Mathematical Model For Computation Research Articles

Multi-disciplinary engineering design of a high-speed nature-inspired unmanned aquatic vehicle

Recently, small unmanned vehicles have increased their technological importance and practical relevance in private and public interest maritime applications. However, due to this technology's novelty and early stages, complex challenges in engineering design remain unsolved. Therefore, the purpose of this article is to demonstrate the development of an innovative high-speed Unmanned Aquatic Vehicle (UAV) with the inclusion of robust and multi-objective optimization-based methods. This work implemented four robust optimization methods (e.g., efficient low drag generation, theoretical calculation, the production of hydrodynamic forces, and fluid-structure interaction) to design, components, performance, and material optimization. Furthermore, robust computational simulations and mathematical modelling were applied during the engineering design process. The main research findings show that the version of the UAV developed is optimized and able to operate in several working conditions in oceanic applications. Findings also complement previous related studies and offer novel technological alternatives for maritime applications and species detection in complex oceanic conditions. Finally, the aspects of theoretical significance and application value of the research are discussed in the paper.

Research of the process of air separation of grain material in a vertical zigzag channel

The aim of the research is to determine ways to improve the efficiency of grain materials pneumatic separation based on the study of the interaction mechanism of grains with the air flow in the channel elements, which are inclined sections of the air duct. The paper considers a modified separation method that separates the grain material according to the aerodynamic properties of the components in a vertical zigzag air channel in an aerodynamic and gravitational field. The studies were carried out by means of mathematical modeling followed by experimental confirmation of the modeling results. A computer mathematical model was created in the MathCad 13 application package to determine the parameters of the zigzag aspiration channel. This model describes the influx of parameters in the channel (width, height, cut of the zigzag ledge to the horizon, edge of the zigzag ledge) on the nature of the grain trajectory. As a result of the numerical simulation process using the mathematical package Mathematica, dependence was obtained to determine the trajectory of motion depending on the angular velocity. An increase in the pneumatic separation effect during the grain mixtures division due to the influence of the Magnus effect was established as a result of experimental studies. The design of a zigzag separator with an annular channel section has been improved based of the research carried out.

Self-Aligning Finger Exoskeleton for the Mobilization of the Metacarpophalangeal Joint.

In the context of hand and finger rehabilitation, kinematic compatibility is key for the acceptability and clinical exploitation of robotic devices. Different kinematic chain solutions have been proposed in the state of the art, with different trade-offs between characteristics of kinematic compatibility, adaptability to different anthropometries, and the ability to compute relevant clinical information. This study presents the design of a novel kinematic chain for the mobilization of the metacarpophalangeal (MCP) joint of the long fingers and a mathematical model for the real-time computation of the joint angle and transferred torque. The proposed mechanism can self-align with the human joint without hindering force transfer or inducing parasitic torque. The chain has been designed for integration into an exoskeletal device aimed at rehabilitating traumatic-hand patients. The exoskeleton actuation unit has a series-elastic architecture for compliant human-robot interaction and has been assembled and preliminarily tested in experiments with eight human subjects. Performance has been investigated in terms of (i) accuracy of the MCP joint angle estimation through comparison with a video-based motion tracking system, (ii) residual MCP torque when the exoskeleton is controlled to provide null output impedance and (iii) torque-tracking performance. Results showed a root-mean-square error (RMSE) below 5 degrees in the estimated MCP angle. The estimated residual MCP torque resulted below 7 mNm. Torque tracking performance shows an RMSE lower than 8 mNm in following sinusoidal reference profiles. The results encourage further investigations of the device in a clinical scenario.

