Mathematical Model Of Interaction Research Articles

Mathematical modeling of interactions between colon cancer and immune system with a deep learning algorithm

Colon cancer is a complex disease with genetically unstable cell lines. In order to better understand the complexity of colon cancer cells and their metastatic mechanisms, we develop a mathematical model in this study. The model is based on a system of fractional-order differential equations and Fractional-Cancer-Informed Neural Networks (FCINN). The model captures a dynamic network of interactions between dendritic cells (DCs), cytotoxic T-cells (CD8+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$8^+$$\\end{document}), helper T-cells (CD4+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4^+$$\\end{document}), and colon cancer cells through fractional differential equations. By varying the fractional order between 0 and 1, we can classify patients into different groups based on their immune patterns. The goal of this paper is to identify different immune patterns and cancer cell behaviors, as well as the parameters that play an important role in metastasis, control, or elimination of cancer cells in the model. However, several parameters in the model are difficult to estimate in a patient-specific manner. To address this challenge, we use FCINN as an effective deep-learning tool for parameter estimation and numerical simulation of the model. Our findings suggest that the most effective factors in controlling the progression and preventing metastasis of colon cancer are the initial number of cancer cells, the inhibiting rates of tumor cells by DCs, the source of DCs, and the activation of helper T-cells by DCs. These findings suggest that DCs can be used as an immunotherapy tool for the control and treatment of colon cancer.

Implementation of the mathematical model of interaction of passenger transport modes for sustainable economic development

As part of a research, the study of the level of solving the scientific problem of transport flow management in large cities was carried out as a component of the integrated information-intelligent transport system of the city. A significant amount of research on a number of important components of the problem has been identified, including the application of new approaches, methods and information technologies for planning and forecasting traffic flows, optimization of bimodal urban networks. The software implementation of a mathematical model to optimize the interaction of urban passenger transport, passenger transfer points and urban trains in major transportation hubs in terms of sustainable development and digitalization was proposed. A toolkit for the integrated interaction of city train, urban passenger transport and passenger transfer points in major cities has been implemented. As a result of the study, a high level of versatility of the proposed model and the possibility of its active practical application was determined.

А particle model of interaction between weakly non-spherical bubbles

A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed. It is a system оf the second order ODEs in the radii of bubbles, the position vectors of their centers and the amplitudes of their small deformations in the form of spherical harmonics. Compared to the available analogs, the proposed model equations are more accurate in terms of the ratio of the radii of bubbles to the distance between their centers. This allows one to study bubble-bubble interaction at smaller distances between the bubbles. The model equations are quite compact, which simplifies their theoretical analysis and construction of algorithms of their solution. Five problems (dynamics of a single bubble under harmonic excitation, bubble collapse near a plane rigid wall, interaction of three synchronized and nonsynchronized bubbles located in line, and interaction between sixteen bubbles with the centers located on a plane surface) are considered for validation. It is shown that in all cases the proposed model results well agree with the corresponding available experimental data and numerical solutions. For demonstration of the applicability, the proposed model is used to analyze radial oscillations, spatial movements and surface deformations of the bubbles in rectilinear, planar and spatial clusters under harmonic forcing. Initially 125, 121 and 125 bubbles of the clusters are located at the nodes of 1D, 2D and 3D uniform grids, respectively. It is found that the monotonically decaying radial oscillations of the 1D cluster bubbles during one period of forcing are quite similar to those of a single bubble. Unlike this, the attenuation of the radial oscillations of the central bubbles in the 2D and 3D clusters is essentially non-monotonic. The maximum pressures in the central bubbles of the 2D and 3D clusters are significantly higher than in the single and 1D cluster bubbles. In all clusters the maximum deformations of bubbles are in the form of the second spherical harmonics, except for the central bubble of the 3D cluster, the maximum deformations of which are in the form of the fourth harmonics.

Q-well-posedness of an A$\beta$-protein polymerization model

Abstract. In this work, we consider a Becker-Döring-like mathematical interaction model between Aβ-monomers and Aβ proto-oligomers playing an important role in Alzheimer’s disease. In this context, the clustering process where two or more Aβ-monomers spontaneously aggregate and form a seed of proto-oligomers is highlighted. We prove the quadratic well-posedness [4] of the problem associated with the estimation of clustering rate µ from measured data at different times.

