In biology, economics, sociology as well as other fields, there is often a 2×2×2 asymmetric evolutionary game problem in which each party has a set of strategies, and different strategy combinations correspond to the specific pay-offs of each party. Since each participant dynamically adjusts the strategy for maximizing their own interests, the pay-off matrix plays an important role in the evolution of the game system. Based on the pay-off matrix, we probe into the resulting state of 2×2×2 asymmetric evolutionary games. The results show that from the information of the pay-off matrix, the judgement conditions for the system to evolve into three pure strategies, two pure strategies and one pure strategy can be determined directly. What is more, under a certain type of fixed pay-off matrix, the strategy combinations observed at different evolution times is always varying. Here, we explore the connection between the pay-off matrix and the evolution of behaviours through stability theory, and results obtained are conducive to deeply understand and predict the dynamic evolution of behaviour in game systems.
{"title":"Stability analysis of evolutionary dynamics of 2 × 2 × 2 asymmetric games","authors":"Shan Song, Q. Pan, Xubin Gao, Mingfeng He","doi":"10.1098/rspa.2023.0478","DOIUrl":"https://doi.org/10.1098/rspa.2023.0478","url":null,"abstract":"In biology, economics, sociology as well as other fields, there is often a 2×2×2 asymmetric evolutionary game problem in which each party has a set of strategies, and different strategy combinations correspond to the specific pay-offs of each party. Since each participant dynamically adjusts the strategy for maximizing their own interests, the pay-off matrix plays an important role in the evolution of the game system. Based on the pay-off matrix, we probe into the resulting state of 2×2×2 asymmetric evolutionary games. The results show that from the information of the pay-off matrix, the judgement conditions for the system to evolve into three pure strategies, two pure strategies and one pure strategy can be determined directly. What is more, under a certain type of fixed pay-off matrix, the strategy combinations observed at different evolution times is always varying. Here, we explore the connection between the pay-off matrix and the evolution of behaviours through stability theory, and results obtained are conducive to deeply understand and predict the dynamic evolution of behaviour in game systems.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"139 46","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139537565","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 equations governing the simple shear deformation of an incompressible inelastic material undergoing finite strain are derived in this paper. The constitutive assumptions are kept in their most general form to allow the incorporation of widely used viscoplastic or viscoelastic models from the literature. It is shown that, while for a hyperelastic material the simple shear problem is completely determined by a single parameter, the amount of shear, in the viscoplastic case, the elastic deformation is the superposition of a triaxial stretch and a simple shear, whose determination requires the solution of three coupled nonlinear evolution equations. We evaluate such a solution for different material models and compare it with three-dimensional finite element simulations to assess its accuracy. We further assess the performance of these models using experimental data from filled rubber, focusing on their ability to capture the observed behaviour, such as the well-known Payne effect. Additionally, we extend our simple shear solution to address torsion and the extension of thin-walled cylinders. These derivations and analyses offer valuable insights for experimentalists engaged in the mechanical characterization of soft materials.
