Alexandre Champagne-Ruel, Sascha Zakaib-Bernier, Paul Charbonneau
Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to promote pattern formation in certain classes of systems. Formation of stable structures often serves as a key factor in promoting the emergence and persistence of cooperative behavior in otherwise competitive environments, however an in-depth analysis on the impact of diffusion on such systems is lacking. We therefore investigate the effects of diffusion on cooperative behavior using a cellular automaton (CA) model of the noisy spatial iterated prisoner's dilemma (IPD), physical extension and stochasticity being unavoidable characteristics of several natural phenomena. We further derive a mean-field (MF) model that captures the 3-species predation dynamics from the CA model and highlight how pattern formation arises in this new model, then characterize how including diffusion by interchange similarly enables the emergence of large scale structures in the CA model as well. We investigate how these emerging patterns favors cooperative behavior for parameter space regions where IPD error rates classically forbid such dynamics. We thus demonstrate how the coupling of diffusion with non-linear dynamics can, counter-intuitively, promote large scale structure formation and in return establish new grounds for cooperation to take hold in stochastic spatial systems.
从细菌的定量感应到交通流的动力学，扩散在各种现象中都扮演着重要角色。虽然扩散通常会消除梯度和不均匀性，但在某些类别的系统中，扩散仍被证明能促进模式的形成。稳定结构的形成通常是促进竞争性环境中合作行为的出现和持续的关键因素，但目前还缺乏关于扩散对此类系统影响的深入分析。因此，我们利用噪声空间囚徒困境（IPD）的细胞自动机（CA）模型来研究扩散对合作行为的影响，物理扩展和随机性是一些自然现象不可避免的特征。我们进一步推导出一个平均场（MF）模型，该模型捕捉到了 CA 模型中的 3 种捕食动态，并强调了在这个新模型中模式是如何形成的，然后描述了在 CA 模型中，通过交换扩散也能产生大规模结构。我们研究了这些新出现的模式如何有利于参数空间区域的合作行为，而这些区域的 IPD 误差率通常是禁止这种动态的。因此，我们证明了扩散与非线性动力学的耦合是如何反直觉地促进大尺度结构的形成，并反过来为随机空间系统中的合作建立新的基础。
{"title":"Diffusion and pattern formation in spatial games","authors":"Alexandre Champagne-Ruel, Sascha Zakaib-Bernier, Paul Charbonneau","doi":"arxiv-2407.02385","DOIUrl":"https://doi.org/arxiv-2407.02385","url":null,"abstract":"Diffusion plays an important role in a wide variety of phenomena, from\u0000bacterial quorum sensing to the dynamics of traffic flow. While it generally\u0000tends to level out gradients and inhomogeneities, diffusion has nonetheless\u0000been shown to promote pattern formation in certain classes of systems.\u0000Formation of stable structures often serves as a key factor in promoting the\u0000emergence and persistence of cooperative behavior in otherwise competitive\u0000environments, however an in-depth analysis on the impact of diffusion on such\u0000systems is lacking. We therefore investigate the effects of diffusion on\u0000cooperative behavior using a cellular automaton (CA) model of the noisy spatial\u0000iterated prisoner's dilemma (IPD), physical extension and stochasticity being\u0000unavoidable characteristics of several natural phenomena. We further derive a\u0000mean-field (MF) model that captures the 3-species predation dynamics from the\u0000CA model and highlight how pattern formation arises in this new model, then\u0000characterize how including diffusion by interchange similarly enables the\u0000emergence of large scale structures in the CA model as well. We investigate how\u0000these emerging patterns favors cooperative behavior for parameter space regions\u0000where IPD error rates classically forbid such dynamics. We thus demonstrate how\u0000the coupling of diffusion with non-linear dynamics can, counter-intuitively,\u0000promote large scale structure formation and in return establish new grounds for\u0000cooperation to take hold in stochastic spatial systems.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532436","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}
O. Pavón-Torres, M. A. Agüero-Granados, R. Valencia-Torres
The Heimburg-Jackson model, or thermodynamic soliton theory of nervous impulses, has a well-established record as an alternative model for studying the dynamics of nerve impulses and lipid bilayers. Within this framework, nerve impulses can be represented as nonlinear excitations of low amplitude depicted by the damped nonlinear Schr"odinger equation and their adiabatic evolution can be analyzed using direct perturbative methods. Based on the foregoing, we carry out the current study using the quasi-stationary approach to obtain the adiabatic evolution of solitons embedded in lipid bilayers under the influence of a viscous elastic fluid. This analysis encompasses liquid-to-gel transition of the lipid bilayers, for whose dark and bright solitons arise, respectively.
