.5 times higher than our previously reported superficial power density for the same catalyst combinations. Furthermore, with a Pt anode and Ag cathode catalyst combination, a superficial power density of 2500 W m−2 is achieved with superior performance durability compared to the MnO2 cathode. The fuel cell results are substantiated by impedance spectroscopy analysis and preliminary mathematical model predictions based on mixed potential theory.

Numerical Simulation of High Frequency Vibration Recovery Enhancement Technology in Low-Permeability Reservoirs

The purpose of this article is to make a quantitative research on high frequency vibration recoverys advantages over traditional production methods. In this paper, acoustic pressure relation equation was established and a quantitative description about the porous media reservoir and fluid parameters alteration after high frequency vibration effect were attained. Furthermore, a preliminary mathematical model and computer modeling under high frequency vibration effect in low permeability reservoir were developed. This study was successfully applied to simulation of high frequency vibration recovery in a low permeability reservoir in Western China. The result showed that high frequency vibration recovery could stimulate single well production. By comparing with the well actual production history, it shows that this study can accurately simulate production performance of high frequency vibration recovery enhancement technology in low-permeability reservoirs.

A Solute Gradient in the Tear Meniscus. I. A Hypothesis to Explain Marx's Line

Marx's line is a line of mucosal staining behind the mucocutaneous junction. It can be demonstrated throughout life in all normal lids by staining with lissamine green and related dyes. Of all the body orifices, only the mucosae of the eye and mouth are directly exposed to the atmosphere. In this paper, we suggest that for the eye, this exposure leads to the formation of Marx's line. The tear meniscus thins progressively toward its apex, where it is pinned at the mucocutaneous junction of the lid. It also thins toward the black line, which segregates the meniscus from the tear film after the blink. We predict that, because of the geometry of the tear meniscus, evaporation generates a solute gradient across the meniscus profile in the anteroposterior plane, which peaks at the meniscus apices at the end of the interblink. One outcome would be to amplify the level of tear molarity at these sites so that they reach hyperosmolar proportions. Preliminary mathematical modeling suggests that dilution of this effect by advection and diffusion of solute away from the meniscus apex at the mucocutaneous junction will be restricted by spatial constraints, the presence of tear and surface mucins at this site, and limited fluid flow. We conclude that evaporative water loss from the tear meniscus may result in a physiological zone of hyperosmolar and related stresses to the occlusal conjunctiva, directly behind the mucocutaneous junction. We hypothesize that this stimulates a high epithelial cell turnover at this site, incomplete epithelial maturation, and a failure to express key molecules such as MUC 16 and galectin-3, which, with the tight junctions between surface epithelial cells, are necessary to seal the ocular surface and prevent penetration of dyes and other molecules into the epithelium. This is proposed as the basis for Marx's line. In Part II of this paper (also published in this issue of The Ocular Surface), we address additional pathophysiological consequences of this mechanism, affecting lid margins.

A Study of L‐Lactide Ring‐Opening Polymerization Kinetics

AbstractSummary: The paper presents an experimental study of L‐lactide polymerization in molten state using as initiator the Stannous Octoate. The experiments were performed in a Haake mixer. The operating temperatures were between 170 and 195°C, the reaction time up to 60 min and monomer to initiator initial molecular ratio between 102 and 5 · 103. The conversion was determined by using 1H NMR and the molecular weights distributions by SEC. A preliminary mathematical modeling study was also performed, based on experimental data and a previously published reaction scheme.

RESULTADOS QUALITATIVOS E QUANTITATIVOS DA APLICAÇÃO DE MODIFICADORES DE FLUXO NO DISTRIBUIDOR DA AÇOS VILLARES USINA MOGI DAS CRUZES

This work aims to evaluate the influence and benefits obtained with the utilization of tundish furniture at Acos Villares – Mogi das Cruzes Plant. The expected benefits are inclusion removal and yield improvement in the continuous casting machine. The methodology employed in this work consisted in preliminary mathematical modeling of the system for the furniture project, the systematic Ripple Pad and dams utilization and finally the analysis of results in terms of inclusion removal and yield improvements. Considering the level of inclusions obtained with the systematic utilization of the system Ripple Pad and dams, a reduction around 30% in rejection of final products was obtained for critical applications. Consistent reduction around 10% in the discharge for sequencial casting of different steel grades was also obtained, providing yield improvement.

Calculations of the field distribution of a spectrometric magnet

The design and construction of magnetic systems of electrophysical installations require preliminary mathematical modeling. Mathematical modeling is necessary in the process of adjustment and subsequent operation of an installation. Calculations of fields of magnetic systems, although performed on the basis of the solution of direct magnetostatic problems, are related to the class of inverse magnetostatic problems, since they actually include the search for optimal design of current elements and an iron yoke for a given magnetic field distribution. In this work, the method of numerical solution of the magnetostatic problem for domains with boundaries containing cusps is proposed. Using this numerical method, magnetic systems of rectangular configuration were modeled with high accuracy. In particular, the calculations of several modifications of the magnetic system SP-94 used in certain experimental installations are presented.

Computational modeling of magnets for electrophysical setups

The design, construction and operation of magnetic systems of some electrophysical setups require preliminary mathematical modeling. While calculating the fields of the magnetic systems mentioned (based on solving a set of direct problems of magnetostatics), we attempted to solve the inverse problem of magnetostatics, namely, to find an optimal construction of the current elements and ferromagnetic yoke for a required distribution of the magnetic field. This work discusses the results of numerical modeling of the magnet field distribution for some modifications of the SP-94 spectrometric magnet used in some experimental setups.

Does estradiol induce the preovulatory gonadotropin-releasing hormone (GnRH) surge in the ewe by inducing a progressive change in the mode of operation of the GnRH neurosecretory system.

Estradiol profoundly influences GnRH secretion during the follicular phase of the estrous cycle of the sheep. Estradiol not only regulates the frequency and amplitude of GnRH pulses, but also produces qualitative changes in its pattern of release and induces a sustained GnRH surge during which discrete pulses are not readily evident. In this study, we tested the hypothesis that qualitative changes in GnRH secretion are an integral part of an estradiol-induced change in the mode of operation of the GnRH neurosecretory system that leads to generation of the GnRH surge. This was achieved by the measurement of GnRH in samples of pituitary portal blood collected at 1-min intervals for an 11-h period encompassing the pre- and early surge periods in an artificial follicular phase model. In each of the seven ewes studied, a highly characteristic alteration in the moment to moment pattern of GnRH was observed. This consisted of a progressive change from a strictly episodic pattern of GnRH release to one containing both episodic and nonepisodic components and, after amplification of both components, a period of extremely high values during which individual episodic increases were no longer readily recognizable. Preliminary mathematical modeling of the data suggested that these patterns could be produced by a change in GnRH from a predominantly low to a mixture of low and high amplitude inputs. Similar changes in minute to minute patterns of GnRH secretion were observed during the natural follicular phase. These findings are consistent with the hypothesis that estradiol induces the GnRH surge by altering the mode of neurosecretion, rather than by merely causing quantitative changes in the episodic pattern of release.