Studies of many complex systems have revealed new collective behaviours that emerge through the mechanisms of self-organised critical fluctuations. Subject to the external and endogenous driving forces, these collective states with long-range spatial and temporal correlations often arise from the intrinsic dynamics with the threshold nonlinearity and geometry-conditioned interactions. The self-similarity of critical fluctuations enables us to describe the system using fewer parameters and universal functions that, on the other hand, can simplify the computational and information complexity. Currently, the cutting-edge research on self-organised critical systems across the scales strives to formulate a unifying mathematical framework, utilise the critical universal properties in information theory, and decipher the role of hidden geometry. As a prominent example, we study the field-driven spin dynamics on the hysteresis loop in a network with higher-order structures described by simplicial complexes, which provides a geometric-frustration environment. While providing motivational illustrations from physical, biological, and social systems, along with their networks, we also demonstrate how the self-organised criticality occurs at the interplay of the complex topology and driving mode. This study opens up new promising routes with powerful tools to address a long-standing challenge in the theory and applications of complexity science ingrained in the efficient analysis of self-organised critical states under the competing higher-order interactions embedded in complex geometries.
{"title":"Self-Organised Critical Dynamics as a Key to Fundamental Features of Complexity in Physical, Biological, and Social Networks","authors":"B. Tadić, R. Melnik","doi":"10.3390/dynamics1020011","DOIUrl":"https://doi.org/10.3390/dynamics1020011","url":null,"abstract":"Studies of many complex systems have revealed new collective behaviours that emerge through the mechanisms of self-organised critical fluctuations. Subject to the external and endogenous driving forces, these collective states with long-range spatial and temporal correlations often arise from the intrinsic dynamics with the threshold nonlinearity and geometry-conditioned interactions. The self-similarity of critical fluctuations enables us to describe the system using fewer parameters and universal functions that, on the other hand, can simplify the computational and information complexity. Currently, the cutting-edge research on self-organised critical systems across the scales strives to formulate a unifying mathematical framework, utilise the critical universal properties in information theory, and decipher the role of hidden geometry. As a prominent example, we study the field-driven spin dynamics on the hysteresis loop in a network with higher-order structures described by simplicial complexes, which provides a geometric-frustration environment. While providing motivational illustrations from physical, biological, and social systems, along with their networks, we also demonstrate how the self-organised criticality occurs at the interplay of the complex topology and driving mode. This study opens up new promising routes with powerful tools to address a long-standing challenge in the theory and applications of complexity science ingrained in the efficient analysis of self-organised critical states under the competing higher-order interactions embedded in complex geometries.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81859687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, a tail rotor is modelled with the aid of a multibody software to provide an alternative tool in the field of helicopter research. This advanced application captures the complex behaviour of tail rotor dynamics. The model has been built by using VehicleSim software (Version 1.0, Mechanical Simulation Corporation, Ann Arbor, MI, USA) specialized in modelling mechanical systems composed of rigid bodies. The dynamic behaviour and the control action are embedded in the code. Thereby, VehicleSim does not need an external link to another software package. The rotors are articulated, the tail rotor considers flap and feather degrees of freedom for each of the equispaced blades and their dynamic couplings. Details on the model’s implementation are derived, emphasising the modelling aspects that contribute to the coupled dynamics. The obtained results are contrasted with theoretical approaches and these have displayed to agree with the expected behaviour. This rotorcraft model helps to study the performance of a tail rotor under certain dynamic conditions.
