Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 142-154, March 2024. Abstract. In this article, an improved self-consistent field iteration scheme is introduced. The proposed method has essential applications in Kohn–Sham density functional theory and relies on an extrapolation scheme and the least squares method. Moreover, the proposed solution is easy to implement and can accelerate the convergence of self-consistent field iteration. The main idea is to fit out a polynomial based on the errors of the derived approximate solutions and then extrapolate the errors into zero to obtain a new approximation. The developed scheme can be applied not only to the Kohn–Sham density functional theory but also to accelerate the self-consistent field iterations of other nonlinear equations. Some numerical results for the Kohn–Sham equation and general nonlinear equations are presented to validate the efficiency of the new method.
{"title":"Improved Self-consistent Field Iteration for Kohn–Sham Density Functional Theory","authors":"Fei Xu, Qiumei Huang","doi":"10.1137/23m1558215","DOIUrl":"https://doi.org/10.1137/23m1558215","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 142-154, March 2024. <br/> Abstract. In this article, an improved self-consistent field iteration scheme is introduced. The proposed method has essential applications in Kohn–Sham density functional theory and relies on an extrapolation scheme and the least squares method. Moreover, the proposed solution is easy to implement and can accelerate the convergence of self-consistent field iteration. The main idea is to fit out a polynomial based on the errors of the derived approximate solutions and then extrapolate the errors into zero to obtain a new approximation. The developed scheme can be applied not only to the Kohn–Sham density functional theory but also to accelerate the self-consistent field iterations of other nonlinear equations. Some numerical results for the Kohn–Sham equation and general nonlinear equations are presented to validate the efficiency of the new method.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139459307","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}
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 106-124, March 2024. Abstract. We derive the optimal energy error estimate for a multiscale finite element method with oversampling technique applied to an elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded and measurable, which may admit rough microstructures. As a byproduct of the energy error estimate, we derive the rate of convergence in the [math]-norm.
{"title":"Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited","authors":"Pingbing Ming, Siqi Song","doi":"10.1137/22m1511060","DOIUrl":"https://doi.org/10.1137/22m1511060","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 106-124, March 2024. <br/> Abstract. We derive the optimal energy error estimate for a multiscale finite element method with oversampling technique applied to an elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded and measurable, which may admit rough microstructures. As a byproduct of the energy error estimate, we derive the rate of convergence in the [math]-norm.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139414596","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}
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 66-105, March 2024. Abstract. We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set [math] of a slowly varying domain wall modeling the interface separating two insulating media. We propose a semiclassical oscillatory representation of the propagating wavepackets and provide an estimate of their accuracy in appropriate energy norms. We describe the propagation of relativistic modes along [math] and analyze dispersive modes by a stationary phase method. In the absence of turning points, we show that arbitrary smooth localized initial conditions may be represented as a superposition of such wavepackets. In the presence of turning points, the results apply only for sufficiently high-frequency wavepackets. The theory finds applications for both Dirac systems of equations modeling topologically nontrivial systems as well as Klein–Gordon equations, which are topologically trivial.
{"title":"Semiclassical Propagation Along Curved Domain Walls","authors":"Guillaume Bal","doi":"10.1137/23m1545872","DOIUrl":"https://doi.org/10.1137/23m1545872","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 66-105, March 2024. <br/> Abstract. We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set [math] of a slowly varying domain wall modeling the interface separating two insulating media. We propose a semiclassical oscillatory representation of the propagating wavepackets and provide an estimate of their accuracy in appropriate energy norms. We describe the propagation of relativistic modes along [math] and analyze dispersive modes by a stationary phase method. In the absence of turning points, we show that arbitrary smooth localized initial conditions may be represented as a superposition of such wavepackets. In the presence of turning points, the results apply only for sufficiently high-frequency wavepackets. The theory finds applications for both Dirac systems of equations modeling topologically nontrivial systems as well as Klein–Gordon equations, which are topologically trivial.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139414590","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}
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 39-65, March 2024. Abstract. We consider random wave coupling along a flat boundary in dimension three, where the coupling is between surface and body modes and is induced by scattering by a randomly heterogeneous medium. In an appropriate scaling regime we obtain a system of radiative transfer equations which are satisfied by the mean Wigner transform of the mode amplitudes. We provide a rigorous probabilistic framework for describing solutions to this system using that it has the form of a Kolmogorov equation for some Markov process. We then prove statistical stability of the smoothed Wigner transform under the Gaussian approximation. We conclude with analyzing the nonlinear inverse problem for the radiative transfer equations and establish the unique recovery of phase and group velocities as well as power spectral information for the medium fluctuations from the observed smoothed Wigner transform. The mentioned statistical stability is essential in monitoring applications where the realization of the random medium may change.
