Dynamics (Pembroke, Ont.)最新文献_第3页

The Relationship between Electrical Conductivity and Electromigration in Liquid Metals 液态金属电导率与电迁移的关系

Dynamics (Pembroke, Ont.) Pub Date : 2023-07-28 DOI: 10.3390/dynamics3030022

D. Belashchenko

{"title":"The Relationship between Electrical Conductivity and Electromigration in Liquid Metals","authors":"D. Belashchenko","doi":"10.3390/dynamics3030022","DOIUrl":"https://doi.org/10.3390/dynamics3030022","url":null,"abstract":"The phenomena of electrical conductivity and electromigration in metallic systems are related, since in both cases the basic physical process is the scattering of conduction electrons by metal ions. Numerous searches have been made for equations connecting the conductivity with electromigration. In the case of a liquid metal, when using the Drude–Sommerfeld (DS) conductivity equation, it was not possible to obtain a quantitative relationship between these phenomena, which would be correct. Attempts to find such a relationship when taking into account the N. Mott correction (g-factor) in the DS equation were unsuccessful. This article proposes a different correction (b-factor) to the DS equation, which takes into account the possibility of varying the momentum transferred by the conduction electron to a metal ion during the scattering. This correction allows to establish a quantitative relationship between conductivity and electromigration as well as between electromigration in various binary systems with common components, in agreement with the experiment. The proposed theory describes well, in particular, two- and multi-component metal systems of any concentration (the consistency rule for triangles A–B, B–C, C–A). The value of the b-factor smoothly changes depending on the heat of vaporization of the metal, per unit volume.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77011586","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}

引用次数: 0

The Dynamics of a Turning Ship: Mathematical Analysis and Simulation Based on Free Body Diagrams and the Proposal of a Pleometric Index 船舶转向动力学:基于自由体图的数学分析与仿真及弹性指数的提出

Dynamics (Pembroke, Ont.) Pub Date : 2023-07-03 DOI: 10.3390/dynamics3030021

F. Fuss

{"title":"The Dynamics of a Turning Ship: Mathematical Analysis and Simulation Based on Free Body Diagrams and the Proposal of a Pleometric Index","authors":"F. Fuss","doi":"10.3390/dynamics3030021","DOIUrl":"https://doi.org/10.3390/dynamics3030021","url":null,"abstract":"This study attempts to shed new light on the dynamics of a turning ship using the principles of free body diagrams (FBDs). Unexpectedly, the literature gap is defined by incomplete and flawed FBDs. The method behind this new approach involves the FBD of a turning ship, with all the essential forces included, namely propulsive force, sideward thruster force (producing the initial turning moment), drag force, lift force, centrifugal force, inertial force, and hydrodynamic force couple. From these forces, the force and moment equations are derived. The accelerations are calculated from the force and moment equilibria to simulate the dynamics from input parameters such as mass m, length L, draught D, and fluid density ρ. The turning dynamics are explained in terms of velocities, accelerations, forces, and moments, based on two conditions: flat and steep angles of attack (AoA) and long and short turning radii R. A critical result is the proportionality of lift and centrifugal forces, leading to the proposal of a pleometric index (m·L–2·D–1·ρ–1), which is nonlinearly proportional to the product of AoA and R/L, characterising the dynamics of a turning ship. The FBD approach of this study also identified missing databases required for accurate simulation of turning dynamics, such as drag and lift coefficients of different hull geometries.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72466133","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}

引用次数: 0

Approach to Equilibrium of Statistical Systems: Classical Particles and Quantum Fields Off-Equilibrium 统计系统的平衡方法:经典粒子和非平衡量子场

Dynamics (Pembroke, Ont.) Pub Date : 2023-06-13 DOI: 10.3390/dynamics3020020

R. F. Álvarez-Estrada

{"title":"Approach to Equilibrium of Statistical Systems: Classical Particles and Quantum Fields Off-Equilibrium","authors":"R. F. Álvarez-Estrada","doi":"10.3390/dynamics3020020","DOIUrl":"https://doi.org/10.3390/dynamics3020020","url":null,"abstract":"Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath (hb), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution Weq generates orthogonal (Hermite) polynomials Hn in momenta. Suitable moments Wn of W (using the Hn’s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov–Born–Green–Kirkwood–Yvon one), solved through operator continued fractions. After a long-t approximation, the Wn’s yield irreversibly approach to equilibrium. The approach is extended (without hb) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical ϕ4 field theory (without hb). The extension to one non-relativistic quantum particle (with hb) employs the non-equilibrium Wigner function (WQ): difficulties related to non-positivity of WQ are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum ϕ4 field theory (a meson gas off-equilibrium, without hb), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum ϕ4 theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical ϕ4 one, yielding an approach to equilibrium.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84695507","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}

引用次数: 0

Coexistence of Thread and Sheet Chaotic Attractors for Three-Dimensional Lozi Map 三维Lozi映射的线与片混沌吸引子共存