在这项工作中，尾桨的建模与多体软件的帮助下，为直升机研究领域提供了一个替代工具。这个先进的应用程序捕捉尾桨动力学的复杂行为。该模型是使用专门为刚体组成的机械系统建模的VehicleSim软件(1.0版，Mechanical Simulation Corporation, Ann Arbor, MI, USA)建立的。动态行为和控制动作嵌入在代码中。因此，VehicleSim不需要外部链接到另一个软件包。尾桨是铰接的，尾桨考虑了每一个叶片的襟翼和羽毛自由度及其动态耦合。详细的模型的实现推导，强调建模方面，有助于耦合动力学。所得结果与理论方法进行了对比，结果与预期行为一致。该模型有助于研究尾桨在一定动态条件下的性能。
{"title":"Description of a Dynamical Framework to Analyse the Helicopter Tail Rotor","authors":"S. Castillo-Rivera, M. Tomas-Rodriguez","doi":"10.3390/dynamics1020010","DOIUrl":"https://doi.org/10.3390/dynamics1020010","url":null,"abstract":"In this work, a tail rotor is modelled with the aid of a multibody software to provide an alternative tool in the field of helicopter research. This advanced application captures the complex behaviour of tail rotor dynamics. The model has been built by using VehicleSim software (Version 1.0, Mechanical Simulation Corporation, Ann Arbor, MI, USA) specialized in modelling mechanical systems composed of rigid bodies. The dynamic behaviour and the control action are embedded in the code. Thereby, VehicleSim does not need an external link to another software package. The rotors are articulated, the tail rotor considers flap and feather degrees of freedom for each of the equispaced blades and their dynamic couplings. Details on the model’s implementation are derived, emphasising the modelling aspects that contribute to the coupled dynamics. The obtained results are contrasted with theoretical approaches and these have displayed to agree with the expected behaviour. This rotorcraft model helps to study the performance of a tail rotor under certain dynamic conditions.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82864344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For time dependent Hamiltonians like the parametric oscillator with time-dependent frequency, the energy is no longer a constant of motion. Nevertheless, in 1880, Ermakov found a dynamical invariant for this system using the corresponding Newtonian equation of motion and an auxiliary equation. In this paper it is shown that the same invariant can be obtained from Bohmian mechanics using complex Hamiltonian equations of motion in position and momentum space and corresponding complex Riccati equations. It is pointed out that this invariant is equivalent to the conservation of angular momentum for the motion in the complex plane. Furthermore, the effect of a linear potential on the Ermakov invariant is analysed.
{"title":"Dynamical Invariants for Generalized Coherent States via Complex Quantum Hydrodynamics","authors":"M. Bonilla-Licea, D. Schuch","doi":"10.3390/dynamics1020009","DOIUrl":"https://doi.org/10.3390/dynamics1020009","url":null,"abstract":"For time dependent Hamiltonians like the parametric oscillator with time-dependent frequency, the energy is no longer a constant of motion. Nevertheless, in 1880, Ermakov found a dynamical invariant for this system using the corresponding Newtonian equation of motion and an auxiliary equation. In this paper it is shown that the same invariant can be obtained from Bohmian mechanics using complex Hamiltonian equations of motion in position and momentum space and corresponding complex Riccati equations. It is pointed out that this invariant is equivalent to the conservation of angular momentum for the motion in the complex plane. Furthermore, the effect of a linear potential on the Ermakov invariant is analysed.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88152982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multi-enzymatic reactions can successfully replace complex chemical syntheses, using milder reaction conditions, and generating less waste. The present model-based analysis compares the performances of several optimally operated Batch Reactors (BR) with those of an optimally operated serial Sequence of BRs (SeqBR). In multi-enzymatic systems, SeqBR could be more advantageous and flexible, allowing the optimization of costly enzymes amounts used in each BR in the series. Exemplification was made for the bi-enzymatic reduction of D-fructose to mannitol by using MDH (mannitol dehydrogenase) and the NADH cofactor, with the in situ continuous regeneration of NADH at the expense of formate degradation in the presence of FDH (formate dehydrogenase). For such coupled enzymatic systems, the model-based engineering evaluations are difficult tasks, because they must account for the common species’ initial levels, their interaction, and their dynamics. The determination of optimal operating modes of sole BR or of a SeqBR turns into a multi-objective optimization problem with multiple constraints to be solved for every particular system. The study presents multiple elements of novelty: (i) the proof of higher performances of an optimal SeqBR (including N-BRs) compared to a sole optimal BR operated for N-number of runs and (ii) the effect of using a multi-objective optimization criteria on SeqBR adjustable dynamics.
