Journal articles on the topic 'Structural dynamics – Mathematical models'
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Urbina, Angel, and Thomas Paez. "Statistical Validation of Structural Dynamics Models." Journal of the IEST 46, no. 1 (September 14, 2003): 141–48. http://dx.doi.org/10.17764/jiet.46.1.f430423634885g67.
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There is an increasing reliance in the engineering community on the use of mathematical models to characterize physical system behavior. This is happening even though mathematical models rarely simulate real system behavior perfectly. Due to this reliance, we require objective, well-founded mathematical techniques for model validation. This paper develops a formal approach to the validation of mathematical models of structural dynamics systems. It uses a probabilistic/statistical approach to the characterization of an important measure of behavior of dynamic systems subjected to random excitations, and seeks to validate a mathematical model in a statistical sense. An example is presented.
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Kochuk, Serhii, Dinh Dong Nguyen, Artem Nikitin, and Rafael Trujillo Torres. "Identification of UAV model parameters from flight and computer experiment data." Aerospace technic and technology, no. 6 (November 29, 2021): 12–22. http://dx.doi.org/10.32620/aktt.2021.6.02.
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The object of research in the article is various well-known approaches and methods of structural and parametric identification of dynamic controlled objects - unmanned aerial vehicles (UAVs). The subject of the research is the parameters of linear and nonlinear mathematical models of spatial and isolated movements, describing the dynamics and aerodynamic properties of the UAV and obtained both from the results of flight experiments and using computer object-oriented programs for 3-D UAV models. The goal is to obtain mathematical models of UAV flight dynamics in the form of differential equations or transfer functions, check them for reliability and the possibility of using them in problems of synthesis of algorithms for automatic control systems of UAVs. Tasks to be solved: evaluation of the analytical (parametric), direct (transient), as well as the identification method using the 3-D model of the control object. Methods used structural and parametric identification of dynamic objects; the determination of static and dynamic characteristics of mathematical models by the type of their transient process; the System Identification Toolbox package of the MatLab environment, the Flow Simulation subsystem of the SolidWorks software and the X-Plane software environment. The experimental parameters of UAV flights, as well as the results of modeling in three-dimensional environments, are the initial data for the identification of mathematical models. The following results were obtained: the possibility of analytical and computer identification of mathematical models by highly noisy parameters of the UAV flight was shown; the mathematical models of UAVs obtained after identification is reliable and adequately reproduce the dynamics of a real object. A comparative analysis of the considered UAV identification methods is conducted, their performance and efficiency are confirmed. Conclusions. The scientific novelty of the result obtained is as follows: good convergence, reliability and the possibility of using the considered identification methods for obtaining mathematical models of dynamic objects to synthesize algorithms for automatic control systems of UAVs is shown.
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Kuzmin, Anton. "Mathematical Exchange Rates Modeling: Equilibrium and Nonequilibrium Dynamics." Mathematics 10, no. 24 (December 9, 2022): 4672. http://dx.doi.org/10.3390/math10244672.
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The development of the author’s concept of the International Flows Equilibrium Exchange Rate (IFEER) is the basis for the mathematical exchange rate modeling of two interconnected equal economies. IFEER-concept allows modeling the exchange rate dynamics of relatively medium-term equilibrium and short- and long-term disequilibrium. Discrete and integral versions of the concept are the basis for further modeling. New structural models of medium-, short- and long-term dynamics and new final structural dependencies of the exchange rate on the system of fundamental factors are the main results. The models include mathematically formalized export-import and capital flows and international competitive advantages indicators. The modeling allowed the revealing of the structural pricing mechanism of the exchange rate dynamics from new positions. We verify the US dollar to the Russian ruble exchange rate modeling during periods of financial and economic crises in recent Russian history, based on a systematic analysis of the exchange rate policy. Because of the analysis, the fall in export prices of oil and other energy carriers in international markets, the rise in consumer prices within the country, and the fall in aggregate output are the main reasons for the fall of the Russian ruble. The conducted modeling allows for the evaluation of the short-term contribution to the crisis depreciation dynamics. The mathematical tools allow for the development of the decision-making process on the exchange rate regulation.
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KOZMA, ROBERT, MARKO PULJIC, and LEONID PERLOVSKY. "MODELING GOAL-ORIENTED DECISION MAKING THROUGH COGNITIVE PHASE TRANSITIONS." New Mathematics and Natural Computation 05, no. 01 (March 2009): 143–57. http://dx.doi.org/10.1142/s1793005709001246.
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Cognitive experiments indicate the presence of discontinuities in brain dynamics during high-level cognitive processing. Non-linear dynamic theory of brains pioneered by Freeman explains the experimental findings through the theory of metastability and edge-of-criticality in cognitive systems, which are key properties associated with robust operation and fast and reliable decision making. Recently, neuropercolation has been proposed to model such critical behavior. Neuropercolation is a family of probabilistic models based on the mathematical theory of bootstrap percolations on lattices and random graphs and motivated by structural and dynamical properties of neural populations in the cortex. Neuropercolation exhibits phase transitions and it provides a novel mathematical tool for studying spatio-temporal dynamics of multi-stable systems. The present work reviews the theory of cognitive phase transitions based on neuropercolation models and outlines the implications to decision making in brains and in artificial designs.
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Collins, O. C., T. S. Simelane, and K. J. Duffy. "Analyses of mathematical models for city population dynamics under heterogeneity." African Journal of Science, Technology, Innovation and Development 11, no. 3 (November 15, 2018): 323–37. http://dx.doi.org/10.1080/20421338.2018.1527967.
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Voges, Nicole, Ad Aertsen, and Stefan Rotter. "Structural Models of Cortical Networks with Long-Range Connectivity." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/484812.
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Most current studies of neuronal activity dynamics in cortex are based on network models with completely random wiring. Such models are chosen for mathematical convenience, rather than biological grounds, and additionally reflect the notorious lack of knowledge about the neuroanatomical microstructure. Here, we describe some families of new, more realistic network models and explore some of their properties. Specifically, we consider spatially embedded networks and impose specific distance-dependent connectivity profiles. Each of these network models can cover the range from purely local to completely random connectivity, controlled by a single parameter. Stochastic graph theory is then used to describe and analyze the structure and the topology of these networks.
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ZAVADSKY, SERGEY V., DMITRI A. OVSYANNIKOV, and SHENG-LUEN CHUNG. "PARAMETRIC OPTIMIZATION METHODS FOR THE TOKAMAK PLASMA CONTROL PROBLEM." International Journal of Modern Physics A 24, no. 05 (February 20, 2009): 1040–47. http://dx.doi.org/10.1142/s0217751x09044486.
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Mathematical models of the structural parametric optimization of plasma dynamics are discussed. Optimization approach to plasma dynamic is based on the consideration of trajectory ensemble. This ensemble describes transient process in tokamak subject to the initial data and external disturbances. In the framework of this approach the optimization of dynamics of the trajectory ensemble in ITER tokamak is given. The trajectories of this ensemble are perturbed at the initial point set and the set of external disturbances.
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Kovalskiy, V. F., and I. A. Lagerev. "Impact of wind effects on the loading of hydraulic cranes-manipulators with articulated booms." Izvestiya MGTU MAMI 9, no. 4-1 (February 20, 2015): 21–25. http://dx.doi.org/10.17816/2074-0530-67154.