Stress-strain state of composite multi-layer stay rope considering breakages in reinforcing elements and nonlinear distribution of mechanical properties

Purpose. Formulation of an algorithm for considering the influence of continuity breakages in fiber reinforcing elements on stay rope strength. Methods. Construction and analytical solution of a mathematical model of interaction for parallel fiber reinforcingelements connected through elastic material, in a case of continuity breakage of individual elements in reinforcement. Findings. A static strength calculation algorithm for a multi-layer stay rope with breakages in one cross-section of reinforcing elements is developed. It is established that a continuity breakage of an arbitrary element of a stay rope reinforcement leads to a significant change in internal loads of only the adjacent reinforcing elements and is practically independent of a nonlinear deformation character of cable components. Greater loads on reinforcing elements occur in a case of breakage of a corner reinforcing element, and the smallest loads – in a case of breakage of a central one.It is established that a number of rows of reinforcing elements in a stay rope and location of a damaged reinforcing element do not significantly affect displacement of cable end and do not affect distribution of loads among reinforcing elements in a damaged cross-section. Displacements depend on a ratio of shear modulus of elastic material and Young's modulus of reinforcing elements; the ratio is varied along cable length. It is established that a reinforcing element location with discontinuity does not significantly affect the character of relative growth of stay rope deformations in a case of nonlinear character of elastic shell deformation. Deformation nonlinearity of cable components does not affect redistribution of forces in stay rope with damaged reinforcing elements. Maximum relative displacements of reinforcing elements and the resulting maximum shear angles of material located between reinforcing elements are smaller than a value of the assumed nonlinearity coefficient. Characters of displacements of reinforcing elements are qualitatively similar. Scientific novelty. An analytical algorithm is developed for calculating a stress-strain state of a multilayer stay rope considering its design, nonlinearly of mechanical properties of its components distributed along the cable with damage to an arbitrary group of reinforcing elements in one cross-section. Practical significance. The developed algorithm allows considering a nonlinear deformation character of stay rope components on its stress state in a case of breakages in an arbitrary number of reinforcing elements arbitrarily located in a stay rope with a continuity breakage in one cross-section. The algorithm can be applied to determine a stress-stress state of a stay rope with breakage in a cross-section infinitely distant from rope ends. The algorithm allows considering the influence of breakages in reinforcing elements on rope strength, which increases rope reliability in a structure.

Development and verification of a mathematical model of the wheel mover interaction with deformable soil, based on the application of the method of discrete elements

The vehicle cross-country power depends both on the mover type and its weight-and-dimensional parameters, and on the physico-mechanical soil properties. Research of the interaction between the mover and a deformable soil at the stage of research and development using mathematic simulation makes it possible predicting the vehicle cross-country power.
 The main mechanical soil parameters are the angle of internal friction and cohesion, which affect the process of interaction of the wheel with the deformable soil, since both normal and shear forces in the contact area. In this paper, sandy soil mathematical model is proposed and verified, and its parameters are determined for further research.
 The developed mathematical model of the interaction of the wheel mover with a deformable soil is based on the application of the method of discrete elements. In this paper, the wheel mover force factors when moving on cohesionless soil are analyzed and also forms the dependence of the specific traction force on the specific circumferential force for various wheel rolling modes was obtained. As a result of applying the method of discrete elements to study the interaction of a wheel mover with a deformable support base, it is possible to determine the traction characteristic. Thus, the application of this method will reduce the number and scale of field tests.
 Using the developed mathematical model the planetary wheeled mover traction characteristic was obtained and the comparative analysis with the nature test results was carried out.

Modeling of thermal power plants in the study of reliability of power supply and energy security