{"title":"Model-Based Optimization of Mannitol Production by Using a Sequence of Batch Reactors for a Coupled Bi-Enzymatic Process—A Dynamic Approach","authors":"G. Maria, Ioana Mirela Peptănaru","doi":"10.3390/dynamics1010008","DOIUrl":"https://doi.org/10.3390/dynamics1010008","url":null,"abstract":"Multi-enzymatic reactions can successfully replace complex chemical syntheses, using milder reaction conditions, and generating less waste. The present model-based analysis compares the performances of several optimally operated Batch Reactors (BR) with those of an optimally operated serial Sequence of BRs (SeqBR). In multi-enzymatic systems, SeqBR could be more advantageous and flexible, allowing the optimization of costly enzymes amounts used in each BR in the series. Exemplification was made for the bi-enzymatic reduction of D-fructose to mannitol by using MDH (mannitol dehydrogenase) and the NADH cofactor, with the in situ continuous regeneration of NADH at the expense of formate degradation in the presence of FDH (formate dehydrogenase). For such coupled enzymatic systems, the model-based engineering evaluations are difficult tasks, because they must account for the common species’ initial levels, their interaction, and their dynamics. The determination of optimal operating modes of sole BR or of a SeqBR turns into a multi-objective optimization problem with multiple constraints to be solved for every particular system. The study presents multiple elements of novelty: (i) the proof of higher performances of an optimal SeqBR (including N-BRs) compared to a sole optimal BR operated for N-number of runs and (ii) the effect of using a multi-objective optimization criteria on SeqBR adjustable dynamics.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75426647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Offshore structures are subjected to dynamic environmental loads (wave and wind loads). A stress-life fatigue strength curve is proposed for tubular joints which are in the splash zone area of offshore jacket structures. The Det Norske Veritas (DNV) offshore structures standards given design T-curve in the air is modified with the environment-dependent parameters to obtain this fatigue strength curve. Validity of the curve is done by comparing fatigue lives given by the proposed curve with experimental fatigue lives of tubular joints tested in seawater under different loading conditions. The fatigue assessment of a case study tubular joint is performed using the proposed curve. Nominal stress ranges of the members, which are connected to the joint, are obtained by dynamic analysis of the jacket structure. Stress concentration factors are utilized with the nominal stresses to obtain the hot spot stress ranges. Fatigue lives are calculated and compared with the conventional approach. Hence the applicability and significance of the proposed fatigue strength curve are discussed.
{"title":"Fatigue Strength Curve for Tubular Joints of Offshore Structures under Dynamic Loading","authors":"S. Siriwardane, N. Adasooriya, D. Pavlou","doi":"10.3390/dynamics1010007","DOIUrl":"https://doi.org/10.3390/dynamics1010007","url":null,"abstract":"Offshore structures are subjected to dynamic environmental loads (wave and wind loads). A stress-life fatigue strength curve is proposed for tubular joints which are in the splash zone area of offshore jacket structures. The Det Norske Veritas (DNV) offshore structures standards given design T-curve in the air is modified with the environment-dependent parameters to obtain this fatigue strength curve. Validity of the curve is done by comparing fatigue lives given by the proposed curve with experimental fatigue lives of tubular joints tested in seawater under different loading conditions. The fatigue assessment of a case study tubular joint is performed using the proposed curve. Nominal stress ranges of the members, which are connected to the joint, are obtained by dynamic analysis of the jacket structure. Stress concentration factors are utilized with the nominal stresses to obtain the hot spot stress ranges. Fatigue lives are calculated and compared with the conventional approach. Hence the applicability and significance of the proposed fatigue strength curve are discussed.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89892150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Analytical solutions to a variety of simplified versions of the restricted three-body problem in celestial mechanics possess long running history that encompasses several centuries. Most of the successes were limited either to the planar configuration of the three bodies, to the motion around the Lagrange points, or to the Kozai–Lidov effect. We review some analytical advances obtained by separating rapid and slow subsystems as presented in recently published papers concerning the non-planar motion of the three bodies unrelated to the Lagrange points and to the Kozai–Lidov effect. Most (but not all) of the discussed advances correspond to the bound motion in the considered celestial systems.