{"title":"Viscoplastic simple shear at finite strains","authors":"F. Califano, J. Ciambella","doi":"10.1098/rspa.2023.0603","DOIUrl":"https://doi.org/10.1098/rspa.2023.0603","url":null,"abstract":"The equations governing the simple shear deformation of an incompressible inelastic material undergoing finite strain are derived in this paper. The constitutive assumptions are kept in their most general form to allow the incorporation of widely used viscoplastic or viscoelastic models from the literature. It is shown that, while for a hyperelastic material the simple shear problem is completely determined by a single parameter, the amount of shear, in the viscoplastic case, the elastic deformation is the superposition of a triaxial stretch and a simple shear, whose determination requires the solution of three coupled nonlinear evolution equations. We evaluate such a solution for different material models and compare it with three-dimensional finite element simulations to assess its accuracy. We further assess the performance of these models using experimental data from filled rubber, focusing on their ability to capture the observed behaviour, such as the well-known Payne effect. Additionally, we extend our simple shear solution to address torsion and the extension of thin-walled cylinders. These derivations and analyses offer valuable insights for experimentalists engaged in the mechanical characterization of soft materials.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139187822","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 classical Painlevé paradox consists of a slender rigid rod slipping on a rigid rough surface. If the coefficient of friction μ is high enough, the governing equations predict that the rod would be driven into the surface. The paradox is well studied in two dimensions, in which the paradox is resolved via regularization, where the rod tip meets the surface. In this paper, we consider the three-dimensional problem. There are two significant differences in three dimensions. Firstly, sticking now occurs on a co-dimension 2 surface. This results in a non-smooth problem, even when the three-dimensional problem is regularized. Secondly, unlike the highly singular two-dimensional problem, trajectories can now enter the inconsistent region from slipping, requiring a completely new analysis. We use blowup to investigate the problem and show that a key part of the dynamics of the regularized three-dimensional Painlevé problem is governed by a type I Painlevé equation.
经典的潘列维悖论包括一根细长的刚性杆在刚性粗糙表面上滑动。如果摩擦系数 μ 足够大，根据控制方程的预测，杆将被推入表面。这一悖论在二维空间中得到了很好的研究，在二维空间中，悖论通过正则化得到了解决，杆尖与表面相遇。本文考虑的是三维问题。三维问题有两个重大区别。首先，粘滞现在发生在共维 2 表面上。这导致了一个非光滑问题，即使三维问题经过正则化处理也是如此。其次，与高度奇异的二维问题不同，轨迹现在可以从滑动进入不一致区域，这需要全新的分析。我们利用吹胀来研究这个问题，结果表明正则化三维潘列维问题的动力学的一个关键部分受 I 型潘列维方程的支配。
{"title":"The Painlevé paradox in three dimensions: resolution with regularization","authors":"N. Cheesman, S. Hogan, K. Uldall Kristiansen","doi":"10.1098/rspa.2023.0419","DOIUrl":"https://doi.org/10.1098/rspa.2023.0419","url":null,"abstract":"The classical Painlevé paradox consists of a slender rigid rod slipping on a rigid rough surface. If the coefficient of friction μ is high enough, the governing equations predict that the rod would be driven into the surface. The paradox is well studied in two dimensions, in which the paradox is resolved via regularization, where the rod tip meets the surface. In this paper, we consider the three-dimensional problem. There are two significant differences in three dimensions. Firstly, sticking now occurs on a co-dimension 2 surface. This results in a non-smooth problem, even when the three-dimensional problem is regularized. Secondly, unlike the highly singular two-dimensional problem, trajectories can now enter the inconsistent region from slipping, requiring a completely new analysis. We use blowup to investigate the problem and show that a key part of the dynamics of the regularized three-dimensional Painlevé problem is governed by a type I Painlevé equation.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139189322","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}
Dorsa Nezhad Hajian, Fatemeh Parastesh, K. Rajagopal, S. Jafari, M. Perc, Eva Klemenčič
We study the emergence of meandering spiral waves in a multilayer structure where two spirals, originating independently, evolve in space–time. The FitzHugh-Nagumo model, enhanced with electromagnetic induction effects, defines the nodal dynamics. The layers are chemically coupled, and the drift of spirals is influenced by interlayer flux coupling. An external magnetic flux force is also necessary to destabilize and unpin spiral rotors. The effects of unique characteristics of spiral patterns, like chirality and tip curvature, are assessed. We find that spirals often drift within a bounded meandering area; however, determining the drift directions and overall meandering regions is complex. The forced spiral generally drifts a greater distance, except for identical co-rotating spirals, which drift synchronously. Spirals with opposite chirality exhibit asynchronous drift and wavefront asymmetry, even with identical tip curvature. Regardless of chirality, non-identical spirals are geometrically aligned and amplified before drifting. Stimulating the more loosely curved spiral ensures both spirals drift.
