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Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction 动摩擦预滑动瞬态的能量耗散和迟滞循环
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2023-11-08 DOI: 10.21136/AM.2023.0283-22
Michael Ruderman
{"title":"Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction","authors":"Michael Ruderman","doi":"10.21136/AM.2023.0283-22","DOIUrl":"10.21136/AM.2023.0283-22","url":null,"abstract":"<div><p>The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In this paper, we discuss the energy dissipation and convergence during the pre-sliding cycles and show how a piecewise smooth force-displacement hysteresis map enters into the energy balance of an unforced system of the second order. An existing friction modeling approach with a low number of the free parameters, the Dahl model, is then exemplified alongside the developed analysis.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"68 6","pages":"845 - 860"},"PeriodicalIF":0.7,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2023.0283-22.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A continuum of path-dependent equilibrium solutions induced by sticky expectations 由粘性期望引起的路径依赖均衡解的连续体
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2023-11-06 DOI: 10.21136/AM.2023.0229-22
Pavel Krejčí, Eyram Kwame, Harbir Lamba, Dmitrii Rachinskii, Andrei Zagvozdkin
{"title":"A continuum of path-dependent equilibrium solutions induced by sticky expectations","authors":"Pavel Krejčí,&nbsp;Eyram Kwame,&nbsp;Harbir Lamba,&nbsp;Dmitrii Rachinskii,&nbsp;Andrei Zagvozdkin","doi":"10.21136/AM.2023.0229-22","DOIUrl":"10.21136/AM.2023.0229-22","url":null,"abstract":"<div><p>We analyze a simple macroeconomic model where rational inflation expectations are replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation rate. The stickiness is introduced in a novel way using a mathematical operator that is amenable to rigorous analysis. We prove that, when exogenous noise is absent from the system, the unique equilibrium of the rational expectations model is replaced by an entire line segment of possible equilibria with the one chosen depending, in a deterministic way, upon the previous states of the system. The agents are sufficiently far-removed from the rational expectations paradigm that problems of indeterminacy do not arise.</p><p>The response to exogenous noise is far more subtle than in a unique equilibrium model. After sufficiently small shocks the system will indeed revert to the same equilibrium but larger ones will move the system to a different one (at the same model parameters). The path to this new equilibrium may be very long with a highly unpredictable endpoint. At certain model parameters exogenously-triggered runaway inflation can occur.</p><p>Finally, we analyze a variant model in which the same form of sticky response is introduced into the interest rate rule instead.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"68 6","pages":"751 - 793"},"PeriodicalIF":0.7,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135544675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the stability analysis of Darboux problem on both bounded and unbounded domains 关于达尔布问题在有界域和无界域上的稳定性分析
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2023-11-03 DOI: 10.21136/AM.2023.0200-22
Canan Çelik, Faruk Develi
{"title":"On the stability analysis of Darboux problem on both bounded and unbounded domains","authors":"Canan Çelik,&nbsp;Faruk Develi","doi":"10.21136/AM.2023.0200-22","DOIUrl":"10.21136/AM.2023.0200-22","url":null,"abstract":"<div><p>In this paper, we first investigate the existence and uniqueness of solution for the Darboux problem with modified argument on both bounded and unbounded domains. Then, we derive different types of the Ulam stability for the proposed problem on these domains. Finally, we present some illustrative examples to support our results.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"139 - 150"},"PeriodicalIF":0.6,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Continuity of the non-convex play operator in the space of rectifiable curves 非凸游戏算子在可整流曲线空间中的连续性
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2023-10-25 DOI: 10.21136/AM.2023.0257-22
Jana Kopfová, Vincenzo Recupero
{"title":"Continuity of the non-convex play operator in the space of rectifiable curves","authors":"Jana Kopfová,&nbsp;Vincenzo Recupero","doi":"10.21136/AM.2023.0257-22","DOIUrl":"10.21136/AM.2023.0257-22","url":null,"abstract":"<div><p>We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the <i>BV</i>-norm and to the <i>BV</i>-strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"68 6","pages":"727 - 750"},"PeriodicalIF":0.7,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2023.0257-22.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134973800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On forward and inverse uncertainty quantification for a model for a magneto mechanical device involving a hysteresis operator 含磁滞算子的磁机械装置模型的正、逆不确定性量化
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2023-10-12 DOI: 10.21136/AM.2023.0080-23
Olaf Klein
{"title":"On forward and inverse uncertainty quantification for a model for a magneto mechanical device involving a hysteresis operator","authors":"Olaf Klein","doi":"10.21136/AM.2023.0080-23","DOIUrl":"10.21136/AM.2023.0080-23","url":null,"abstract":"<div><p>Modeling real world objects and processes one may have to deal with hysteresis effects but also with uncertainties. Following D. Davino, P. Krejčí, and C. Visone (2013), a model for a magnetostrictive material involving a generalized Prandtl-Islilinskiĭ-operator is considered here.</p><p>Using results of measurements, some parameters in the model are determined and inverse Uncertainty Quantification (UQ) is used to determine random densities to describe the remaining parameters and their uncertainties. Afterwards, the results are used to perform forward UQ and to compare the generated outputs with measured data. This extends some of the results from O. Klein, D. Davino, and C. Visone (2020).</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"68 6","pages":"795 - 828"},"PeriodicalIF":0.7,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2023.0080-23.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135968013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Anisotropic viscoelastic body subjected to the pulsating load 受脉动载荷作用的各向异性粘弹性体
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2023-09-14 DOI: 10.21136/AM.2023.0256-22