RELEVANCE. Maintaining the required level of energy security (ES) and reliability of fuel and energy supply is one of the priority tasks in the management of the energy sector. In the functioning of the fuel and energy complex various threats are possible, which can lead to the violation of the reliability of fuel and energy supply and the emergence of shortages ofvarious types of energy resources. To assess the level of energy security, approaches are considered to form a mathematical model of the FEC, which combines all sectors of the energy sector. Despite the trends of transition to low-carbon energy sources associated with energy transformation, thermal power plants remain one of the main sources of heat and electricity.Due to the ability to generate large amounts of heat only thermal power plants can be a source of centralized energy supply of large territories. In this regard, when modeling the fuel and energy complex, it is necessary to develop mathematical models of TPPs, which will correctly reflect the technological processes that affect the reliability of energy supply. OBJECT. Development of mathematical models of interaction of electric power, heat supply and fuel systems within the framework of thermal power plants designed to study energy security and reliability of fuel and energy supply. METHODS. Mathematical modeling of fuel consumption dependences on electrical and thermal load at thermal power plants is used as methods. To obtain analytical dependencies, the least squares approximation of the consumption characteristics of thermal power plants was carried out. RESULTS. As part of the work, analytical dependences of fuel consumption on thermal and electrical load for various types of thermal units were obtained. For all considered steam turbines, linear dependences of theamount of heat supplied to the turbine on its load (electrical and / or heating depending on the type of turbine) were obtained. For boilers, an approximation of the dependence of efficiency on thermal load was carried out. According to the results of the approximation, a linear dependence is assumed. For gas turbine installations, an approximation of the dependence of the efficiency on the load was carried out, according to the results of which a second-order polynomial was obtained. CONCLUSION. The paper investigates the problem of mathematical modeling of the interconnected operation of fuel, heat and power and electric power systems within the framework of the functioning of the energy sector. Analytical dependences are obtained for different types of generating equipment, including boilers, steam turbines and gas turbine installations. The obtained dependences are necessary for the analysis of energy security and reliability offuel and energy supply. The models of thermal power plants presented in the paper are the most suitable for the analysis of energy security and reliability of fuel and power supply, as they provide the necessary accuracy of calculations and take into account the specifics of various generating equipment, without dropping to the level of microparameters.

Research of the operation of the turnstile support-fastening device during the transportation of a long-dimensional heavy load

The article analyzes the motion of a wheelset along a path of unequal length with shaft wear of the rails. The authors have studied the influence of an external disturbing force on the parametric system “wheel-rail”. The considered problem is solved on the basis of a mathematical model of interaction of a pair of wheels and an unequal rail, taking into account the additive effect of unequal stiffness on a rail vehicle. It is shown that taking into account the unequal elasticity of the track in the longitudinal direction allows to determine more precisely the resonance regions and to evaluate the decrease or increase of the acceleration level and the amplitudes of the impact of the unsprung mass of the rail vehicle.

Lateral Force Evaluation in Vehicle’s Wheel Interaction with a Rut

The operation of roads under modern conditions associated with high speeds and traffic density results in wear of pavement and formation of a rut. When crossing the ruts, instability can occur when relatively small steering inputs lead to large changes in the trajectory. The lateral force acting on a wheel of a car is of particular importance in the study of stability and controllability. The magnitude of this force is determined by various factors: tire stiffness, speed, change in the angle of rotation of the wheel, the geometry of the transverse profile of the rut.The objective of the study refers to the problem of determining the angles of inclination of side walls of the rut that are safe for movement at different speeds. The paper considers the interaction of a car wheel with the road surface, proposes a mathematical model for interaction of a tire with ruts, considers the angle of the wheel running on the rut wall. To describe the elastic response of a tire in contact with a rut, an elastic foundation model and a plane section method are used. The lateral force was estimated based on equations of motion of the wheel when crossing the rut. The dependences of the ratio of the lateral force to the normal load for various rut depths and angles of inclination of its walls on the angle of rotation of the wheel and the speed of the vehicle were obtained. It is shown that at a rut inclination angle exceeding five degrees, the lateral force begins to increase significantly with an increase in the angle of rotation of the wheel, as well as the speed of the vehicle, and may exceed the applied normal load. According to the condition of vehicle stability against skidding on a wet surface, limiting average angles of inclination of the side walls of the rut are estimated for various values of the vehicle speed and wheel rotation angles.

Serotonin Signaling in the Enteric Nervous System and Connection to Autism Spectrum Disorder: A Translational Mathematical Model

While the causes of autism spectrum disorder (ASD) remain unclear, some studies have shown that serotonin-mediated effects on the enteric nervous system (ENS) correlate with an ASD-like behavioral phenotype in mice. Introduced here is a mathematical model of interactions between gut serotonin and its impact on the ENS. The model was used to identify three key factors that affect ENS size, namely, serotonin production, its clearance, and its ability to act as a growth factor for the ENS. The model was used to reproduce experimentally reported results from a mouse model by Margolis et al. (2016), which connected serotonin-mediated ENS hypoplasia to an ASD phenotype. The proposed mathematical model was used to scale the quantified relationship from mice to humans to show how the combination of these three factors can translate to a quantifiable metric that could potentially be correlated to the ASD spectrum. A detailed discussion of how ENS hypoplasia could mechanistically affect CNS activity concludes this paper.