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This article analyzes the influence of intensity of the longitudinal and transverse wind effects on its loading, using universal mathematical models for investigating of the dynamics of a hydraulic crane boom when moving units. The authors showed that the wind load not only causes additional stresses in structural elements, but also affects the kinematic and dynamic motion parameters of links articulated boom crane.
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BEREC, LUDĚK. "MODELS OF ALLEE EFFECTS AND THEIR IMPLICATIONS FOR POPULATION AND COMMUNITY DYNAMICS." Biophysical Reviews and Letters 03, no. 01n02 (April 2008): 157–81. http://dx.doi.org/10.1142/s1793048008000678.
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Allee effects are broadly defined as a decline in individual fitness at low population sizes or densities. Although the roots of the concept go back at least to 1920's, until recently, Allee effects eked out on the periphery of ecological theory, in the shade of the prominently discussed negative density dependence. The situation has changed dramatically in the last ten years or so, and we can find an ever increasing number of studies considering Allee effects from an ever increasing range of disciplines. Mathematical models have always been an important tool by which to assess impacts of Allee effects for population and community dynamics. Actually, much of what we know about Allee effects comes from mathematical models. Up to now, Allee effects have been examined in the context of most existing model structures, and significantly altered our picture of population and community dynamics based on assuming negative density dependence only.
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Grigorov, Otto, Evgenij Druzhynin, Galina Anishchenko, Marjana Strizhak, and Vsevolod Strizhak. "Analysis of Various Approaches to Modeling of Dynamics of Lifting-Transport Vehicles." International Journal of Engineering & Technology 7, no. 4.3 (September 15, 2018): 64. http://dx.doi.org/10.14419/ijet.v7i4.3.19553.
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The results of analytical and numerical modeling of dynamic characteristics of linear and non-linear mathematical models of the “trolley-load” system of bridge and container cranes are presented. KiDyM software complex is used for numerical modeling, which, based on the use of the apparatus of structural matrices and the built-in computer algebra system, allows the construction of ordinary differential equations of motion of the class of systems under consideration at the analytical level. Recommendations on the possible use of the considered mathematical models of the “trolley-load” system in various regular and forced operation modes of bridge and container cranes are given on the basis of the analysis. The ratio of the results of calculations for various design models of regular and forced operation of the bridge crane has been established. The magnitude of the distribution of the maximum values of the dynamic characteristics of motion of the container crane has been designed by calculating the forced operation mode using various mathematical models.
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Burgin, Mark. "Triadic Structures in Interpersonal Communication." Information 9, no. 11 (November 16, 2018): 283. http://dx.doi.org/10.3390/info9110283.
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Communication, which is information exchange between systems, is one of the basic information processes. To better understand communication and develop more efficient communication tools, it is important to have adequate and concise, static and dynamic, structured models of communication. The principal goal of this paper is explication of the communication structures, formation of their adequate mathematical models and description of their dynamic interaction. Exploring communication in the context of structures and structural dynamics, we utilize the most fundamental structure in mathematics, nature and cognition, which is called a named set or a fundamental triad because this structure has been useful in a variety of areas including networks and networking, physics, information theory, mathematics, logic, database theory and practice, artificial intelligence, mathematical linguistics, epistemology and methodology of science, to mention but a few. In this paper, we apply the theory of named sets (fundamental triads) for description and analysis of interpersonal communication. As a result, we explicate and describe of various structural regularities of communication, many of which are triadic by their nature allowing more advanced and efficient organization of interpersonal communication.
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Eliseev, S. V., A. S. Mironov, and Quang Truc Vuong. "Dynamic damping under introduction of additional couplings and external actions." Vestnik of Don State Technical University 19, no. 1 (April 1, 2019): 38–44. http://dx.doi.org/10.23947/1992-5980-2019-19-1-38-44.
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Introduction.The dynamic interaction features in mechanical oscillating systems, whose structure includes additional couplings, are considered. In practice, such cases occur when using various optional mechanisms and motion translation devices under the formation of technical objects. The study objective is to develop a method for constructing mathematical models in the problems of dynamics of the mechanical oscillating systems with optional devices and features in the system of external disturbing factors.Materials and Methods. The techniques used to study properties of the systems and the dynamic effects are based on the ideas of structural mathematical modeling. It is believed that the mechanical oscillating system, considered as a design model of a technical object, can be compared to the dynamically equivalent automatic control system. The mathematical apparatus of the automatic control theory is used.Research Results.A method for constructing mathematical models is developed. The essential analytical relations for plotting oscillating systems are obtained, which enable to form a methodological basis for the integral estimation and comparative analysis of the initial system properties in various dynamic states. Dynamic properties of the two-degree-offreedom systems within the framework of the computer simulation are investigated. The implementability of dynamic oscillation damping mode simultaneously in two coordinates with the joint action of two in-phase kinematic perturbations in the mechanical oscillating systems is shown.Discussion and Conclusions.The possibilities of new dynamic effects, which are associated with the change in the system structure under certain forms of dynamic interactions, are noted. The study is of interest to experts in machine dynamics, robotics, mechatronics, nano and mesomechanics.
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Harmati, István Á. "Dynamics of Fuzzy-Rough Cognitive Networks." Symmetry 13, no. 5 (May 15, 2021): 881. http://dx.doi.org/10.3390/sym13050881.
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Fuzzy-rough cognitive networks (FRCNs) are interpretable recurrent neural networks, primarily designed for solving classification problems. Their structure is simple and transparent, while the performance is comparable to the well-known black-box classifiers. Although there are many applications on fuzzy cognitive maps and recently for FRCNS, only a very limited number of studies discuss the theoretical issues of these models. In this paper, we examine the behaviour of FRCNs viewing them as discrete dynamical systems. It will be shown that their mathematical properties highly depend on the size of the network, i.e., there are structural differences between the long-term behaviour of FRCN models of different size, which may influence the performance of these modelling tools.
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Srinivasan, R. Srini, Wayne A. Gerth, and Michael R. Powell. "Mathematical models of diffusion-limited gas bubble dynamics in tissue." Journal of Applied Physiology 86, no. 2 (February 1, 1999): 732–41. http://dx.doi.org/10.1152/jappl.1999.86.2.732.
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Mathematical models of bubble evolution in tissue have recently been incorporated into risk functions for predicting the incidence of decompression sickness (DCS) in human subjects after diving and/or flying exposures. Bubble dynamics models suitable for these applications assume the bubble to be either contained in an unstirred tissue (two-region model) or surrounded by a boundary layer within a well-stirred tissue (three-region model). The contrasting premises regarding the bubble-tissue system lead to different expressions for bubble dynamics described in terms of ordinary differential equations. However, the expressions are shown to be structurally similar with differences only in the definitions of certain parameters that can be transformed to make the models equivalent at large tissue volumes. It is also shown that the two-region model is applicable only to bubble evolution in tissues of infinite extent and cannot be readily applied to bubble evolution in finite tissue volumes to simulate how such evolution is influenced by interactions among multiple bubbles in a given tissue. Two-region models that are incorrectly applied in such cases yield results that may be reinterpreted in terms of their three-region model equivalents but only if the parameters in the two-region model transform into consistent values in the three-region model. When such transforms yield inconsistent parameter values for the three-region model, results may be qualitatively correct but are in substantial quantitative error. Obviation of these errors through appropriate use of the different models may improve performance of probabilistic models of DCS occurrence that express DCS risk in terms of simulated in vivo gas and bubble dynamics.