Nonlinear mathematical model of an economic soliton

In modern conditions of economic transformation, the functioning and development of production systems is characterized by instability, nonlinearity and dynamism of the main indicators and parameters. The financial and production system is affected by a large number of market, inflationary, social and other disturbances, which leads to the losses in financial stability, a decrease in production volumes, a decrease in demand for manufactured products, etc. Therefore, it is necessary to have an effective management system and operational decision-making. The relevant direction for solving this problem is the development of a flexible intelligent control system that makes it possible to diagnose quickly the unfavorable state of the financial and production system and activate promptly the mechanisms that return the system to equilibrium. In this case, information becomes the main resource of management, which performs an integrating role and is a necessary component when using all other resources. All this predetermines the use of information technology management. With a high dynamism and instability of the external environment, it becomes necessary to apply the methods and approaches of the new science of management, concentrating its attention on the theory of complex systems and nonlinear dynamics, with the help of which complex control systems can cope effectively with uncertainty and rapid changes. The development and use of modern information technologies for enterprise management are based on the introduction of integrated information processing technology and the creation of mathematical methods and computer modeling tools. In the work of information technologies, management is implemented by creating an integrated intelligent computerized system based on the use of economic and mathematical methods, computer technology and communication means, i.e. implements a fundamentally new management platform, which is based on the integration of management information through a mechanism for generalizing the information database and knowledge.

Single-cell and long-read sequencing to enhance modelling of splicing and cell-fate determination

Single-cell sequencing technologies have revolutionised the life sciences and biomedical research. Single-cell sequencing provides high-resolution data on cell heterogeneity, allowing high-fidelity cell type identification, and lineage tracking. Computational algorithms and mathematical models have been developed to make sense of the data, compensate for errors and simulate the biological processes, which has led to breakthroughs in our understanding of cell differentiation, cell-fate determination and tissue cell composition. The development of long-read (a.k.a. third-generation) sequencing technologies has produced powerful tools for investigating alternative splicing, isoform expression (at the RNA level), genome assembly and the detection of complex structural variants (at the DNA level).In this review, we provide an overview of the recent advancements in single-cell and long-read sequencing technologies, with a particular focus on the computational algorithms that help in correcting, analysing, and interpreting the resulting data. Additionally, we review some mathematical models that use single-cell and long-read sequencing data to study cell-fate determination and alternative splicing, respectively. Moreover, we highlight the emerging opportunities in modelling cell-fate determination that result from the combination of single-cell and long-read sequencing technologies.

Algorithm-Oriented SIMD Computer Mathematical Model and Its Application

This paper has designed a professional and practical SIMD computer mathematical model based on the SIMD physical machine model combined with the variable addition method. Furthermore, the model is applied in image collection, processing, and display operations, and a SIMD data parallel image processing system is finally established by absorbing the parallel computing advantages of the mathematical model. In addition, the data-parallel image processing algorithm is introduced and the convolutional neural network algorithm is optimized to promote the significant improvement of the main performance such as the accuracy of the application system. The final experimental results have shown that the highest accuracy of the data-parallel image processing algorithm reaches 93.3% and the lowest error rate reaches 0.11%, which proves the superiority of the SIMD computer mathematical model in image processing applications.

ECONOMICS AND ADVANCED CALCULATION METHODS OF FINANCIAL ENGINEERING

Topicality. The article defines the place and implementation of the tasks of financial engineering. In recent years, against the background of the active use of trade and financial instruments, the complexity of monetary relations between enterprises and financial institutions and the wide spread of computer technologies increase the relevance of the topic.Aim and tasks. The main purpose of the article is to determine the possibility of misuse of financial instruments reflecting the system of risk management, which is an element of financial engineering, which is considered as a means of achieving the competitiveness and strategic advantage of organizations.Research results. In the modern world, the processes of making managerial decisions are becoming more and more complex, while it is necessary to take into account an increasing number of factors that affect the financial results of an enterprise. Decision-makers are required to use mathematical skills in the design of financial transactions, knowledge of the basics of computer modeling. Today, not a single major financial institution in the world, including central banks, can work without computer mathematical models of modern financial science. From this point of view, a new direction in the training of specialists is relevant - financial engineering.Materials and methods. While conducting the research, sources related to financial engineering were examined, articles related to the complexity of monetary relations between enterprises and financial institutions and the wide spread of computer technologies were analyzed. Content analysis, induction, deduction, and comparative analysis methods were used during the research.Conclusion. The conclusion of the study is that the use of innovative financial technologies or the borrowing and use of advanced financial instruments from us requires a qualitatively new arrangement of cooperation, which is not possible under implementing sanctions. The final result is that the use of innovative financial technologies, the organization of the professional association of economists and financiers of the country, the creation and development of self-regulating organizations, the formation of a community of highly qualified specialists and the development of the quality management system of educational services are necessary for the development of machine building in Azerbaijan.