{"title":"Adiabatic evolution of solitons embedded on lipid membranes","authors":"O. Pavón-Torres, M. A. Agüero-Granados, R. Valencia-Torres","doi":"arxiv-2407.00601","DOIUrl":"https://doi.org/arxiv-2407.00601","url":null,"abstract":"The Heimburg-Jackson model, or thermodynamic soliton theory of nervous\u0000impulses, has a well-established record as an alternative model for studying\u0000the dynamics of nerve impulses and lipid bilayers. Within this framework, nerve\u0000impulses can be represented as nonlinear excitations of low amplitude depicted\u0000by the damped nonlinear Schr\"odinger equation and their adiabatic evolution\u0000can be analyzed using direct perturbative methods. Based on the foregoing, we\u0000carry out the current study using the quasi-stationary approach to obtain the\u0000adiabatic evolution of solitons embedded in lipid bilayers under the influence\u0000of a viscous elastic fluid. This analysis encompasses liquid-to-gel transition\u0000of the lipid bilayers, for whose dark and bright solitons arise, respectively.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530072","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}
The Ivancevic option pricing model is studied via variational approach. Both the Gaussian anstz and the (sech ansatz are used, and each has a unique results from one another. But in terms of existance of soliton solutions they both agree that hot market temperatures support the existance of soliton solutions.
{"title":"Variational approach to nonlinear pulse evolution in stock derivative markets","authors":"Christopher Gaafele","doi":"arxiv-2407.00554","DOIUrl":"https://doi.org/arxiv-2407.00554","url":null,"abstract":"The Ivancevic option pricing model is studied via variational approach. Both\u0000the Gaussian anstz and the (sech ansatz are used, and each has a unique results\u0000from one another. But in terms of existance of soliton solutions they both\u0000agree that hot market temperatures support the existance of soliton solutions.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"321 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509590","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}
The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary waves in the different areas of physics. Using both the slowly varying envelope approximation and the generalized perturbation reduction method, the generalized equation is transformed into the coupled nonlinear Schrodinger equations and the two-component nonlinear solitary wave solution is obtained. Explicit analytical expressions for the shape and parameters of two-component nonlinear wave consisting of two breathers oscillating with the sum and difference frequencies and wave numbers are presented. The solution of the generalized equation coincides with the vector 0pi pulse of the self-induced transparency.
{"title":"Two-component nonlinear waves","authors":"G. T. Adamashvili","doi":"arxiv-2407.00112","DOIUrl":"https://doi.org/arxiv-2407.00112","url":null,"abstract":"The generalized equation for the study of two-component nonlinear waves in\u0000different fields of physics is considered. In special cases, this equation is\u0000reduced to a set of the various well-known equations describing nonlinear\u0000solitary waves in the different areas of physics. Using both the slowly varying\u0000envelope approximation and the generalized perturbation reduction method, the\u0000generalized equation is transformed into the coupled nonlinear Schrodinger\u0000equations and the two-component nonlinear solitary wave solution is obtained.\u0000Explicit analytical expressions for the shape and parameters of two-component\u0000nonlinear wave consisting of two breathers oscillating with the sum and\u0000difference frequencies and wave numbers are presented. The solution of the\u0000generalized equation coincides with the vector 0pi pulse of the self-induced\u0000transparency.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509591","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 tricritical point as a crossover between (stationary finite-wavelength) type-I$_s$ and (stationary longwave) type-II$_s$ bifurcations is identified in the study of diffusive-thermal (Turing) instability of flames propagating in a Hele-Shaw channel in a direction transverse to a shear flow. Three regimes exhibiting different scaling laws are identified in the neighbourhood of the tricritical point. For these three regimes, sixth-order partial differential equations are obtained governing the weakly nonlinear evolution of unstable solutions near the onset of instability. These sixth-order PDES may be regarded as the substitute for the classical fourth-order Kuramoto--Sivashinsky equation which is not applicable near the tricritical point.