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Mallapur, Shashidhar, and Roland Platz. "Quantification of Uncertainty in the Mathematical Modelling of a Multivariable Suspension Strut Using Bayesian Interval Hypothesis-Based Approach." Applied Mechanics and Materials 885 (November 2018): 3–17. http://dx.doi.org/10.4028/www.scientific.net/amm.885.3.
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Mathematical models of a suspension strut such as an aircraft landing gear are utilized by engineers in order to predict its dynamic response under different boundary conditions. The prediction of the dynamic response, for example the external loads, the stress and the strength as well as the maximum compression in the spring-damper component aids engineers in early decision making to ensure its structural reliability under various operational conditions. However, the prediction of the dynamic response is influenced by model uncertainty. As far as the model uncertainty is concerned, the prediction of the dynamic behavior via different mathematical models depends upon various factors such as the model's complexity in terms of the degrees of freedom, material and geometrical assumptions, their boundary conditions and the governing functional relations between the model input and output parameters. The latter can be linear or nonlinear, axiomatic or empiric, time variant or time-invariant. Hence, the uncertainty that arises in the prediction of the dynamic response of the resulting different mathematical models needs to be quantified with suitable validation metrics, especially when the system is under structural risk and failure assessment. In this contribution, the authors utilize the Bayesian interval hypothesis-based method to quantify the uncertainty in the mathematical models of the suspension strut.
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Popkov, Yu S. "A New Class of Dynamic Macrosystem Models with Self-Reproduction." Environment and Planning A: Economy and Space 21, no. 6 (June 1989): 739–51. http://dx.doi.org/10.1068/a210739.
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The author considers a class of macrosystems where the relaxation time of the distribution process of elements is significantly less than the relaxation time of the self-reproduction process. The proposed model of such macrosystems defines the system of differential equations with nonlinearity generated by the solution of a mathematical programming problem with an entropy objective function. Methods for the structural analysis of this model are considered, and applications to demographic modelling, biological dynamics, and chemical kinetics are given.
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Zolotnitsky, Aleksandr, Nataliy Sytnik, Sergei Chernyi, and Natalya Logunova. "Analysis of the Dynamics of Marine Structures and Species with Criterial Mathematical Models." Journal of Marine Science and Engineering 9, no. 12 (December 14, 2021): 1431. http://dx.doi.org/10.3390/jmse9121431.
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The influence of the area of artificial substrates (collectors) on the biological parameters of populations of mussels (Mytilus galloprovincialis Lamarck) during their cultivation in the Black Sea has been investigated. For growing mollusks, four types of collectors were used, with different relative areas (ω), i.e., with different ratios of the substrate area (S) per unit length of the collector (L), which were 0.09, 0.21, 0.34, and 0.55. It was found that, during a 1.5-year cultivation, the density (N, ind./m) and biomass (B, kg/m) change and reach a certain stationary state, determined by the relative area of the substrate. It was shown that, on collectors with a higher value of ω, there was a decrease in the average length (L, mm) and weight (W, g) of the mollusk yield. The Boysen–Jensen method was used to calculate the total production of mollusks (P), elimination (E), and specific production (P/B coefficient) for each type of reservoir, and it was shown that P increased with an increase in the substrate area, while E and P/B coefficients decreased. Based on the analysis of the obtained results, it was concluded that during the cultivation of mussels these parameters are regulated by density-dependent population factors (intraspecific competition) for space (substrate) and food.
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Mottershead, J. E., T. K. Tee, C. D. Foster, and R. Stanway. "An Experiment to Identify the Structural Dynamics of a Portal Frame." Journal of Vibration and Acoustics 112, no. 1 (January 1, 1990): 78–83. http://dx.doi.org/10.1115/1.2930102.
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This paper describes the application of sequential frequency domain techniques to the estimation of mass, stiffness, and damping parameters using measured frequency response functions from a portal frame rig. The theory of the method has been described in the authors’ previous publications. A portal frame is representative of many engineering structures. It is lightly damped and may be thought of as an element of several larger structures such as bridges, transmission towers, and the steel foundations of modern power generating plant. The results offered in this paper are thus of interest to a broad range of engineering problems where it is required to obtain mathematical models in terms of physical parameters.
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Eliseev, Sergey Viktorovich, Sergey Konstantinovich Kargapoltsev, Roman Sergeevich Bolshakov, and Andrey Vladimirovich Eliseev. "Lever ties: possibilities of creating dynamic conditions in mechanical oscillation systems." Transport of the Urals, no. 3 (2020): 17–23. http://dx.doi.org/10.20291/1815-9400-2020-3-17-23.
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The paper considers the possibilities to assess, create and change dynamic conditions of mechanical oscillation systems with additional ties in tasks of dynamics that are typical to technological and transport objects. The aim of the paper is in development of methodological basics of system analysis, detailed elaboration of notions about shapes, peculiarities and possibilities of functions interaction of elements in oscillation systems in the presence of dynamic ties in the shape of lever mechanisms. The paper uses methods of structural mathematical modeling based on analytical apparatus of automatic control theory. The authors developed a method of creating mathematical models obtained with the use of the Laplace transformations of the original equations formed on the basis of the Lagrange formalism. They propose a technology of creating structural mathematical models with the exception of intermediate coordinates. They also consider the introduction of new type transfer functions surrounding the distribution of the oscillation amplitudes of the mass-inertial element in the form of a rigid body performing plane motion and variants of appearance of specific dynamic modes in a connected motion under the influence of external disturbances. The study shows the possibilities of interpreting the modes of dynamic absorption of oscillations through a connection with definition of a node (or centre) of oscillations. As a result, the authors propose a number of analytical ratios to evaluate peculiarities of the dynamic conditions of vibrational interactions and present the results of numeric modeling.
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Онищенко, В. М. "МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ УДАРУ ПРУЖНОГО ЛІТАЛЬНОГО АПАРАТА НА ПОСАДЦІ." Open Information and Computer Integrated Technologies, no. 84 (July 2, 2019): 165–69. http://dx.doi.org/10.32620/oikit.2019.84.09.
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The development of a direction oriented towards the creation and advanced operation of mathematical models (MM) of aircraft - their mathematical doublers on the example of calculating the impact dynamics and loading of an elastic plane on landing is shown. The relevance of such an approach in the design and operation of aircraft due to the complexity and limited capabilities of terrestrial experimental facilities and flight experiment are noted. The example of a lightweight aircraft presents the results of the application of a simplified MM and the numerical calculation of the impact dynamics on the computer and the load of the elastic construction at landing. Determination of the dynamic reaction of the aircraft and the load of the elastic structure at landing refers to the actual problem of dynamic aeroelasticity. In the article the basic equations used to construct the MM of an elastic plane with a nonlinear landing gear are given. The basic parameters that characterize the structural load are determined. The results of the calculation analysis of the impact of the aircraft are presented, extensive parametric studies have been carried out on the influence of a number of constructive and operational factors on dynamic processes, and analyzed the patterns and features of impact and loading of an elastic aircraft on landing. It is shown that the load must be determined taking into account elastic structural vibrations. Dynamic loads from elastic oscillations are significant in magnitude and, as it turns out, most often determine the strength of the glider and the chassis. It is emphasized that the condition of the application of the calculated method is the mathematical models of the operation of the aircraft and the availability of information on the aircraft – mass-inertial, rigid and aerodynamic characteristics.