Mathematical model of interaction Escherichia coli and Coliphages.

We propose a mathematical model based in ordinary differential equations between bacterial pathogen and Bacteriophages to describe the infection dynamics of these populations, for which we use a nonlinear function with an inhibitory effect. We study the stability of the model using the Lyapunov theory and the second additive compound matrix and perform a global sensitivity analysis to elucidate the most influential parameters in the model, besides we make a parameter estimation using growth data of Escherichia coli (E.coli) bacteria in presence of Coliphages (bacteriophages that infect E.coli) with different multiplicity of infection. We found a threshold that indicates whether the bacteriophage concentration will coexist with the bacterium (the coexistence equilibrium) or become extinct (phages extinction equilibrium), the first equilibrium is locally asymptotically stable while the other is globally asymptotically stable depending on the magnitude of this threshold. Beside we found that the dynamics of the model is particularly affected by infection rate of bacteria and Half-saturation phages density. Parameter estimation show that all multiplicities of infection are effective in eliminating infected bacteria but the smaller one leaves a higher number of bacteriophages at the end of this elimination.

Mathematical Model of Interaction of Therapist and Patients with Bipolar Disorder: A Systematic Literature Review.

Mood swings in patients with bipolar disorder (BD) are difficult to control and can lead to self-harm and suicide. The interaction between the therapist and BD will determine the success of therapy. The interaction model between the therapist and BD begins by reviewing the models that were previously developed using the Systematic Literature Review and Bibliometric methods. The limit of articles used was sourced from the Science Direct, Google Scholar, and Dimensions databases from 2009 to 2022. The results obtained were 67 articles out of a total of 382 articles, which were then re-selected. The results of the selection of the last articles reviewed were 52 articles. Using VOSviewer version 1.6.16, a visualization of the relationship between the quotes “model”, “therapy”, “emotions”, and “bipolar disorder” can be seen. This study also discusses the types of therapy that can be used by BD, as well as treatment innovations and the mathematical model of the therapy itself. The results of this study are expected to help further researchers to develop an interaction model between therapists and BD to improve the quality of life of BD.

ОСОБЛИВОСТІ ПРОЕКТУВАННЯ ПРИСТРОЇВ З ПОСТІЙНИМИ МАГНІТАМИ ДЛЯ ВІДВЕДЕННЯ ОБ’ЄКТІВ КОСМІЧНОГО СМІТТЯ З НИЗЬКИХ НАВКОЛОЗЕМНИХ ОРБІТ

The analysis of effectiveness of devices with permanent magnets implementation for the space debris objects deorbiting from Law Earth Orbits has been carried out. The deorbit time of space debris objects from Law Earth Orbits with using different mathematical models of interaction of space object own magnetic fields with dynamic flux of ionospheric plasma, has been calculated. The design features of devices with permanent magnets for deorbiting of space debris objects from Law Earth Orbit has been considered.

Process Parameter Optimization on Selective Laser Melting of CuSn10 Powders Based on Response Surface Methodology

Abstract A shaping test of CuSn10 powders was carried out by using the selective laser melting (SLM) technology to study influences of process parameters of SLM on compactness of specimens. Meanwhile, process parameters were optimized based on the response surface methodology. Meanwhile, phase composition and microstructure of formed part were analyzed by XRD and OM. Results demonstrated that as the energy density of laser body increases from 146.7 J·mm-3 to 181.3 J·mm-3, pores of samples decrease and the compactness increases from 98.97% to about 99.7%. Subsequently, the compactness begins to decrease with the continuous increase of laser energy density. The incomplete melting of powder under low energy density and gasification of powders under high energy density are major factors that influence the compactness. Over low or high laser energy density is disadvantageous for the improvement of compactness. A mathematical model of interaction between three factors (laser power, laser scanning speed and scanning space) and response value (compactness) was built up by using the BBD principle design test of response surface methodology. The degree of fitting (R2) and correction coefficient (R2 adj) of the model were 0.9952 and 0.9866, which agree well with the fitting degree of experimental tests. Among three factors, influences of laser power and scanning speed on compactness are equivalent and more significant than scanning space. The optimal process parameters which were predicted by the model were laser power=331.471 W, scanning speed=648.045 mm·s-1, scanning space=69.9302 μm. Under this circumstance, the compactness of CuSn10 powders after SLM is 99.75%. According to experimental verification, the practical value of compactness is 99.74%, showing a very small relative error. This proves that the BBD model is reliable. The shaped part is mainly composed of α-Cu phase and metastable phase β’-Cu13.7Sn. Compared with the original powders, the content of metastable phase β’ increases significantly, while the δ-Cu41Sn11 phase disappears.