{"title":"Chirality and curvature determine the meandering of spirals in multilayer excitable media","authors":"Dorsa Nezhad Hajian, Fatemeh Parastesh, K. Rajagopal, S. Jafari, M. Perc, Eva Klemenčič","doi":"10.1098/rspa.2023.0730","DOIUrl":"https://doi.org/10.1098/rspa.2023.0730","url":null,"abstract":"We study the emergence of meandering spiral waves in a multilayer structure where two spirals, originating independently, evolve in space–time. The FitzHugh-Nagumo model, enhanced with electromagnetic induction effects, defines the nodal dynamics. The layers are chemically coupled, and the drift of spirals is influenced by interlayer flux coupling. An external magnetic flux force is also necessary to destabilize and unpin spiral rotors. The effects of unique characteristics of spiral patterns, like chirality and tip curvature, are assessed. We find that spirals often drift within a bounded meandering area; however, determining the drift directions and overall meandering regions is complex. The forced spiral generally drifts a greater distance, except for identical co-rotating spirals, which drift synchronously. Spirals with opposite chirality exhibit asynchronous drift and wavefront asymmetry, even with identical tip curvature. Regardless of chirality, non-identical spirals are geometrically aligned and amplified before drifting. Stimulating the more loosely curved spiral ensures both spirals drift.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"29 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139190507","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 modified active disturbance rejection control (ADRC) strategy for the frequency regulation of sustainable microgrid against hybrid cyber-attacks is proposed in this paper. The proposed technique mitigates the effect of attacks which in turn regulates the frequency of microgrid. The sustainable microgrid consists of solar and wind as renewable energy sources, energy storage systems (ESSs) like battery ESS and flywheel ESS, and controllable sources of energy like fuel cell and diesel generator. The cyber-attacks such as false data injection, denial-of-service and time delay attack are considered for designing the proposed ADRC technique. The robustness of the microgrid system with the proposed controller is investigated by varying generation and load, stochastic nature of attacks, parametric uncertainties and generation rate constraint and governor dead band nonlinearities. Further, the stability analysis of the microgrid with proposed ADRC is investigated under the aforementioned cyber-attacks using the small gain theorem.
{"title":"Hybrid cyber-attack compensation of sustainable microgrid using active disturbance rejection control strategy","authors":"Komal Sharma, Anil Kumar Yadav, Bharat Bhushan Sharma","doi":"10.1098/rspa.2023.0585","DOIUrl":"https://doi.org/10.1098/rspa.2023.0585","url":null,"abstract":"A modified active disturbance rejection control (ADRC) strategy for the frequency regulation of sustainable microgrid against hybrid cyber-attacks is proposed in this paper. The proposed technique mitigates the effect of attacks which in turn regulates the frequency of microgrid. The sustainable microgrid consists of solar and wind as renewable energy sources, energy storage systems (ESSs) like battery ESS and flywheel ESS, and controllable sources of energy like fuel cell and diesel generator. The cyber-attacks such as false data injection, denial-of-service and time delay attack are considered for designing the proposed ADRC technique. The robustness of the microgrid system with the proposed controller is investigated by varying generation and load, stochastic nature of attacks, parametric uncertainties and generation rate constraint and governor dead band nonlinearities. Further, the stability analysis of the microgrid with proposed ADRC is investigated under the aforementioned cyber-attacks using the small gain theorem.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"245 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139296818","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}
Haotian Wang, Qin Zhou, Hujiang Yang, Xiankui Meng, Ye Tian, Wenjun Liu
This paper investigates a higher-order modified nonlinear Schrödinger equation with higher-order dispersion and self-steepening effects, which can be used to study the dynamics of asymmetric and steepened optical pulse transmission in optical fibres. The modulation instability of the plane-wave solution has been analysed, and the state transition of the rogue waves under the higher-order dispersion effect is presented. The findings demonstrate that the self-steepening effect may also produce an asymmetric unstable frequency band. Combined with the modulation instability, the rogue wave, rational soliton and mixed interaction of localized waves have a quantitative relationship with plane-wave parameters. Various exact solutions can be accurately located and obtained according to the generalized Darboux transformation. The asymptotic analysis of rational solutions demonstrates the state transition of higher-order rogue waves. This paper illustrates the significance of modulation instability for studying the integrable systems by the Darboux transformation. It is a new guidance to solve the difficulty of exact excitation of asymmetric localized waves in complex integrable systems. The results have prospective applications and references for the emergence, amplification and compression of asymmetric pulses in optical experiments.