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Chandrasekhar, Parvathy, Janis Kreiselmeier, Andreas Schwen, Thomas Weninger, Stefan Julich, Karl-Heinz Feger, and Kai Schwärzel. "Why We Should Include Soil Structural Dynamics of Agricultural Soils in Hydrological Models." Water 10, no. 12 (December 15, 2018): 1862. http://dx.doi.org/10.3390/w10121862.
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Surface soil structure is sensitive to natural and anthropogenic impacts that alter soil hydraulic properties (SHP). These alterations have distinct consequences on the water cycle. In this review, we summarized published findings on the quantitative effects of different agricultural management practices on SHP and the subsequent response of the water balance components. Generally, immediately after tillage, soils show a high abundance of large pores, which are temporally unstable and collapse due to environmental factors like rainfall. Nevertheless, most hydrological modeling studies consider SHP as temporally constant when predicting the flow of water and solutes in the atmosphere-plant-soil system. There have been some developments in mathematical approaches to capture the temporal dynamics of soil pore space. We applied one such pore evolution model to two datasets to evaluate its suitability to predict soil pore space dynamics after disturbance. Lack of knowledge on how dispersion of pore size distribution behaves after tillage may have led to over-estimation of some values predicted by the model. Nevertheless, we found that the model predicted the evolution of soil pore space reasonably well (r2 > 0.80 in most cases). The limiting factor to efficiently calibrate and apply such modeling tools is not in the theoretical part but rather the lack of adequate soil structural and hydrologic data.
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Pérez, Maria del Carmen, Alejandro López, and Pablo Padilla. "Space-time dynamics of Stem Cell Niches: a unified approach for Plants." Journal of Integrative Bioinformatics 10, no. 2 (June 1, 2013): 48–57. http://dx.doi.org/10.1515/jib-2013-219.
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Summary Many complex systems cannot be analyzed using traditional mathematical tools, due to their irreducible nature. This makes it necessary to develop models that can be implemented computationally to simulate their evolution. Examples of these models are cellular automata, evolutionary algorithms, complex networks, agent-based models, symbolic dynamics and dynamical systems techniques.We review some representative approaches to model the stem cell niche in Arabidopsis thaliana and the basic biological mechanisms that underlie its formation and maintenance. We propose a mathematical model based on cellular automata for describing the space-time dynamics of the stem cell niche in the root. By making minimal assumptions on the cell communication process documented in experiments, we classify the basic developmental features of the stem-cell niche, including the basic structural architecture, and suggest that they could be understood as the result of generic mechanisms given by short and long range signals. This could be a first step in understanding why different stem cell niches share similar topologies, not only in plants. Also the fact that this organization is a robust consequence of the way information is being processed by the cells and to some extent independent of the detailed features of the signaling mechanism.
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Provornaya, Darya, Sergey Glushkov, and Leonid Solovyev. "Damping of vertical and horizontal transverse vibrations in the bridge span structures." MATEC Web of Conferences 216 (2018): 01015. http://dx.doi.org/10.1051/matecconf/201821601015.
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The paper considers the issues of vibration isolation of railway bridge units on high-speed lines and seismic protection using dynamic vibration dampers. The purpose of the research is to justify the efficiency of damping the dynamic vibrations of the bridge supports with seismic insulating support parts. The research methodology involves building mathematical models of the systems under consideration and their numerical analysis. The methods of structural mechanics and dynamics of structures were used for solving the assigned tasks. The basic mathematical dependences of the vibration system with two seismic masses were developed. The rolling stock was represented by concentrated forces moving along the span structure. As a result, a new scheme for dynamic damping of vibration of the bridge supports was proposed according to which the span structure used as the dynamic vibration damper has an additional fastening on a rigid abutment.
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Adams, Johnathan A., Gentry White, and Robyn P. Araujo. "Mathematical measures of societal polarisation." PLOS ONE 17, no. 10 (October 4, 2022): e0275283. http://dx.doi.org/10.1371/journal.pone.0275283.
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In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies and information-theoretic divergences or distance metrics. Two of the methods, min-max flow and spectral radius, rely on graph theory and define polarisation in terms of the structural characteristics of networks. The other two methods represent opinions as probability density functions and use the Kullback–Leibler divergence and the Hellinger distance as polarisation measures. We present a series of opinion dynamics simulations from two common models to test the effectiveness of the methods. Results show that the four measures provide insight into the different aspects of polarisation and allow real-time monitoring of social networks for indicators of polarisation. The three measures, the spectral radius, Kullback–Leibler divergence and Hellinger distance, smoothly delineated between different amounts of polarisation, i.e. how many cluster there were in the simulation, while also measuring with more granularity how close simulations were to consensus. Min-max flow failed to accomplish such nuance.
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Stetsyuk, Petro, Maria Grygorak, Oleg Berezovskyi, and Oleksii Lykhovyd. "Mathematical Models of M.V. Mykhalevych for Forecasting Structural and Technological Changes." Cybernetics and Computer Technologies, no. 3 (November 29, 2022): 56–66. http://dx.doi.org/10.34229/2707-451x.22.3.6.
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Introduction. The identification of structural and technological disproportions that affect crisis phenomena in the economy and the analysis of ways to eliminate them require a wide application of quantitative research methods, in particular, mathematical modeling. “Input-Output” tables of Leontief turned out to be quite a convenient tool for analyzing these economic issues. In Leontief-type models, the matrix of technical coefficients (matrix of direct costs) is assumed to be known and calculated on the basis of statistical information from the “input-output” tables. M.V. Mykhalevych formulated the “inverse” problem: how to determine those structural and technological changes that would reduce the cost of production and thereby increase the incomes of end consumers and make the economy more dynamic. Or, in other words, how to choose or adjust technical coefficients to improve the properties of the economic process. This work is devoted to two optimization problems built on the basis of models of this type. The purpose of the article is to optimize the interdisciplinary planning of structural and technological changes. Results. Inverse models of the Leontief type for optimization of structural and technological transformations in economic systems are considered. These models are formulated in terms of nonlinear programming problems and include two objective functions for maximization: total consumer incomes and the “income growth–production growth” multiplier. Algorithms and software for solving these problems are presented. Numerical optimization procedures are based on Shor's r-algorithm. Conclusions. The use of inverse models of the Leontief type will allow choosing promising directions of structural and technological transformations in both the macro- and microeconomy. The proposed mathematical apparatus based on non-smooth optimization algorithms proved to be a sufficiently effective tool for solving appropriate optimization problems in practice. Keywords: structural and technological changes, inter-industry balance, Leontief model, “input-output” matrix, inverse Leontief-type models, non-smooth optimization algorithms, software.
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Toroptsev, E. L., A. S. Marakhovskii, and R. R. Duszynski. "Intersectoral modeling of transients." Economic Analysis: Theory and Practice 19, no. 3 (March 30, 2020): 564–85. http://dx.doi.org/10.24891/ea.19.3.564.