Exploring the Optimal Curves of Intersection for Enhanced 3D Shape Designing A Comprehensive Study on Geometric Optimization Techniques

Surface and solid intersection is emerging swiftly in many applications of computer graphics, engineering and mathematical models. In engineering science, several algorithms are produced for some unique purposes like intersection of prism/cone, cone/cone, prism/cylinder etc. All such procedures used different 3D drawing tools for creating geometrical interpretation of their required models. Surface intersection deals with numerous algorithms in computational and applied mathematics, needed for intersection of different surfaces such as rational polynomial parametric, implicit algebraic etc. In this paper, a novel surface intersection approach is proposed which works for all types of intersection like; parametric-parametric, explicit-explicit, implicit-explicit surfaces. This scheme includes a method for determination of significant points (boundary and turning points) from surface intersection sequence points. Optimal curve is fitted to these points by rational quadratic spline and a soft computing technique Genetic Algorithm (GA) is applied for attaining optimized curve, by allotting specific shape parameter values in the depiction of rational quadratic spline. However, some experimental results show the efficiency and robustness of this technique.

Patient-specific 0D–3D modeling of blood flow in newborns to predict risks of complications after surgery

Abnormal developments of the cardiovascular system are common congenital malformations. Computational fluid dynamics and mathematical modeling can be used to perform quantitative predictive assessments of hemodynamic properties in varied conditions. This article addresses the development of a coupled 0D–3D model of blood flow in newborns to predict risks of complications after surgery. The 0D-model of systemic circulations is created by using the analogy between the blood flow in vessels and the flow of current through an electric circuit. A shunted section of the aorta and pulmonary artery is replaced with a 3D-model with two-way fluid-solid interaction (FSI).A section in a vessel with the aortic valve is examined in a separate 3D-model. Three-dimensional geometry is based on real CT-scans of a patient. The algorithm for coupling models of different levels relies on meeting the condition that pressures and volumetric blood flows are equal at the interaction boundary. We have developed an algorithm for identifying personal parameters from the results obtained by solving an optimization problem. Computational experiments with different individual geometry of the aorta and aortic valve made it possible to analyze blood flow velocities, near-wall stresses, flows, and valve deformations. Observable near-wall stresses can be considered risk factors that could cause calcification on valve leaflets and other valve diseases. Computational solutions in the “aorta – shunt – pulmonary artery” 3D-system allowed obtaining spatial distributions of velocities, pressures, near-wall stresses and other parameters that are significant in respect to probable pathology development. The developed approaches are primarily relevant for decision-making in surgical practice to predict risks of postoperative complications. In future, our plans are to develop the model so that it covers also saturation and oxygen exchange. This is necessary for assessing whether oxygen supply to the lungs is adequate.

Персонализированное 0d–3d-моделирование течения крови у новорожденных для прогнозирования рисков осложнений после оперативного лечения

Abnormal developments of the cardiovascular system are common congenital malformations. Computational fluid dynamics and mathematical modeling can be used to perform quantitative predictive assessments of hemodynamic properties in varied conditions. This article addresses the development of a coupled 0D–3D model of blood flow in newborns to predict risks of complications after surgery. The 0D-model of systemic circulations is created by using the analogy between the blood flow in vessels and the flow of current through an electric circuit. A shunted section of the aorta and pulmonary artery is replaced with a 3D-model with two-way fluid-solid interaction (FSI).A section in a vessel with the aortic valve is examined in a separate 3D-model. Three-dimensional geometry is based on real CT-scans of a patient. The algorithm for coupling models of different levels relies on meeting the condition that pressures and volumetric blood flows are equal at the interaction boundary. We have developed an algorithm for identifying personal parameters from the results obtained by solving an optimization problem. Computational experiments with different individual geometry of the aorta and aortic valve made it possible to analyze blood flow velocities, near-wall stresses, flows, and valve deformations. Observable near-wall stresses can be considered risk factors that could cause calcification on valve leaflets and other valve diseases. Computational solutions in the “aorta – shunt – pulmonary artery” 3D-system allowed obtaining spatial distributions of velocities, pressures, near-wall stresses and other parameters that are significant in respect to probable pathology development. The developed approaches are primarily relevant for decision-making in surgical practice to predict risks of postoperative complications. In future, our plans are to develop the model so that it covers also saturation and oxygen exchange. This is necessary for assessing whether oxygen supply to the lungs is adequate.