{"title":"Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics","authors":"Haotian Wang, Qin Zhou, Hujiang Yang, Xiankui Meng, Ye Tian, Wenjun Liu","doi":"10.1098/rspa.2023.0601","DOIUrl":"https://doi.org/10.1098/rspa.2023.0601","url":null,"abstract":"This paper investigates a higher-order modified nonlinear Schrödinger equation with higher-order dispersion and self-steepening effects, which can be used to study the dynamics of asymmetric and steepened optical pulse transmission in optical fibres. The modulation instability of the plane-wave solution has been analysed, and the state transition of the rogue waves under the higher-order dispersion effect is presented. The findings demonstrate that the self-steepening effect may also produce an asymmetric unstable frequency band. Combined with the modulation instability, the rogue wave, rational soliton and mixed interaction of localized waves have a quantitative relationship with plane-wave parameters. Various exact solutions can be accurately located and obtained according to the generalized Darboux transformation. The asymptotic analysis of rational solutions demonstrates the state transition of higher-order rogue waves. This paper illustrates the significance of modulation instability for studying the integrable systems by the Darboux transformation. It is a new guidance to solve the difficulty of exact excitation of asymmetric localized waves in complex integrable systems. The results have prospective applications and references for the emergence, amplification and compression of asymmetric pulses in optical experiments.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139291370","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 prove a claim by Brian Straughan who conjectured that Payne–Song’s and modified Guyer–Krumhansl’s equations can be justified in (and derived from) the general model-building framework for the mechanics of complex bodies, so they emerge from the modelling of microstructural effects. The proof is based on taking into account micro-to-macro spatial scaling and a decomposition of the heat flux into a standard Fourier-type component and one measuring microstructural event with associated and balanced actions.
{"title":"Proof of Straughan’s claim on Payne–Song’s and modified Guyer–Krumhansl’s equations","authors":"P. M. Mariano","doi":"10.1098/rspa.2023.0439","DOIUrl":"https://doi.org/10.1098/rspa.2023.0439","url":null,"abstract":"We prove a claim by Brian Straughan who conjectured that Payne–Song’s and modified Guyer–Krumhansl’s equations can be justified in (and derived from) the general model-building framework for the mechanics of complex bodies, so they emerge from the modelling of microstructural effects. The proof is based on taking into account micro-to-macro spatial scaling and a decomposition of the heat flux into a standard Fourier-type component and one measuring microstructural event with associated and balanced actions.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139292780","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}
D. Bigoni, Francesco Dal Corso, Oleg N. Kirillov, D. Misseroni, G. Noselli, A. Piccolroaz
The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.
{"title":"Flutter instability in solids and structures, with a view on biomechanics and metamaterials","authors":"D. Bigoni, Francesco Dal Corso, Oleg N. Kirillov, D. Misseroni, G. Noselli, A. Piccolroaz","doi":"10.1098/rspa.2023.0523","DOIUrl":"https://doi.org/10.1098/rspa.2023.0523","url":null,"abstract":"The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139299379","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 exploration of collisional fragmentation pheno-mena remains largely unexplored, yet it holds considerable importance in numerous engineering and physical processes. Given the nonlinear nature of the governing equation, only a limited number of analytical solutions for the number density function corresponding to empirical kernels are available in the literature. This article introduces a semi-analytical approach using the homotopy perturbation method to obtain series solutions for the nonlinear collisional fragmentation equation. The method presented here can be readily adapted to solve both linear and nonlinear integral equations, eliminating the need for domain discretization. To gain deeper insights intothe accuracy of the proposed method, a convergence analysis is conducted. This analysis employs the concept of contractive mapping within the Banach space, a well-established technique universally acknowledged for ensuring convergence. Various collisional kernels (product and polymerization kernels), breakage distribution functions (binary and multiple breakage) and various initial particle distributions are considered to obtain the new series solutions. The obtained results are successfully compared against finite volume method [26] solutions in terms of number density functions and their moments. The error between the exact and obtained series solutions is shown in plots and tables to confirm the applicability and accuracy of the proposed method.