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Subject. The article considers structural transition processes in macroeconomics. Objectives. The aim is to present our own concept and mathematical tools to study structural transitions in macroeconomics. Dynamic inter-industry balance enables to formalize the problem in the form of a Koshi task for ordinary differential equations. Methods. The methodology components include the basics of inter-industry and numerical analysis and modeling of linear or linearized dynamic systems, integral criteria of system dynamics, stability and quality of transitional processes. We also apply a technique for analyzing the own dynamic properties of economic systems that solve the same sustainability-related challenges, but on the basis of algebraic methods and criteria. Results. We offer methods and mathematical tools for numerical study of sustainability and structural dynamics of macroeconomics. These methods are focused on integrating high-dimensional balance models and integral criteria for the quality of transition periods in the economy. The paper unveils advantages of calculating the matrix exponential and its integral in tasks involving analysis and forecasting, over other numerical methods. The proposed method permits to effectively build a difference scheme to integrate with any step of observation of the solution. In this case, the work step of integration is generated in the algorithm automatically, depending on changes in gross output. Conclusions. The paper presents a unique option to analyze transitional processes in macroeconomics. It is designed to develop and evaluate the results of pursued economic policy.
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Lakhova, T. N., F. V. Kazantsev, S. A. Lashin, and Yu G. Matushkin. "The finding and researching algorithm for potentially oscillating enzymatic systems." Vavilov Journal of Genetics and Breeding 25, no. 3 (June 2, 2021): 318–30. http://dx.doi.org/10.18699/vj21.035.
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Many processes in living organisms are subject to periodic oscillations at different hierarchical levels of their organization: from molecular-genetic to population and ecological. Oscillatory processes are responsible for cell cycles in both prokaryotes and eukaryotes, for circadian rhythms, for synchronous coupling of respiration with cardiac contractions, etc. Fluctuations in the numbers of organisms in natural populations can be caused by the populations’ own properties, their age structure, and ecological relationships with other species. Along with experimental approaches, mathematical and computer modeling is widely used to study oscillating biological systems. This paper presents classical mathematical models that describe oscillatory behavior in biological systems. Methods for the search for oscillatory molecular-genetic systems are presented by the example of their special case – oscillatory enzymatic systems. Factors influencing the cyclic dynamics in living systems, typical not only of the molecular-genetic level, but of higher levels of organization as well, are considered. Application of different ways to describe gene networks for modeling oscillatory molecular-genetic systems is considered, where the most important factor for the emergence of cyclic behavior is the presence of feedback. Techniques for finding potentially oscillatory enzymatic systems are presented. Using the method described in the article, we present and analyze, in a step-by-step manner, first the structural models (graphs) of gene networks and then the reconstruction of the mathematical models and computational experiments with them. Structural models are ideally suited for the tasks of an automatic search for potential oscillating contours (linked subgraphs), whose structure can correspond to the mathematical model of the molecular-genetic system that demonstrates oscillatory behavior in dynamics. At the same time, it is the numerical study of mathematical models for the selected contours that makes it possible to confirm the presence of stable limit cycles in them. As an example of application of the technology, a network of 300 metabolic reactions of the bacterium Escherichia coli was analyzed using mathematical and computer modeling tools. In particular, oscillatory behavior was shown for a loop whose reactions are part of the tryptophan biosynthesis pathway.
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Lederman, Dylan, Raghav Patel, Omar Itani, and Horacio G. Rotstein. "Parameter Estimation in the Age of Degeneracy and Unidentifiability." Mathematics 10, no. 2 (January 6, 2022): 170. http://dx.doi.org/10.3390/math10020170.
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Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one’s ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (Λ-Ω) models. These are an extension of the classical lambda-omega (λ-ω) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square wave to spike like. We show that the Λ-Ω models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the Λ-Ω models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of Λ-Ω models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data.
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Bianca, Carlo. "Mathematical and computational modeling of biological systems: advances and perspectives." AIMS Biophysics 8, no. 4 (2021): 318–21. http://dx.doi.org/10.3934/biophy.2021025.
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<abstract> <p>The recent developments in the fields of mathematics and computer sciences have allowed a more accurate description of the dynamics of some biological systems. On the one hand new mathematical frameworks have been proposed and employed in order to gain a complete description of a biological system thus requiring the definition of complicated mathematical structures; on the other hand computational models have been proposed in order to give both a numerical solution of a mathematical model and to derive computation models based on cellular automata and agents. Experimental methods are developed and employed for a quantitative validation of the modeling approaches. This editorial article introduces the topic of this special issue which is devoted to the recent advances and future perspectives of the mathematical and computational frameworks proposed in biosciences.</p> </abstract>
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Dvornik, Josko, Enco Tireli, and Srdjan Dvornik. "Analysis of the performance of the ship steam boiler using simulation." Thermal Science 13, no. 4 (2009): 11–20. http://dx.doi.org/10.2298/tsci0904011d.
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The aim of this paper is to demonstrate the successful application of system dynamics simulation modelling at investigating performance dynamics of the ship steam boiler. Ship steam boiler is a complex non-linear system which needs to be systematically investigated as a unit consisting of a number of subsystems and elements, which are linked by cause-effect feedback loops, both within the system and with the relevant surrounding. In this paper the authors will present the efficient application of scientific methods for the research of complex dynamic systems called qualitative and quantitative simulation system dynamics methodology, which will allow for production and use of higher number and kinds of simulation models of the observed elements, and finally allow for the continuous computer simulation, which will contribute to acquisition of new information about the non-linear character of performance dynamics of ship steam boilers in the process of designing and education. Ship steam boiler will be presented in POWERSIM simulation language in mental-verbal, structural, and mathematical computer models.
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Volnikov, M. I. "Application of the finite difference method for modeling cantilever bar vibrations." E3S Web of Conferences 224 (2020): 02002. http://dx.doi.org/10.1051/e3sconf/202022402002.
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The paper is devoted to mathematical modeling of cantilever bars using the finite difference method. This method is widely used in structural mechanics for solving static problems. The novelty lies in the application of the finite difference method to simulate the dynamics of free and forced vibrations of the cantilever. Models have been developed that allow calculating the static and dynamic deflections of the cantilevers during free and forced vibrations, as well as simulating the vibrations of cantilever beams with attached vibration dampers. The resulting models of cantilever structures make it easy to modify system parameters, external influences and damping elements. All calculations were performed using the finite difference approach when moving along geometric and temporal coordinates.
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Vdovin, D. S., I. V. Chichekin, Ya Yu Levenkov, and A. B. Fominykh. "Development of a quadricycle dynamic mathematical model methodology to calculate early design stages loads on the frame and chassis." Trudy NAMI, no. 2 (July 17, 2021): 46–57. http://dx.doi.org/10.51187/0135-3152-2021-2-46-57.
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Introduction (problem statement and relevance). To create a competitive vehicle in modern conditions, it is important to be able to determine its power elements loads at the early stages of design. A vehicle dynamic mathematical models allows you to solve this problem.The purpose of the study was to develop a dynamic mathematical model methodology of a quadricycle to determine its power elements loads under given operating conditions.Methodology and research methods. The article presents a dynamic mathematical model of a wheeled vehicle (quadricycle) technique using a created mathematical model within a solids dynamics modeling program and a real object experimental study to verify the mathematical model with an example of the obtained frame strength calculation under computer simulation loads.Scientific novelty and results. In the article the main stages of an utility quadricycle development and its dynamic mathematical model have been presented taking into account its design features and operating conditions. The main initial data necessary for creating an all-terrain vehicle dynamic mathematical model were identified. To confirm the developed dynamic model adequacy, a series of test site experiments was carried out. The obtained simulated results having been compared to the experimental data were highly convergent, which indicated the adequacy of the developed dynamic model of the ATV.Practical significance. The technique presented in the article allows to carry out virtual experiments to determine the main structural elements loads for subsequent strength, optimization and durability calculations.