{"title":"Tricritical point as a crossover between type-I$_s$ and type-II$_s$ bifurcations","authors":"Prabakaran Rajamanickam, Joel Daou","doi":"arxiv-2407.00109","DOIUrl":"https://doi.org/arxiv-2407.00109","url":null,"abstract":"A tricritical point as a crossover between (stationary finite-wavelength)\u0000type-I$_s$ and (stationary longwave) type-II$_s$ bifurcations is identified in\u0000the study of diffusive-thermal (Turing) instability of flames propagating in a\u0000Hele-Shaw channel in a direction transverse to a shear flow. Three regimes\u0000exhibiting different scaling laws are identified in the neighbourhood of the\u0000tricritical point. For these three regimes, sixth-order partial differential\u0000equations are obtained governing the weakly nonlinear evolution of unstable\u0000solutions near the onset of instability. These sixth-order PDES may be regarded\u0000as the substitute for the classical fourth-order Kuramoto--Sivashinsky equation\u0000which is not applicable near the tricritical point.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532605","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 tricritical point as a crossover between (stationary finite-wavelength) type-I$_s$ and (stationary longwave) type-II$_s$ bifurcations is identified in the study of diffusive-thermal (Turing) instability of flames propagating in a Hele-Shaw channel in a direction transverse to a shear flow. Three regimes exhibiting different scaling laws are identified in the neighbourhood of the tricritical point. For these three regimes, sixth-order partial differential equations are obtained governing the weakly nonlinear evolution of unstable solutions near the onset of instability. These sixth-order PDES may be regarded as the substitute for the classical fourth-order Kuramoto--Sivashinsky equation which is not applicable near the tricritical point.
{"title":"Tricritical point as a crossover between type-I$_s$ and type-II$_s$ bifurcations","authors":"Prabakaran Rajamanickam, Joel Daou","doi":"arxiv-2407.00109","DOIUrl":"https://doi.org/arxiv-2407.00109","url":null,"abstract":"A tricritical point as a crossover between (stationary finite-wavelength)\u0000type-I$_s$ and (stationary longwave) type-II$_s$ bifurcations is identified in\u0000the study of diffusive-thermal (Turing) instability of flames propagating in a\u0000Hele-Shaw channel in a direction transverse to a shear flow. Three regimes\u0000exhibiting different scaling laws are identified in the neighbourhood of the\u0000tricritical point. For these three regimes, sixth-order partial differential\u0000equations are obtained governing the weakly nonlinear evolution of unstable\u0000solutions near the onset of instability. These sixth-order PDES may be regarded\u0000as the substitute for the classical fourth-order Kuramoto--Sivashinsky equation\u0000which is not applicable near the tricritical point.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532437","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}
We study the existence of BPS configurations in a restricted baby Skyrme-Maxwell enlarged via the inclusion of a nontrivial magnetic permeability. In order to attain such a goal, we use the Bogomol'nyi-Prasad-Sommerfield prescription, which allows us to obtain the lower bound for the energy and the BPS equations whose [electrically neutral] solutions saturate that bound. During the energy minimization procedure, we find a differential constraint which involves the self-dual potential, the superpotential itself and also the magnetic permeability. In order to solve the BPS system, we focus our attention on those solutions with rotational symmetry. For that, we fix the magnetic permeability and select two BPS potentials which exhibit a similar behavior near to the vacuum. We depict the resulting profiles and proceed to an analytical description of the properties of the BPS magnetic field. Furthermore, we consider some essential aspects of our model, such as the conditions for the overall existence of the BPS solutions, and how the permeability affects the magnetic flux. Finally, we present a family of exact BPS solutions.