Dynamics (Pembroke, Ont.) Pub Date : 2023-06-09 DOI: 10.3390/dynamics3020019

R. Lozi

{"title":"Coexistence of Thread and Sheet Chaotic Attractors for Three-Dimensional Lozi Map","authors":"R. Lozi","doi":"10.3390/dynamics3020019","DOIUrl":"https://doi.org/10.3390/dynamics3020019","url":null,"abstract":"Since its original publication in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure or applied its properties in many fields (electronic devices such as memristors, A.I. with swarm intelligence, etc.). Several generalizations have been proposed, transforming the initial two-dimensional map into a multidimensional one. However, they do not respect the original constraint that allows this map to be one of the few strictly hyperbolic: a constant Jacobian. In this paper, we introduce a three-dimensional piece-wise linear extension respecting this constraint and we explore a special property never highlighted for chaotic mappings: the coexistence of thread chaotic attractors (i.e., attractors that are formed by a collection of lines) and sheet chaotic attractors (i.e., attractors that are formed by a collection of planes). This new three-dimensional mapping can generate a large variety of chaotic and hyperchaotic attractors. We give five examples of such behavior in this article. In the first three examples, there is the coexistence of thread and sheet chaotic attractors. However, their shapes are different and they are constituted by a different number of pieces. In the last two examples, the blow up of the attractors with respect to parameter a and b is highlighted.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75966803","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}

引用次数: 0

Unraveling Soft Squeezing Transformations in Time-Variant Elastic Fields 时变弹性场中的软压缩变换

Dynamics (Pembroke, Ont.) Pub Date : 2023-06-01 DOI: 10.3390/dynamics3020018

J. Fuentes

引用次数: 0

Mutual Stabilization in Chaotic Hindmarsh–Rose Neurons 混沌Hindmarsh-Rose神经元的相互稳定

Dynamics (Pembroke, Ont.) Pub Date : 2023-05-19 DOI: 10.3390/dynamics3020017

J. Parker, K. Short

{"title":"Mutual Stabilization in Chaotic Hindmarsh–Rose Neurons","authors":"J. Parker, K. Short","doi":"10.3390/dynamics3020017","DOIUrl":"https://doi.org/10.3390/dynamics3020017","url":null,"abstract":"Recent work has highlighted the vast array of dynamics possible within both neuronal networks and individual neural models. In this work, we demonstrate the capability of interacting chaotic Hindmarsh–Rose neurons to communicate and transition into periodic dynamics through specific interactions which we call mutual stabilization, despite individual units existing in chaotic parameter regimes. Mutual stabilization has been seen before in other chaotic systems but has yet to be reported in interacting neural models. The process of chaotic stabilization is similar to related previous work, where a control scheme which provides small perturbations on carefully chosen Poincaré surfaces that act as control planes stabilized a chaotic trajectory onto a cupolet. For mutual stabilization to occur, the symbolic dynamics of a cupolet are passed through an interaction function such that the output acts as a control on a second chaotic system. If chosen correctly, the second system stabilizes onto another cupolet. This process can send feedback to the first system, replacing the original control, so that in some cases the two systems are locked into persistent periodic behavior as long as the interaction continues. Here, we demonstrate how this process works in a two-cell network and then extend the results to four cells with potential generalizations to larger networks. We conclude that stabilization of different states may be linked to a type of information storage or memory.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89133882","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}

引用次数: 0

Dynamic Ramsey Theory of Mechanical Systems Forming a Complete Graph and Vibrations of Cyclic Compounds 机械系统形成完全图的动态拉姆齐理论与环状化合物的振动

Dynamics (Pembroke, Ont.) Pub Date : 2023-05-07 DOI: 10.3390/dynamics3020016

N. Shvalb, M. Frenkel, S. Shoval, E. Bormashenko

{"title":"Dynamic Ramsey Theory of Mechanical Systems Forming a Complete Graph and Vibrations of Cyclic Compounds","authors":"N. Shvalb, M. Frenkel, S. Shoval, E. Bormashenko","doi":"10.3390/dynamics3020016","DOIUrl":"https://doi.org/10.3390/dynamics3020016","url":null,"abstract":"Ramsey theory constitutes the dynamics of mechanical systems, which may be described as abstract complete graphs. We address a mechanical system which is completely interconnected by two kinds of ideal Hookean springs. The suggested system mechanically corresponds to cyclic molecules, in which functional groups are interconnected by two kinds of chemical bonds, represented mechanically with two springs k1 and k2. In this paper, we consider a cyclic system (molecule) built of six equal masses m and two kinds of springs. We pose the following question: what is the minimal number of masses in such a system in which three masses are constrained to be connected cyclically with spring k1 or three masses are constrained to be connected cyclically with spring k2? The answer to this question is supplied by the Ramsey theory, formally stated as follows: what is the minimal number R(3,3)? The result emerging from the Ramsey theory is R(3,3)=6. Thus, in the aforementioned interconnected mechanical system at least one triangle, built of masses and springs, must be present. This prediction constitutes the vibrational spectrum of the system. Thus, the Ramsey theory and symmetry considerations supply the selection rules for the vibrational spectra of the cyclic molecules. A symmetrical system built of six vibrating entities is addressed. The Ramsey approach works for 2D and 3D molecules, which may be described as abstract complete graphs. The extension of the proposed Ramsey approach to the systems, partially connected by ideal springs, viscoelastic systems and systems in which elasticity is of an entropic nature is discussed. “Multi-color systems” built of three kinds of ideal springs are addressed. The notion of the inverse Ramsey network is introduced and analyzed.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83228458","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}