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Noguera, Daniel R., Satoshi Okabe, and Cristian Picioreanu. "Biofilm modeling: present status and future directions." Water Science and Technology 39, no. 7 (April 1, 1999): 273–78. http://dx.doi.org/10.2166/wst.1999.0369.
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Biofilm models are commonly used as simulation tools in engineering applications and as research tools to identify and fill gaps in our knowledge of biofilm processes. While models used in engineering applications rely on simplifying assumptions to make them practical, recent experimental evidence of biofilm heterogeneity questions the validity of these assumptions. On the other hand, research models are becoming more complex and use advanced computational tools to mathematically investigate which factors determine the structural heterogeneity and the population dynamics of biofilms. One of the goals of advanced models is to evaluate the relevance of three-dimensional heterogeneities to the predictive capability of traditional biofilm models. In addition, biofilm models are used to evaluate experimental observations when studying a diversity of biofilm-related phenomena. Given the variety of applications of biofilm models and the different approaches that modelers have taken in recent years, a specialist group was convened to evaluate the present status and determine future directions of biofilm modeling research. The education of scientists and engineers on the fundamentals of biofilm models, the development of mathematical models for real-time control of biofilm processes, and the ability to “engineer” the biofilm structure and function (or performance) were identified as the most important objectives for the practical application of biofilm models. As mathematical research tools, biofilm models are directed towards gaining a better understanding of biofilm structure and population dynamics. Specific topics identified as priorities on biofilm research include the behavior of specialist microorganisms, the elucidation of attachment and detachment mechanisms, the determination of mechanical properties of exopolymeric substances, and the study of ecological interactions among different microorganisms. The need to evaluate parameter sensitivity in the different models was identified as an essential component of modeling research. A group decision from this meeting was to initiate a collaborative effort to identify similarities and differences among current modeling approaches. Such comparative analysis will enhance our understanding of biofilm processes and mathematical approaches, and will facilitate the future use of biofilm models by scientists and engineers involved in biofilm research.
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Minati, Gianfranco. "On Modelling the Structural Quasiness of Complex Systems." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 16 (December 23, 2021): 715–34. http://dx.doi.org/10.37394/23203.2021.16.65.
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Complex systems are usually represented by invariant models which at most admit only parametric variations. This approach assumes invariant idealized simplifications to model these systems. This standard approach is considered omitting crucial features of phenomenological interaction mechanisms related to processes of emergence of such systems. The quasiness of the structural dynamics that generate emergence of complex systems is considered as the main feature. Generation achieved through prevalently coherent sequences and combinations of interactions. Quasiness (dynamics of loss and recovery, equivalences, inhomogeneity, multiplicity, non-regularity, and partiality) represents the incompleteness of the interaction mechanisms, incompleteness necessary even if not sufficient for the establishment of processes of emergence. The emergence is extinguished by completeness. Complex systems possess local coherences corresponding to the phenomenological complexity. While quasi-systems are not necessarily complex systems, complex systems are considered quasi-systems, being not always systems, not always the same system, and not only systems. It is addressed the problem of representing the quasiness of coherence (quasicoherence), such as the ability to recover and tolerate temporary levels of incoherence. The main results of the study focus on research approaches to model quasicoherence through the changing of rules in models of emergence. It is presented a version of standard analytical approaches compatible with quasiness of systemic emergence and related mathematical issues. The same approach is considered for networks, artificial neural networks, and it is introduced the concept of quasification for fixed models. Finally, it is considered that suitable representations of structural dynamics and its quasiness are needed to model, simulate, and adopt effective interventions on emergence of complex systems.
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Tilocca, Antonio. "Structural models of bioactive glasses from molecular dynamics simulations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2104 (January 13, 2009): 1003–27. http://dx.doi.org/10.1098/rspa.2008.0462.
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The bioactive mechanism, by which living tissues attach to and integrate with an artificial implant through stable chemical bonds, is at the core of many current medical applications of biomaterials, as well as of novel promising applications in tissue engineering. Having been employed in these applications for almost 40 years, soda-lime phosphosilicate glasses such as 45S5 represent today the paradigm of bioactive materials. Despite their strategical importance in the field, the relationship between the structure and the activity of a glass composition in a biological environment has not been studied in detail. This fundamental gap negatively affects further progress, for instance, to improve the chemical durability and tailor the biodegradability of these materials for specific applications. This paper reviews recent advances in computer modelling of bioactive glasses based on molecular dynamics simulations, which are starting to unveil key structural features of these materials, thus contributing to improve our fundamental understanding of how bioactive materials work.
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Benveniste, Albert, Benoît Caillaud, Mathias Malandain, and Joan Thibault. "Algorithms for the Structural Analysis of Multimode Modelica Models." Electronics 11, no. 17 (September 1, 2022): 2755. http://dx.doi.org/10.3390/electronics11172755.
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Since its 3.3 release, Modelica offers the possibility to specify models of dynamical systems with multiple modes having different DAE-based dynamics. However, the handling of such models by the current Modelica tools is not satisfactory, with mathematically sound models yielding exceptions at runtime. In this article, we propose several contributions to this multifaceted issue, namely: an efficient and scalable multimode extension of the structural analysis of Modelica models; a systematic way of rewriting a multimode Modelica model, based on this analysis, so that the rewritten model is guaranteed to be correctly compiled by state-of-the-art Modelica tools; a proposal for the handling of the consistent initialization of multimode models; multimode structural analysis algorithms that handle both multiple modes and mode change events in a unified framework, coupled with a compile-time algorithm for identifying and quantifying impulsive behaviors at mode changes. Our approach is illustrated on relevant example models, and the performance of our implementations is assessed on a variable dimension large-scale model.
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Amaechi, Chiemela Victor, Facheng Wang, and Jianqiao Ye. "Mathematical Modelling of Bonded Marine Hoses for Single Point Mooring (SPM) Systems, with Catenary Anchor Leg Mooring (CALM) Buoy Application—A Review." Journal of Marine Science and Engineering 9, no. 11 (October 26, 2021): 1179. http://dx.doi.org/10.3390/jmse9111179.
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The application of mathematical analysis has been an essential tool applied on Catenary Anchor Leg Mooring (CALM) buoys, Wave Energy Converters (WEC), point absorber buoys, and various single point mooring (SPM) systems. This enables having mathematical models for bonded marine hoses on SPM systems with application with CALM buoys, which are obviously a requisite for the techno-economic design and operation of these floating structures. Hose models (HM) and mooring models (MM) are utilized on a variety of applications such as SPARs, Semisubmersibles, WECs and CALM buoys. CALM buoys are an application of SPM systems. The goal of this review is to address the subject of marine hoses from mathematical modeling and operational views. To correctly reproduce the behavior of bonded marine hoses, including nonlinear dynamics, and to study their performance, accurate mathematical models are required. The paper gives an overview of the statics and dynamics of offshore/marine hoses. The reviews on marine hose behavior are conducted based on theoretical, numerical, and experimental investigations. The review also covers challenges encountered in hose installation, connection, and hang-off operations. State-of-the-art, developments and recent innovations in mooring applications for SURP (subsea umbilicals, risers, and pipelines) are presented. Finally, this study details the relevant materials that are utilized in hoses and mooring implementations. Some conclusions and recommendations are presented based on this review.