Jozef Sumec, Mária Minárová, L’uboš Hruštinec
{"title":"Anisotropic viscoelastic body subjected to the pulsating load","authors":"Jozef Sumec,&nbsp;Mária Minárová,&nbsp;L’uboš Hruštinec","doi":"10.21136/AM.2023.0256-22","DOIUrl":"10.21136/AM.2023.0256-22","url":null,"abstract":"<div><p>Constitutive equations of continuum mechanics of the solid phase of anisotropic material is focused in the paper. First, a synoptic one-dimensional Maxwell model is explored, subjected to arbitrary deformation load. The explicit form is derived for stress on strain dependence. Further, the analogous explicit constitutive equation is taken in three spatial dimensions and treated mathematically. Later on, a simply supported straight concrete beam reinforced by the steel fibres is taken as an investigated domain. The reinforcement is considered and dealt as scattered within the beam. Material characteristics are determined in line with the theory of the reinforcement. Sinusoidal load is taken as the action, stress reaction function is observed. By exploitation of the Fourier transform within the stress-strain relation analysis, both time and frequency interpretation of the constitutive relation can be performed.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"68 6","pages":"829 - 844"},"PeriodicalIF":0.7,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134912083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inexact Newton-type method for solving large-scale absolute value equation Ax − |x| = b 求解大规模绝对值方程 Ax - |x| = b 的非精确牛顿式方法
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2023-08-31 DOI: 10.21136/AM.2023.0171-22
Jingyong Tang
{"title":"Inexact Newton-type method for solving large-scale absolute value equation Ax − |x| = b","authors":"Jingyong Tang","doi":"10.21136/AM.2023.0171-22","DOIUrl":"10.21136/AM.2023.0171-22","url":null,"abstract":"<div><p>Newton-type methods have been successfully applied to solve the absolute value equation <i>Ax</i> − |<i>x</i>| = <i>b</i> (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line search technique, which is well-defined and easy to implement. We prove that the proposed method has global and local superlinear convergence under the condition that the interval matrix [<i>A</i> − <i>I</i>, <i>A</i> + <i>I</i>] is regular. This condition is much weaker than those used in some Newton-type methods. Numerical results show that our method has fairly good practical efficiency for solving large-scale AVEs.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"49 - 66"},"PeriodicalIF":0.6,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90644064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory 用特罗特理论对具有诺顿或特雷斯卡摩擦的非线性开尔文-沃依格粘弹性薄板的瞬态响应进行渐近建模
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2023-07-21 DOI: 10.21136/AM.2023.0013-23
Yotsawat Terapabkajornded, Somsak Orankitjaroen, Christian Licht, Thibaut Weller
{"title":"Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory","authors":"Yotsawat Terapabkajornded,&nbsp;Somsak Orankitjaroen,&nbsp;Christian Licht,&nbsp;Thibaut Weller","doi":"10.21136/AM.2023.0013-23","DOIUrl":"10.21136/AM.2023.0013-23","url":null,"abstract":"<div><p>We study the dynamic response of a thin viscoelastic plate made of a nonlinear Kelvin-Voigt material in bilateral contact with a rigid body along a part of its lateral boundary with Norton or Tresca friction. We opt for a direct use of the Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the various relative behaviors of the physical and geometrical data of the problem, the asymptotic analysis of its unique solution leads to different limit models whose properties are detailed. We highlight the appearance of an additional state variable that allows us to write these limit systems of equations in the same form as the genuine problem.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"25 - 48"},"PeriodicalIF":0.6,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74216655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse rate-dependent Prandtl-Ishlinskii operators and applications 逆速率相关Prandtl-Ishlinskii算子及其应用
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2023-02-09 DOI: 10.21136/AM.2023.0231-22
Mohammad Al Janaideh, Pavel Krejčí, Giselle Antunes Monteiro
{"title":"Inverse rate-dependent Prandtl-Ishlinskii operators and applications","authors":"Mohammad Al Janaideh,&nbsp;Pavel Krejčí,&nbsp;Giselle Antunes Monteiro","doi":"10.21136/AM.2023.0231-22","DOIUrl":"10.21136/AM.2023.0231-22","url":null,"abstract":"<div><p>In the past years, we observed an increased interest in rate-dependent hysteresis models to characterize complex time-dependent nonlinearities in smart actuators. A natural way to include rate-dependence to the Prandtl-Ishlinskii model is to consider it as a linear combination of play operators whose thresholds are functions of time. In this work, we propose the extension of the class of rate-dependent Prandtl-Ishlinskii operators to the case of a whole continuum of play operators with time-dependent thresholds. We prove the existence of an analytical inversion formula, and illustrate its applicability in the study of error bounds for inverse compensation.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"68 6","pages":"713 - 726"},"PeriodicalIF":0.7,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82505233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact controllability of linear dynamical systems: A geometrical approach 线性动力系统的精确可控性:一种几何方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2016-01-01 DOI: 10.21136/AM.2016.0427-15
M. García-Planas
{"title":"Exact controllability of linear dynamical systems: A geometrical approach","authors":"M. García-Planas","doi":"10.21136/AM.2016.0427-15","DOIUrl":"https://doi.org/10.21136/AM.2016.0427-15","url":null,"abstract":"In recent years there has been growing interest in the descriptive analysis of complex systems, permeating many aspects of daily life, obtaining considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems it is of interest to study the exact controllability; this measure is defined as the minimum set of controls that are needed in order to steer the whole system toward any desired state. In this paper, we focus the study on the obtention of the set of all B making the system (A, B) exact controllable.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"15 1","pages":"1-11"},"PeriodicalIF":0.7,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75302587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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