{"title":"Restricted baby Skyrme-Maxwell theory in a magnetic medium: BPS configurations and some properties","authors":"J. Andrade, R. Casana, E. da Hora, A. C. Santos","doi":"arxiv-2406.18357","DOIUrl":"https://doi.org/arxiv-2406.18357","url":null,"abstract":"We study the existence of BPS configurations in a restricted baby\u0000Skyrme-Maxwell enlarged via the inclusion of a nontrivial magnetic\u0000permeability. In order to attain such a goal, we use the\u0000Bogomol'nyi-Prasad-Sommerfield prescription, which allows us to obtain the\u0000lower bound for the energy and the BPS equations whose [electrically neutral]\u0000solutions saturate that bound. During the energy minimization procedure, we\u0000find a differential constraint which involves the self-dual potential, the\u0000superpotential itself and also the magnetic permeability. In order to solve the\u0000BPS system, we focus our attention on those solutions with rotational symmetry.\u0000For that, we fix the magnetic permeability and select two BPS potentials which\u0000exhibit a similar behavior near to the vacuum. We depict the resulting profiles\u0000and proceed to an analytical description of the properties of the BPS magnetic\u0000field. Furthermore, we consider some essential aspects of our model, such as\u0000the conditions for the overall existence of the BPS solutions, and how the\u0000permeability affects the magnetic flux. Finally, we present a family of exact\u0000BPS solutions.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"198 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509597","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}
We study the dynamics of fundamental and vortex solitons in the framework of the nonlinear Schr"{o}dinger equation with the spatial dimension $Dgeqslant 2$ with a multiplicative random term depending on the time and space coordinates. To this end, we develop a new technique for calculating the even moments of the $N$th order. The proposed formalism does not use closure procedures for the nonlinear term, as well as the smallness of the random term and the use of perturbation theory. The essential point is the quadratic form of the autocorrelation function of the random field and the special stochastic change of variables. Using variational analysis to determine the field of structures in the deterministic case, we analytically calculate a number of statistical characteristics describing the dynamics of fundamental and vortex solitons in random medium, such as the mean intensities, the variance of the intensity, the centroid and spread of the structures, the spatial mutual coherence function etc. In particular, we show that, under the irreversible action of fluctuations, the solitons spread out, i.e., no collapse occurs.
{"title":"Dynamics of multidimensional fundamental and vortex solitons in random media","authors":"Volodymyr M. Lashkin","doi":"arxiv-2406.17939","DOIUrl":"https://doi.org/arxiv-2406.17939","url":null,"abstract":"We study the dynamics of fundamental and vortex solitons in the framework of\u0000the nonlinear Schr\"{o}dinger equation with the spatial dimension $Dgeqslant\u00002$ with a multiplicative random term depending on the time and space\u0000coordinates. To this end, we develop a new technique for calculating the even\u0000moments of the $N$th order. The proposed formalism does not use closure\u0000procedures for the nonlinear term, as well as the smallness of the random term\u0000and the use of perturbation theory. The essential point is the quadratic form\u0000of the autocorrelation function of the random field and the special stochastic\u0000change of variables. Using variational analysis to determine the field of\u0000structures in the deterministic case, we analytically calculate a number of\u0000statistical characteristics describing the dynamics of fundamental and vortex\u0000solitons in random medium, such as the mean intensities, the variance of the\u0000intensity, the centroid and spread of the structures, the spatial mutual\u0000coherence function etc. In particular, we show that, under the irreversible\u0000action of fluctuations, the solitons spread out, i.e., no collapse occurs.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509592","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}
Turing instability in complex networks have been shown in the literature to be dominated by the distribution of the nodal degrees. The conditions for Turing instability have been derived with an explicit dependence on the eigenvalues of the Laplacian, which in turn depends on the network topology. This study reveals that apart from average degree of the network, another global network measure - the nodal clustering - also plays a crucial role. Analytical and numerical results are presented to show the importance of clustering for several network topologies ranging from the $mathbb{S}^1$ / $mathbb{H}^2$ hyperbolic geometric networks that enable modelling the naturally occurring clustering in real world networks, as well as the random and scale free networks, which are obtained as limiting cases of the $mathbb{S}^1$ / $mathbb{H}^2$ model. Analysis of eigenvector localization properties in these networks are shown to reveal distinct signatures that enable identifying the so called Turing patterns even in complex networks.