Computer simulation of the dynamics of heat release in diesel cylinders

The relevance of computer mathematical modeling, and processing of initial experimental data for follow-up assessment and analysis of the dynamics of heat release in diesel cylinders is growing every day. The main goal of our research consists in the development of a computer model defining the dynamics of heat release in diesel cylinders when it is running on fuels with different fractional composition, based on the application of the method of the Central Research Diesel Institute by analyzing the experimental data obtained in the form of an indicator diagram. The object of research is the method of processing the obtained experimental indicator diagrams. For this purpose, indicator diagrams of a 4CHN 11.0/12.5 diesel engine of the D-245.5S2 brand were obtained in the nominal mode. To implement the software module, a Java programming procedure was used, including the Java Development Kit where the writing, launching and compilation of Java code took place, the Java Runtime Environment, the Java runtime system, where the software distribution mechanism consisted of an autonomous Java virtual machine, standard Java libraries and tools for configuring it; and the Integrated Development Environment of an integrated development environment, where tools that helped launch, edit, and compile codes that provided thermal characteristics. As a result, an analysis of the available methods for determining the characteristics of the dynamics of diesel heat release was carried out, for the first time an algorithm was developed for performing calculations by the method of the Central Research Diesel Institute and a software module for calculating the characteristics of the dynamics of heat release in diesel cylinders when using fuels of various fractional composition based on experimentally obtained indicator diagrams. The use of the proposed technique and the corresponding software module for processing indicator diagrams, and subsequent analysis of the characteristics of the dynamics of heat release in diesel cylinders provides the required quality of the research results.

Multiscale Modeling of Protein-RNA Condensation in and Out of Equilibrium.

A vast number of intracellular membraneless bodies also known as biomolecular condensates form through a liquid-liquid phase separation (LLPS) of biomolecules. To date, phase separation has been identified as the main driving force for a membraneless organelles such as nucleoli, Cajal bodies, stress granules, and chromatin compartments. Recently, the protein-RNA condensation is receiving increased attention, because it is closely related to the biological function of cells such as transcription, translation, and RNA metabolism. Despite the multidisciplinary efforts put forth to study the biophysical properties of protein-RNA condensates, there are many fundamental unanswered questions regarding the mechanism of formation and regulation of protein-RNA condensates in eukaryotic cells. Major challenges in studying protein-RNA condensation stem from (i) the molecular heterogeneity and conformational flexibility of RNA and protein chains and (ii) the nonequilibrium nature of transcription and cellular environment. Computer simulations, bioinformatics, and mathematical models are uniquely positioned for shedding light on the microscopic nature of protein-RNA phase separation. To this end, there is an urgent need for innovative models with the right spatiotemporal resolution for confronting the experimental observables in a comprehensive and physics-based manner. In this chapter, we will summarize the currently emerging research efforts, which employ atomistic and coarse-grained molecular models and field theoretical models to understand equilibrium and nonequilibrium aspects of protein-RNA condensation.

Evaluation of the Effect of Induction Motors on Short-Circuit Current in Electrical Installations with a Rated Voltage above 1 kV

The growth of 6(10) kV electrical networks in large cities generates the need to improve the method of calculating short-circuit (SC) currents to ensure sufficient sensitivity of the main and backup protections of cable lines, which take power supply from the generator switchgears of thermal power plants (TPP GS), which often have a galvanic link between their auxiliaries and local load. The effect an induction motor (IM) has on the SC current in electrical installations for a rated voltage above 1 kV is studied. To analyze the effect an IM has on the SC current, a computational mathematical model was developed in the MathCad software package, and variant calculations were carried out. The electrical equipment parameters and standard electric circuits of TPP GS that are applied in Russia were used as input data. It is shown that the SC current decreases depending on the IM capacity and the electrical distance of the SC from the SC current level relative to the calculations carried out without taking the IM into account. The criteria under which an IM leads to a decrease in the SC current are determined. Practical recommendations for reducing the IM influence on the SC current to ensure the necessary relay protection sensitivity are proposed.