{"title":"Orbital Dynamics in the Restricted Three Body Problem: Overview of Recent Analytical Advances Obtained by Separating Rapid and Slow Subsystems in Non-Planar Configurations","authors":"E. Oks","doi":"10.3390/dynamics1010006","DOIUrl":"https://doi.org/10.3390/dynamics1010006","url":null,"abstract":"Analytical solutions to a variety of simplified versions of the restricted three-body problem in celestial mechanics possess long running history that encompasses several centuries. Most of the successes were limited either to the planar configuration of the three bodies, to the motion around the Lagrange points, or to the Kozai–Lidov effect. We review some analytical advances obtained by separating rapid and slow subsystems as presented in recently published papers concerning the non-planar motion of the three bodies unrelated to the Lagrange points and to the Kozai–Lidov effect. Most (but not all) of the discussed advances correspond to the bound motion in the considered celestial systems.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80780132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived using the general virtual work variational principle. The presented model contains, apart from the two classical Lame constants, one additional microstructure material parameter g for the static case and one micro-inertia parameter h for the dynamic case. The formal reduction of this model to a Kirchhoff-type plate model is also presented. Upon diminishing the microstructure parameters g and h, the classical Mindlin–Reissner and Kirchhoff plate theories are derived. Three points distinguish the present work from other similar published in the literature. First, the plane stress assumption, fundamental for the development of plate theories, is expressed by the vanishing of the z-component of the generalized true traction vector and not merely by the zz-component of the Cauchy stress tensor. Second, micro-inertia terms are included in the expression of the kinetic energy of the model. Finally, the detailed structure of classical and non-classical boundary conditions is presented for both Mindlin–Reissner and Kirchhoff micro-plates. An example of a simply supported rectangular plate is used to illustrate the proposed model and to compare it with results from the literature. The numerical results reveal the significance of the strain gradient effect on the bending and free vibration response of the micro-plate, when the plate thickness is at the micron-scale; in comparison to the classical theories for Mindlin–Reissner and Kirchhoff plates, the deflections, the rotations, and the shear-thickness frequencies are smaller, while the fundamental flexural frequency is higher. It is also observed that the micro-inertia effect should not be ignored in estimating the fundamental frequencies of micro-plates, primarily for thick plates, when plate thickness is at the micron scale (strain gradient effect).
{"title":"Strain Gradient Theory Based Dynamic Mindlin-Reissner and Kirchhoff Micro-Plates with Microstructural and Micro-Inertial Effects","authors":"S. Markolefas, D. Fafalis","doi":"10.3390/dynamics1010005","DOIUrl":"https://doi.org/10.3390/dynamics1010005","url":null,"abstract":"In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived using the general virtual work variational principle. The presented model contains, apart from the two classical Lame constants, one additional microstructure material parameter g for the static case and one micro-inertia parameter h for the dynamic case. The formal reduction of this model to a Kirchhoff-type plate model is also presented. Upon diminishing the microstructure parameters g and h, the classical Mindlin–Reissner and Kirchhoff plate theories are derived. Three points distinguish the present work from other similar published in the literature. First, the plane stress assumption, fundamental for the development of plate theories, is expressed by the vanishing of the z-component of the generalized true traction vector and not merely by the zz-component of the Cauchy stress tensor. Second, micro-inertia terms are included in the expression of the kinetic energy of the model. Finally, the detailed structure of classical and non-classical boundary conditions is presented for both Mindlin–Reissner and Kirchhoff micro-plates. An example of a simply supported rectangular plate is used to illustrate the proposed model and to compare it with results from the literature. The numerical results reveal the significance of the strain gradient effect on the bending and free vibration