{"title":"Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations","authors":"Nisha Yadav, Ashok Das, Mehakpreet Singh, Sukhjit Singh, Jitendra Kumar","doi":"10.1098/rspa.2023.0567","DOIUrl":"https://doi.org/10.1098/rspa.2023.0567","url":null,"abstract":"The exploration of collisional fragmentation pheno-mena remains largely unexplored, yet it holds considerable importance in numerous engineering and physical processes. Given the nonlinear nature of the governing equation, only a limited number of analytical solutions for the number density function corresponding to empirical kernels are available in the literature. This article introduces a semi-analytical approach using the homotopy perturbation method to obtain series solutions for the nonlinear collisional fragmentation equation. The method presented here can be readily adapted to solve both linear and nonlinear integral equations, eliminating the need for domain discretization. To gain deeper insights intothe accuracy of the proposed method, a convergence analysis is conducted. This analysis employs the concept of contractive mapping within the Banach space, a well-established technique universally acknowledged for ensuring convergence. Various collisional kernels (product and polymerization kernels), breakage distribution functions (binary and multiple breakage) and various initial particle distributions are considered to obtain the new series solutions. The obtained results are successfully compared against finite volume method [26] solutions in terms of number density functions and their moments. The error between the exact and obtained series solutions is shown in plots and tables to confirm the applicability and accuracy of the proposed method.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139304630","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}
There has not been a satisfying numerical validation of the theory of effective waves in random particulate materials. Validation has been challenging because the theoretical methods for effective waves have been limited to random particulate media in infinite slabs or half-spaces, which require a very large number of particles to perform accurate numerical simulations. This paper offers a solution by providing, from first principles, a method to calculate effective waves for a sphere filled with particles for a spherically symmetric incident wave. We show that this case can excite exactly the same effective wavenumbers, which are the most important feature to validate for effective waves. To check correctness, we also deduce an integral equation method which does not assume the effective wave solution. Our methods are, in principal, valid for any frequency, particle volume fraction and disordered pair-correlation. With the methods we provide, it is now possible to validate, with a heavier Monte Carlo simulation, the predictions from effective wave theory.
{"title":"A model to validate effective waves in random particulate media: spherical symmetry","authors":"A. Gower, Stuart C. Hawkins, Gerhard Kristensson","doi":"10.1098/rspa.2023.0444","DOIUrl":"https://doi.org/10.1098/rspa.2023.0444","url":null,"abstract":"There has not been a satisfying numerical validation of the theory of effective waves in random particulate materials. Validation has been challenging because the theoretical methods for effective waves have been limited to random particulate media in infinite slabs or half-spaces, which require a very large number of particles to perform accurate numerical simulations. This paper offers a solution by providing, from first principles, a method to calculate effective waves for a sphere filled with particles for a spherically symmetric incident wave. We show that this case can excite exactly the same effective wavenumbers, which are the most important feature to validate for effective waves. To check correctness, we also deduce an integral equation method which does not assume the effective wave solution. Our methods are, in principal, valid for any frequency, particle volume fraction and disordered pair-correlation. With the methods we provide, it is now possible to validate, with a heavier Monte Carlo simulation, the predictions from effective wave theory.","PeriodicalId":509915,"journal":{"name":"Proceedings of the Royal Society A","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139292663","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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