Reconstruction of anisotropic 3D medium using multiple 2D images

Constructing three-dimensional (3D) structures from two-dimensional (2D) images using computer mathematical modeling methods is the principal method of obtaining the 3D structure of a porous medium. In a typical anisotropic medium, orthogonal slices show different characteristics. This study uses multiple 2D images to characterize the orthogonal slices of an anisotropic 3D medium. First, a completeness analysis method is proposed, according to which a reasonable reconstruction model can be determined while using multiple 2D images to reconstruct an anisotropic 3D structure. A 3D grid reconstruction framework is also proposed by which the morphology of multiple 2D images can be effectively reproduced on the corresponding orthogonal slices of a 3D structure. In addition, a pattern replication method based on an orthogonal chord is adopted to improve the reconstructed morphology. Finally, two groups of experiments are performed on core samples to validate the performance of the proposed method. Based on experiments, our proposed method can successfully reconstruct an anisotropic structure from multiple 2D images.

Computational Analysis of a Multi-Layered Skin and Cardiac Pacemaker Model Based on Neural Network Approach.

The presented study discusses the possible disturbing effects of the electromagnetic field of antennas used in mobile phones or WiFi technologies on the pacemaker in the patient’s body. This study aims to obtain information on how the thickness of skin layers (such as the thickness of the hypodermis) can affect the activity of a pacemaker exposed to a high-frequency electromagnetic field. This study describes the computational mathematical analysis and modeling of the heart pacemaker inserted under the skin exposed to various electromagnetic field sources, such as a PIFA antenna and a tuned dipole antenna. The finite integration technique (FIT) for a pacemaker model was implemented within the commercially available CST Microwave simulation software studio. Likewise, the equations that describe the mathematical relationship between the subcutaneous layer thickness and electric field according to different exposures of a tuned dipole and a PIFA antenna are used and applied for training a neural network. The main output of this study is the creation of a mathematical model and a multilayer feedforward neural network, which can show the dependence of the thickness of the hypodermis on the size of the electromagnetic field, from the simulated data from CST Studio.

Апроксимаційно-марківські моделі зміни параметрів технічного стану силових та енергетичних установок у довготривалій експлуатації

The design and implementation of systems for automatic control of changes in the coordinates of the state and the output variables of power and energy installations consist of several successive stages, which implementation is widely used mathematical modeling. One of the most important such stages is the development of the created system (regulator) on a semi-natural stand. Such a stand usually contains a sample of a system with physically implemented measuring channels, and the control object and actuators are made in the form of a real-time computer mathematical model (stand-simulator). The problem is to resolve the contradiction between the requirements of the adequacy of the computer experiment to the real operating conditions and the capabilities of the simulator stand because the mathematical model of the control object is deterministic. In real conditions, there are random disturbances, which determine the random nature of the original-measuring coordinates of the control object. The use of known statistical modeling techniques is limited by the stationary requirements because the controlled objects are multi-mode. A solution to this contradiction is proposed by applying new information technology, which consists of the consistent implementation of the stages of preliminary approximation of time series of deviations of such variables from the formed approximation model, and the stage of statistical modeling. As a statistical model of random processes of deviations of such variables from the formed approximation model, the Markov process model is proposed, which considers the possible correlation of the initial data. The application of the approximation model provides the conditions of stationary and correctness of the proposed model. The applied problem of modeling the change of parameters of the technical conditions of a multi-mode technical object in long-term operation on the basis of the proposed model and experimental data is solved.

Research of the operation of an autonomous electrical complex with a combined composition of backup power sources