response of the micro-plate, when the plate thickness is at the micron-scale; in comparison to the classical theories for Mindlin–Reissner and Kirchhoff plates, the deflections, the rotations, and the shear-thickness frequencies are smaller, while the fundamental flexural frequency is higher. It is also observed that the micro-inertia effect should not be ignored in estimating the fundamental frequencies of micro-plates, primarily for thick plates, when plate thickness is at the micron scale (strain gradient effect).","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80258594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Lykakos, P. Kostazos, Odysseas-Vasilios Venetsanos, D. Manolakos
Offshore structures are exposed to risks of vessel collisions and impacts from dropped objects. Tubular members are extensively used in offshore construction, and thus, there is scope to investigate their crashworthiness behaviour. Aluminium, glass fibre reinforced polymer (GFRP) and hybrid aluminium/GFRP circular tube specimens were fabricated and then tested under quasi-static and dynamic axial loading conditions. Two hybrid configurations were examined: external and internal layers from respectively aluminium and GFRP, and vice versa. The material impregnated with epoxy resin woven glass fabric was allowed to cure attached to the aluminium layer to ensure interlayer bonding. The quasi-static and dynamic tests were conducted using respectively a universal testing machine at a prescribed crosshead speed of 10 mm/min, and a 78 kg drop hammer released from 2.5 m. The non-hybrid configurations (aluminium and GFRP specimens) outperformed their hybrid counterparts in terms of crashworthiness characteristics.
{"title":"Crashworthiness Performance of Aluminium, GFRP and Hybrid Aluminium/GFRP Circular Tubes under Quasi-Static and Dynamic Axial Loading Conditions: A Comparative Experimental Study","authors":"S. Lykakos, P. Kostazos, Odysseas-Vasilios Venetsanos, D. Manolakos","doi":"10.3390/dynamics1010004","DOIUrl":"https://doi.org/10.3390/dynamics1010004","url":null,"abstract":"Offshore structures are exposed to risks of vessel collisions and impacts from dropped objects. Tubular members are extensively used in offshore construction, and thus, there is scope to investigate their crashworthiness behaviour. Aluminium, glass fibre reinforced polymer (GFRP) and hybrid aluminium/GFRP circular tube specimens were fabricated and then tested under quasi-static and dynamic axial loading conditions. Two hybrid configurations were examined: external and internal layers from respectively aluminium and GFRP, and vice versa. The material impregnated with epoxy resin woven glass fabric was allowed to cure attached to the aluminium layer to ensure interlayer bonding. The quasi-static and dynamic tests were conducted using respectively a universal testing machine at a prescribed crosshead speed of 10 mm/min, and a 78 kg drop hammer released from 2.5 m. The non-hybrid configurations (aluminium and GFRP specimens) outperformed their hybrid counterparts in terms of crashworthiness characteristics.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83738007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nowadays, the subject of studying system dynamics behavior has become very important in many branches of technology [...]
如今，研究系统动力学行为在许多技术分支中已经变得非常重要[…]
{"title":"Editorial for the Launching of Dynamics","authors":"C. Volos","doi":"10.3390/DYNAMICS1010003","DOIUrl":"https://doi.org/10.3390/DYNAMICS1010003","url":null,"abstract":"Nowadays, the subject of studying system dynamics behavior has become very important in many branches of technology [...]","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87673763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. N. Impiombato, Giorgio La Civita, F. Orlandi, Flavia Schwarz Franceschini Zinani, Luiz Alberto Oliveira Rocha, C. Biserni
As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of the Womersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated.
{"title":"A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow","authors":"A. N. Impiombato, Giorgio La Civita, F. Orlandi, Flavia Schwarz Franceschini Zinani, Luiz Alberto Oliveira Rocha, C. Biserni","doi":"10.3390/DYNAMICS1010002","DOIUrl":"https://doi.org/10.3390/DYNAMICS1010002","url":null,"abstract":"As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of the Womersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76988859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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