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Chu, Yuanbo, Zhaohui Yuan, and Wenchao Chang. "Research on the Dynamic Erosion Wear Characteristics of a Nozzle Flapper Pressure Servo Valve Used in Aircraft Brake System." Mathematical Problems in Engineering 2020 (August 24, 2020): 1–13. http://dx.doi.org/10.1155/2020/3136412.
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The nozzle flapper pressure servo valve is a kind of high-precision hydraulic component that can be widely used in the aircraft brake system. In actual service, the dynamic erosion wear behavior will occur at the pilot stage because of the gradual contamination of oil and the variable distance between nozzle and flapper. For this purpose, the paper proposes a dynamic erosion wear characteristics analysis and service life prediction method in which firstly the structural feature and working principle of the nozzle flapper pressure valve are analyzed using the brake cavity as the load blind cavity. Secondly, the dynamics simulation model and the performance experiment system of the pressure valve are separately constructed, and then the validation of the constructed model is conducted by contrasting the results between simulation and experiment. Finally, the mathematical models of the degradation process induced by the dynamic erosion wear are established, and then the dynamic erosion wear characteristics under dynamic structural distance and contamination conditions are analyzed, which are combined with the failure threshold value determined by the dynamics simulation to finish the service life prediction of the nozzle flapper pressure servo valve.
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Bhonsle, Sakshi, and Sahaj Saxena. "A review on control-relevant glucose–insulin dynamics models and regulation strategies." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 234, no. 5 (August 30, 2019): 596–608. http://dx.doi.org/10.1177/0959651819870328.
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This article presents a state-of-the-art review on automated control of blood sugar, especially for Type 1 diabetic patients. A brief introduction is provided so as to justify how this biomedical issue proves to be a control system problem in sense of blood glucose regulation. Various mathematical models and control strategies that have been used in recent research work for automated insulin delivery are discussed. An attempt has been made to provide a structural survey of research done till date in the development of artificial pancreas system. At the end, a general idea is presented on how control system can be designed for this biomedical control problem by employing Bergman’s minimal model for blood glucose regulation and an internal model–based proportional–integral controller is designed. The controller exhibits faster response in maintaining the blood glucose when compared with other existing techniques.
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Szalai, R., K. Tsaneva-Atanasova, M. E. Homer, A. R. Champneys, H. J. Kennedy, and N. P. Cooper. "Nonlinear models of development, amplification and compression in the mammalian cochlea." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1954 (November 13, 2011): 4183–204. http://dx.doi.org/10.1098/rsta.2011.0192.
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This paper reviews current understanding and presents new results on some of the nonlinear processes that underlie the function of the mammalian cochlea. These processes occur within mechano-sensory hair cells that form part of the organ of Corti. After a general overview of cochlear physiology, mathematical modelling results are presented in three parts. First, the dynamic interplay between ion channels within the sensory inner hair cells is used to explain some new electrophysiological recordings from early development. Next, the state of the art is reviewed in modelling the electro-motility present within the outer hair cells (OHCs), including the current debate concerning the role of cell body motility versus active hair bundle dynamics. A simplified model is introduced that combines both effects in order to explain observed amplification and compression in experiments. Finally, new modelling evidence is presented that structural longitudinal coupling between OHCs may be necessary in order to capture all features of the observed mechanical responses.
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Cho, D. W., K. F. Eman, and S. M. Wu. "A New Time Domain Multiple Input Modal Analysis Method." Journal of Engineering for Industry 109, no. 4 (November 1, 1987): 377–84. http://dx.doi.org/10.1115/1.3187142.
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A time domain approach for multiple input modal analysis of oscillatory systems is proposed. The mathematical foundation for the approach is given along with its applications to a simulated lumped parameter system and the structural dynamics analysis of a milling machine. It has been shown that the proposed multivariate time series models are able to identify the complex mode shapes from multiple input structural test data. The advantages of the proposed method in comparison to existing methods are also highlighted.
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Lo Schiavo, M. "Population kinetic models for social dynamics: Dependence on structural parameters." Computers & Mathematics with Applications 44, no. 8-9 (October 2002): 1129–46. http://dx.doi.org/10.1016/s0898-1221(02)00221-3.
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Ellam, L., M. Girolami, G. A. Pavliotis, and A. Wilson. "Stochastic modelling of urban structure." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2213 (May 2018): 20170700. http://dx.doi.org/10.1098/rspa.2017.0700.
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The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban structure to formally account for uncertainty arising from less predictable events. Standard practice has been to calibrate the spatial interaction models independently and to explore the dynamics through simulation. We present two significant results that will be transformative for both elements. First, we represent the structural variables through a single potential function and develop stochastic differential equations to model the evolution. Second, we show that the parameters of the spatial interaction model can be estimated from the structure alone, independently of flow data, using the Bayesian inferential framework. The posterior distribution is doubly intractable and poses significant computational challenges that we overcome using Markov chain Monte Carlo methods. We demonstrate our methodology with a case study on the London, UK, retail system.
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Aralova, Nataliya, Olena Klyuchko, Valery Mashkin, and Irina Mashkina. "Mathematical Model for the Investigation of Human Organism Functional Self-organisation." Electronics and Control Systems 2, no. 68 (November 22, 2021): 9–17. http://dx.doi.org/10.18372/1990-5548.68.16083.
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Mathematical modeling of processes occurring in living organism is convenient and reliable tool for the understanding of mechanisms of human organism self-organization, interaction and inter-influence of its functional systems. The simulations of processes occurring in organism during various extreme perturbations at mathematical models allow us to study the parameters of self-organization in these perturbations at the level unavailable currently for modern invasive methods as well as to predict the organism steady state at given level of perturbing effects. The objects of study were the reactions of respiratory and blood circulatory systems, because these systems, according to the theory of adaptation by F. Meerson, are the most sensitive to the disturbing effects of environment. The paper provides a brief overview of mathematical models of respiratory and blood circulatory system; in the construction of these models rather complex mathematical apparatus was used and, accordingly, the implementation of which requires significant computational resources. The mathematical model of the functional respiratory system was proposed; it is based on the principle of the main function of respiratory system realization and takes into account conflict situations that occur in organism during this function fulfillment. This conflict happens between the governing and executive self-regulatory organism organs as well as between the different tissues groups in their fight for the oxygen. Mathematically, the model is a system of ordinary nonlinear differential equations that describe the transport and mass transfer of respiratory gases in all structural parts of respiratory system. The task of control of gases dynamics in organism was solved using the principle of Pontryagin maximum.
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Wang, Peng, and Fengqi Si. "Dynamic Prediction of the Thermal Nonlinear Process Based on Deep Hybrid Neural Network." E3S Web of Conferences 162 (2020): 01007. http://dx.doi.org/10.1051/e3sconf/202016201007.