THE PURPOSE. To analyze scientific and technical information and practical experience of the functioning of autonomous electrical complexes with asynchronous electric motors in the composition. To develop a mathematical model of an autonomous electrical complex of a drilling rig with the presence of an active rectifier, an inverter with pulse-width control signals, as well as combined backup power sources – a battery and a diesel generator set. To establish the influence and expediency of using a combined composition of backup power sources on reliable operation and the possibility of overcoming the voltage failure caused by a sharp increase in load in the steady-state operation of an autonomous electrical complex. METHODS. For the successful fulfillment of the tasks set, this study applied the methods of mathematical modeling of power supply systems, methods of simulation modeling, the theories of automatic control, automated electric drive, and electrical circuits. Also, in research used the MATLAB software package with the built-in Simulink graphic modeling environment to create a mathematical computer model and to process the data obtained analytically. RESULTS. The article describes the relevance of the research topic. The study provides criteria for choosing the composition of backup power sources. Mathematical and simulation models of an autonomous ETC have been developed according to the “power source-frequency converter-industrial load” scheme, taking into account the influence of a non-linear load on the specified power quality indicators. The study has developed the structure of an autonomous electrical complex with a combined composition of backup power sources, which allows to overcome the voltage drop in the network caused by a sharp load surge, while ensuring the required indicators of electricity quality. CONCLUSIONS. The use of a rechargeable battery makes it possible to increase the overload threshold of the main diesel generator set regulated by GOST R 53987-2010 from 30% to 60%, as well as to ensure reliable connection of a backup diesel generator set without interrupting technological processes.

Computational modeling of capillary perfusion and gas exchange in alveolar tissue

Gas exchange is an essential function of the respiratory system that couples fundamentally with perfusion in respiratory alveoli. Current mathematical formulations and computational models of these two phenomena rely on one-dimensional approximations that neglect the intricate volumetric microstructure of alveolar structures. In this work, we introduce a coupled three-dimensional computational model of pulmonary capillary perfusion and gas exchange that conforms to alveolar morphology. To this end, we derive non-linear partial differential equations and boundary conditions from physical principles that govern the behavior of blood and gases in arbitrary alveolar domains. We numerically solve the resulting formulation by proposing and implementing a non-linear finite-element scheme. Further, we carry out several numerical experiments to validate our model against one-dimensional simulations and demonstrate its applicability to morphologically-inspired geometries. Numerical simulations show that our model predicts blood pressure drops and blood velocities expected in the pulmonary capillaries. Moreover, we replicate partial pressure dynamics of oxygen and carbon dioxide reported in previous studies. This overall behavior is also observed in three-dimensional alveolar geometries, providing more detail associated with the spatial distribution of fields of interest and the influence of the shape of the domain. We envision that this model opens the door for enhanced in silico studies of gas exchange and perfusion on realistic geometries, coupled models of respiratory mechanics and gas exchange, and multi-scale analysis of lung function; furthering our understanding of lung physiology and pathology. Codes are available at https://github.com/comp-medicine-uc/num-model-alv-perfusion-gas-exchange.

A Software System for A Finite State Machine (FSM)

Abstract: A finite-state machine (FSM) is a computational mathematical model. For design and analysis, circuits and system operations can be represented in a variety of ways. FSM is one of the methods for using a drawing to represent the operations of many circuits and systems in electronic engineering, computer engineering, and so on. In terms of design, the finite state machine is a very simple machine. It is made up of a set of input symbols, output symbols, and states that must be designed. Furthermore, a function of input and output symbols with the current state to give the next state must be present. To simulate the Finite State machine, a software simulator is implemented in this paper using the Visual Basic programming language (in terms of design and operation).Several general examples are represented in this model. However, the software can be used to teach students about FSM and how it works.

Algorithm for ionosphere delay computation based on Klobuchar-like coefficients for regional navigation satellite system users

The ionospheric effect on radio wave propagation error has a significant impact on navigation, positioning, and real-time measurements. It is the primary source of errors in high precision aviation and measurement systems. A set of eight coefficients is used to correct ionospheric errors for Indian Regional Navigation Satellite System (IRNSS) users. Currently, the Klobuchar model is an effective low computational mathematical model for ionospheric range error mitigation through a set of eight coefficients. It has low accuracy in Equatorial Ionization Anomaly (EIA) regions and can correct up to ∼60% of the ionospheric range error. This paper proposes an ionospheric error correction model that can be applied to such measurements as well as an associated error model to compute accuracy with a differential interval of observations 5 m, 30 m and 60 m. The numerical simulation results show that compared to widely used algorithms, the proposed strategy can enhance the 83.13% ionospheric correction with Klobuchar- like coefficients at a sampling rate of 5 m. The proposed solution could be effective for Regional Navigational Satellite Systems (RNSS) for ionospheric delay corrections in low-latitude regions.