引用次数: 2

Absolute Mueller Polarimeters Based on Dual-Rotating Imperfect Retarders and Arbitrary Ratio of Angular Velocities 基于双旋转不完全缓速器和任意角速度比的绝对穆勒偏振仪

Dynamics (Pembroke, Ont.) Pub Date : 2023-04-21 DOI: 10.3390/dynamics3020015

J. Gil

引用次数: 1

Nonlinear Fault-Tolerant Vibration Control for Partial Actuator Fault of a Flexible Arm 柔性臂部分作动器故障的非线性容错振动控制

Dynamics (Pembroke, Ont.) Pub Date : 2023-04-17 DOI: 10.3390/dynamics3020014

Ximei Li, Guang Jin, M. Deng

{"title":"Nonlinear Fault-Tolerant Vibration Control for Partial Actuator Fault of a Flexible Arm","authors":"Ximei Li, Guang Jin, M. Deng","doi":"10.3390/dynamics3020014","DOIUrl":"https://doi.org/10.3390/dynamics3020014","url":null,"abstract":"This paper presents a nonlinear fault-tolerant vibration control system for a flexible arm, considering partial actuator fault. A lightweight flexible arm with lower stiffness will inevitably cause vibration which will impair the performance of the high-precision control system. Therefore, an operator-based robust nonlinear vibration control system is integrated by a double-sided interactive controller actuated by the Shape Memory Alloy (SMA) actuators for the flexible arm. Furthermore, to improve the safety and reliability of the safety-critical application, fault-tolerant dynamics for partial actuator fault are considered as an essential part of the proposed control system. The experimental cases are set to the partial actuator as faulty conditions, and the proposed vibration control scheme has fault-tolerant dynamics which can still effectively stabilize the vibration displacement. The reconfigurable controller improves the fault-tolerant performance by shortening the vibration time and reducing the vibration displacement of the flexible arm. In addition, compared with a PD controller, the proposed nonlinear vibration control has better performance than the traditional controller. The experimental results show that the effectiveness of the proposed method is confirmed. That is, the safety and reliability of the proposed fault-tolerant vibration control are verified even if in the presence of an actuator fault.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77322897","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}

引用次数: 1

Uncovering the Origins of Instability in Dynamical Systems: How Can the Attention Mechanism Help? 揭示动力系统不稳定性的起源:注意机制如何起作用?

Dynamics (Pembroke, Ont.) Pub Date : 2023-04-17 DOI: 10.3390/dynamics3020013

N. Bahador, M. Lankarany

{"title":"Uncovering the Origins of Instability in Dynamical Systems: How Can the Attention Mechanism Help?","authors":"N. Bahador, M. Lankarany","doi":"10.3390/dynamics3020013","DOIUrl":"https://doi.org/10.3390/dynamics3020013","url":null,"abstract":"The behavior of the network and its stability are governed by both dynamics of the individual nodes, as well as their topological interconnections. The attention mechanism as an integral part of neural network models was initially designed for natural language processing (NLP) and, so far, has shown excellent performance in combining the dynamics of individual nodes and the coupling strengths between them within a network. Despite the undoubted impact of the attention mechanism, it is not yet clear why some nodes of a network obtain higher attention weights. To come up with more explainable solutions, we tried to look at the problem from a stability perspective. Based on stability theory, negative connections in a network can create feedback loops or other complex structures by allowing information to flow in the opposite direction. These structures play a critical role in the dynamics of a complex system and can contribute to abnormal synchronization, amplification, or suppression. We hypothesized that those nodes that are involved in organizing such structures could push the entire network into instability modes and therefore need more attention during analysis. To test this hypothesis, the attention mechanism, along with spectral and topological stability analyses, was performed on a real-world numerical problem, i.e., a linear Multi-Input Multi-Output state-space model of a piezoelectric tube actuator. The findings of our study suggest that the attention should be directed toward the collective behavior of imbalanced structures and polarity-driven structural instabilities within the network. The results demonstrated that the nodes receiving more attention cause more instability in the system. Our study provides a proof of concept to understand why perturbing some nodes of a network may cause dramatic changes in the network dynamics.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89403019","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}

引用次数: 0