Mathematical Model of Interaction between Civilization Center and Tribal Periphery: An Analysis

Mathematical Model of Interaction between Civilization Center and Tribal Periphery: An Analysis

Dynamical aspects of corona virus infection

In this paper, we consider five mathematical models of corona virus infection. The first model is a mathematical model of corona virus entry. The second model is a mathematical model for interactions of virus N-protein and viral RNA. Here, we prove that phosphorylated N protein increases the affinity of viral RNA. The third model is a mathematical model of virion assembly. It is a six-dimensional model. But there is an invariant three-dimensional submodel, which we can prove has a positive stable equilibrium. The fourth model is a model of an enzyme inhibitor that blocks viral replication. The fifth model is a model of a virus and a vaccine.

Stability Analysis of Mathematical Modeling of Interaction between Target Cells and COVID-19 Infected Cells

The stability analysis in this mathematical model was related to the infection of the Coronavirus Disease 2019 (Covid-19). In this mathematical model there were two balance points, namely the point of balance free from Covid-19 and the one infected with Covid-19. The stability of the equilibrium point was influenced by all parameters, i.e. target cells die during each cycle, number of target cells at  = 0, target cells infected during each cycle based on virion unit density, effective surface area of the network, the ratio of the number of virus particles to the number of virions, infected cells die during each cycle, the number of virus particles produced by each infected cell during each cycle, and virus particles die during each cycle. In the simulation model, immunity is divided into high, medium and low immunity. For high, moderate and low immunity, respectively, the highest number of target cells is in high, medium and low immunity, whereas for the number of infected cells and the number of Covid-19, it is in the opposite sequence of the number of target cells.

Gyrotron Development at High Order Modes

The present work has been characterized by higher order modes in the cavities of the Gyrotron; they are capable of producing RF plasma by developments of it. It uses for fusion systems. We choose the TE31,8 mode in our study. The main problem of gyrotron is the device of the thermal cavity loading. The problem of the thermal loading is solved when any parasitic modes suppress, absence of desired modes; the thermal loading is increased when the high power tube of gyrotron operation is unstable. The mathematical interaction model contains equations that describe the electron motion and the field profiles of the transferred electric modes of the resonator, these are interacting with electrons based on the finite difference method that has been designed to study the starting current, the frequency, quality factor and calculates the roots of the Bessel function by the program we designed in Fortran language. They are used to calculate the operation frequency. Good agreement is between our results and the previous published results both confirm the accuracy of the performance of the designed program.

Modeling of dynamic interaction of a fabric airbag with an anthropometric dummy

In this paper, a physical and mathematical model of interaction between a fabric expanding automobile airbag and biological objects is formulated. Bioobjects are represented using finite element models of anthropometric dummies of the Hybrid III 50th Male type. As a model of the airbag material, a model of multi-layer fabric orthotropic material was used. The method of corpuscular particles was used for numerical simulation of the airbag functioning in the LS-DYNA multiphysics simulation software package. The results of calculating the dynamic interaction of an expanding airbag with three standing dummies are presented.

Bifurcations in a Cancer and Immune Model with Allee Effect

Modeling the interplay between immune system components and cancer cells via immunotherapy is the purpose of this work. We present a simple mathematical model of interaction between tumor cells and the immune system’s effector cells. With rigorous mathematical analysis and numerical continuation, we study the generalized Hopf bifurcations (GH), known as Bautin bifurcation, including the Allee effect, presenting also Hopf bifurcation. The Hopf bifurcation indicates the existence of limit cycles. Bautin suggests two limit cycles; consequently, the model presents the equilibrium phase in immunoediting theory. Finally, the numerical continuation is performed to support the analytical results.