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Nonlinear system prediction plays an important role in the practical thermal process, and deep learning algorithm is now popular in nonlinear dynamic system modeling because of its powerful learning ability. In this paper, the dynamic artificial neural networks (DANNs), which can be divided into two different types with external dynamic characteristics and internal dynamic characteristics, are analyzed. The mathematical formulations of feedforward deep neural network (DNN), traditional recurrent neural network (RNN) and Long-Short Term Memory network (LSTM) models are given. Furthermore, the structure of deep Hybrid Neural Network (DHNN) is described. Finally, the applicability of the above models in the thermal nonlinear process with different structural features is discussed. Simulation experiments reveal that DANNs with internal dynamic characteristics more suitable for solving thermal nonlinear system modeling problems with unknown order, and DHNN based on LSTM model has performed much better in approximating the dynamics of the thermal process with state parameters.
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Vilenskii, O., S. Dushev, D. Lapshin, E. Novinskii, and A. Tatarskii. "MATHEMATICAL ANALYSIS OF AIRCRAFT TURBINE COLLISION WITH SHIPPING PACKAGE." PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS 2021, no. 3 (September 26, 2021): 106–22. http://dx.doi.org/10.55176/2414-1038-2021-3-106-122.
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The aim of the paper is to substantiate the developed shipping package integrity on the basis of mathematical analysis of postulated scenarios for the heaviest dynamic effects using verified behavior models for applied structural materials and modern certified finite element software package. The shipping package is permitted to transfer to the limiting condition in the result of impact, when its further operation is not acceptable, and recovery of its functional condition is not expedient, excluding the possibility of falling out of the nuclear fuel (NF) or distortion of the relative position of the NF in the shipping package. The paper presents main analysis results of the process of an aircraft turbine collision with a shipping package. The calculation analysis was performed using the dynamic calculation module LS-DYNA of the certified software package ANSYS. The LS-DYNA module is meant for computational analysis of high linear dynamic processes under explicit scheme of integration of the dynamics equations. The completed full-scale mathematical 3D modeling permitted to carry out sufficiently deep and detailed analysis of dynamic processes, reducing the design duration, and it permitted to reduce the self-cost of the developed design. The obtained results of mathematical analysis of shipping package behavior during interaction with aircraft turbine enabled to form the approach to substantiation of equipment safety in incidents. The detailed design study performed at the design stage formed basis for the final appearance of the developed structure.
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Gasanov, A. R., R. A. Gasanov, R. A. Ahmadov, and M. V. Sadikhov. "Mathematical Models of the Acousto-Optic Delay Line Characteristics and Their Adequacy Assessment." Proceedings of Universities. Electronics 26, no. 5 (2021): 410–25. http://dx.doi.org/10.24151/1561-5405-2021-26-5-410-425.
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In radioengineering systems, various methods and technical means are used for signal processing, the selection criteria of which are optimized for the best result of assigned task solution. The study of an analog signal shift on the time axis is one of the widely used radio engineering problems. In this work, the functional capabilities of an acousto-optic delay line (AODL) in the context of processing analog signals in the time domain are listed. The urgency of creating mathematical models of the AODL main characteristics and their study was substantiated. The AODL circuit and its operation principle were discussed, and an expression for the current at its output was obtained. Based on the structural and electrical parameters of the AODL, mathemati-cal models of its transient, impulse and amplitude-frequency characteristics have been con-structed. It was shown that the diameter of the light beam interacting with the elastic wave has the greatest effect on the characteristics of a particular AODL sample. A numerical analysis of the above characteristics was carried out. The results of the numerical analysis were tested expe-rimentally on the AODL model. To avoid accidental coincidences, numerical analysis and expe-rimental approbation were carried out for two values of the laser beam diameter. The adequacy of the transient, impulse and amplitude-frequency characteristics was assessed by the results ob-tained in statics and dynamics. It was shown that the transient, impulse or amplitude-frequency response can be used to determine the AODL frequency and time parameters. Static and dynamic comparison of the results of numerical analysis and experimental studies have shown their unambiguous adequacy.
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Moon, Francis C., and Preston D. Stiefel. "Coexisting chaotic and periodic dynamics in clock escapements." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1846 (July 28, 2006): 2539–64. http://dx.doi.org/10.1098/rsta.2006.1839.
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This paper addresses the nature of noise in machines. As a concrete example, we examine the dynamics of clock escapements from experimental, historical and analytical points of view. Experiments on two escapement mechanisms from the Reuleaux kinematic collection at Cornell University are used to illustrate chaotic-like noise in clocks. These vibrations coexist with the periodic dynamics of the balance wheel or pendulum. A mathematical model is presented that shows how self-generated chaos in clocks can break the dry friction in the gear train. This model is shown to exhibit a strange attractor in the structural vibration of the clock. The internal feedback between the oscillator and the escapement structure is similar to anti-control of chaos models.
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Eliseev, Andrey, Sergey Eliseev, and Alexey Orlenko. "Features of dynamic loading of transport vehicles in intensive operation." MATEC Web of Conferences 216 (2018): 01012. http://dx.doi.org/10.1051/matecconf/201821601012.
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The paper proposes a method to construct mathematical models of technical objects exposed to intense vibrational interactions, which is typical for assemblies of transport vehicles. A technique has been developed to construct structural mathematical models in the form of structural diagrams, which are dynamically equivalent to automatic control systems. Analytical tools have been adopted from the theory of automatic control. The paper demonstrates the possibilities of changing dynamic properties of technical objects, design schemes of which are represented by mechanical oscillatory systems. Changes in the dynamic effects arising from the introduction of additional inertial couplings have been estimated. Effects of new dynamic properties have been considered. Analytic relations have been proposed for detailed estimates.
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Kulik, Anatoliy, Konstantin Dergachov, Sergey Pasichnik, and Sergey Yashyn. "Motions models of a two-wheeled experimental sample." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 1 (February 27, 2021): 40–49. http://dx.doi.org/10.32620/reks.2021.1.03.
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The subject of study is the physical processes of translational and angular motion of a two-wheeled experimental sample. The goal is to develop physical, mathematical, and graphic models of the translational and angular motions of a two-wheeled experimental sample as an object of automatic control. The objectives: to form physical models of a two-wheeled experimental sample; to develop a nonlinear mathematical description of the processes of translational and angular sample`s motions using the Lagrange approach; to obtain a linearized mathematical sample`s description as an object of automatic control in the state space and frequency domain; to generate graphic models in the form of structural diagrams in the time and frequency domains; to analyze the functional properties of an object of automatic control: stability, controllability, observability, structural and signal diagnosability concerning violations of the functional properties of electric drives and sensors of the angular position of the body and wheels. The methods of the study: the Lagrange method, Taylor series, state-space method, Laplace transformations, Lyapunov, Kalman criteria, and diagnosability criterion. The results: physical models of a two-wheeled experimental sample have been obtained in the form of a kinematic diagram of the mechanical part and the electric circuit of an electric drive; mathematical descriptions of translational and angular motions have been developed in nonlinear and linearized forms; structural diagrams have been developed; functional characteristics of a two-wheeled experimental model as an object of automatic control have been analyzed to solve problems of control algorithms synthesis. Conclusions. The scientific novelty lies in obtaining new models that describe the translational and angular motion of a two-wheeled experimental model as an object of automatic control. The obtained models differ from the known ones by considering the dynamic properties of sensors and electric drives, as well as the relationship of movements.