{"title":"Effect of clustering on Turing instability in complex networks","authors":"Samana Pranesh, Devanand Jaiswal, Sayan Gupta","doi":"arxiv-2406.17440","DOIUrl":"https://doi.org/arxiv-2406.17440","url":null,"abstract":"Turing instability in complex networks have been shown in the literature to\u0000be dominated by the distribution of the nodal degrees. The conditions for\u0000Turing instability have been derived with an explicit dependence on the\u0000eigenvalues of the Laplacian, which in turn depends on the network topology.\u0000This study reveals that apart from average degree of the network, another\u0000global network measure - the nodal clustering - also plays a crucial role.\u0000Analytical and numerical results are presented to show the importance of\u0000clustering for several network topologies ranging from the $mathbb{S}^1$ /\u0000$mathbb{H}^2$ hyperbolic geometric networks that enable modelling the\u0000naturally occurring clustering in real world networks, as well as the random\u0000and scale free networks, which are obtained as limiting cases of the\u0000$mathbb{S}^1$ / $mathbb{H}^2$ model. Analysis of eigenvector localization\u0000properties in these networks are shown to reveal distinct signatures that\u0000enable identifying the so called Turing patterns even in complex networks.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509593","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}
F. Zhu, B. Wu, M. Destrade, H. Wang, R. Bao, W. Chen
Material properties of soft electro-active (SEA) structures are significantly sensitive to external electro-mechanical biasing fields (such as pre-stretch and electric stimuli), which generate remarkable knock-on effects on their dynamic characteristics. In this work, we analyze the electrostatically tunable non-axisymmetric vibrations of an incompressible SEA cylindrical tube under the combination of a radially applied electric voltage and an axial pre-stretch. Following the theory of nonlinear electro-elasticity and the associated linearized theory for superimposed perturbations, we derive the nonlinear static response of the SEA tube to the inhomogeneous biasing fields for the Gent ideal dielectric model. Using the State Space Method, we efficiently obtain the frequency equations for voltage-controlled small-amplitude three-dimensional non-axisymmetric vibrations, covering a wide range of behaviors, from the purely radial breathing mode to torsional modes, axisymmetric longitudinal modes, and prismatic diffuse modes. We also perform an exhaustive numerical analysis to validate the proposed approach compared with the conventional displacement method, as well as to elucidate the influences of the applied voltage, axial pre-stretch, and strain-stiffening effect on the nonlinear static response and vibration behaviors of the SEA tube. The present study clearly indicates that manipulating electro-mechanical biasing fields is a feasible way to tune the small-amplitude vibration characteristics of an SEA tube. The results should benefit experimental work on, and design of, voltage-controlled resonant devices made of SEA tubes.
{"title":"Voltage-controlled non-axisymmetric vibrations of soft electro-active tubes with strain-stiffening effect","authors":"F. Zhu, B. Wu, M. Destrade, H. Wang, R. Bao, W. Chen","doi":"arxiv-2406.13483","DOIUrl":"https://doi.org/arxiv-2406.13483","url":null,"abstract":"Material properties of soft electro-active (SEA) structures are significantly\u0000sensitive to external electro-mechanical biasing fields (such as pre-stretch\u0000and electric stimuli), which generate remarkable knock-on effects on their\u0000dynamic characteristics. In this work, we analyze the electrostatically tunable\u0000non-axisymmetric vibrations of an incompressible SEA cylindrical tube under the\u0000combination of a radially applied electric voltage and an axial pre-stretch.\u0000Following the theory of nonlinear electro-elasticity and the associated\u0000linearized theory for superimposed perturbations, we derive the nonlinear\u0000static response of the SEA tube to the inhomogeneous biasing fields for the\u0000Gent ideal dielectric model. Using the State Space Method, we efficiently\u0000obtain the frequency equations for voltage-controlled small-amplitude\u0000three-dimensional non-axisymmetric vibrations, covering a wide range of\u0000behaviors, from the purely radial breathing mode to torsional modes,\u0000axisymmetric longitudinal modes, and prismatic diffuse modes. We also perform\u0000an exhaustive numerical analysis to validate the proposed approach compared\u0000with the conventional displacement method, as well as to elucidate the\u0000influences of the applied voltage, axial pre-stretch, and strain-stiffening\u0000effect on the nonlinear static response and vibration behaviors of the SEA\u0000tube. The present study clearly indicates that manipulating electro-mechanical\u0000biasing fields is a feasible way to tune the small-amplitude vibration\u0000characteristics of an SEA tube. The results should benefit experimental work\u0000on, and design of, voltage-controlled resonant devices made of SEA tubes.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509596","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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