{"title":"Three-Dimensional Random Wave Coupling Along a Boundary and an Associated Inverse Problem","authors":"Maarten V. de Hoop, Josselin Garnier, Knut Sølna","doi":"10.1137/23m1544842","DOIUrl":"https://doi.org/10.1137/23m1544842","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 39-65, March 2024. <br/> Abstract. We consider random wave coupling along a flat boundary in dimension three, where the coupling is between surface and body modes and is induced by scattering by a randomly heterogeneous medium. In an appropriate scaling regime we obtain a system of radiative transfer equations which are satisfied by the mean Wigner transform of the mode amplitudes. We provide a rigorous probabilistic framework for describing solutions to this system using that it has the form of a Kolmogorov equation for some Markov process. We then prove statistical stability of the smoothed Wigner transform under the Gaussian approximation. We conclude with analyzing the nonlinear inverse problem for the radiative transfer equations and establish the unique recovery of phase and group velocities as well as power spectral information for the medium fluctuations from the observed smoothed Wigner transform. The mentioned statistical stability is essential in monitoring applications where the realization of the random medium may change.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139414621","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}
Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 1-38, March 2024. Abstract. In this work we study time-domain sound-soft scattering by small circles. Our goal is to derive an asymptotic model for this problem that is valid when the size of the particles tends to zero. We present a systematic approach to constructing such models based on a well-chosen Galerkin discretization of a boundary integral equation. The convergence of the method is achieved by decreasing the asymptotic parameter rather than increasing the number of basis functions. We prove the second-order convergence of the field error with respect to the particle size. Our findings are illustrated with numerical experiments.
{"title":"A New Class of Uniformly Stable Time-Domain Foldy–Lax Models for Scattering by Small Particles. Acoustic Sound-Soft Scattering by Circles","authors":"Maryna Kachanovska","doi":"10.1137/22m1495512","DOIUrl":"https://doi.org/10.1137/22m1495512","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 1-38, March 2024. <br/> Abstract. In this work we study time-domain sound-soft scattering by small circles. Our goal is to derive an asymptotic model for this problem that is valid when the size of the particles tends to zero. We present a systematic approach to constructing such models based on a well-chosen Galerkin discretization of a boundary integral equation. The convergence of the method is achieved by decreasing the asymptotic parameter rather than increasing the number of basis functions. We prove the second-order convergence of the field error with respect to the particle size. Our findings are illustrated with numerical experiments.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"217 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095429","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}
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1746-1774, December 2023. Abstract. This work presents a systematic methodology for describing the transient dynamics of coarse-grained molecular systems inferred from all-atom simulated data. We suggest Langevin-type dynamics where the coarse-grained interaction potential depends explicitly on time to efficiently approximate the transient coarse-grained dynamics. We apply the path-space force matching approach at the transient dynamics regime to learn the proposed model parameters. In particular, we parameterize the coarse-grained potential both with respect to the pair distance of the coarse-grained particles and the time, and we obtain an evolution model that is explicitly time dependent. Moreover, we follow a data-driven approach to estimate the friction kernel, given by appropriate correlation functions directly from the underlying all-atom molecular dynamics simulations. To explore and validate the proposed methodology we study a benchmark system of a moving particle in a box. We examine the suggested model’s effectiveness in terms of the system’s correlation time and find that the model can well approximate the transient time regime of the system, depending on the correlation time of the system. As a result, in the less correlated case, it can represent the dynamics for a longer time interval. We present an extensive study of our approach to a realistic high-dimensional water molecular system. Posing the water system initially out of thermal equilibrium we collect trajectories of all-atom data for the, empirically estimated, transient time regime. Then, we infer the suggested model and strengthen the model’s validity by comparing it with simplified Markovian models.
{"title":"Bottom-Up Transient Time Models in Coarse-Graining Molecular Systems","authors":"Georgia Baxevani, Vagelis Harmandaris, Evangelia Kalligiannaki, Ivi Tsantili","doi":"10.1137/23m1548451","DOIUrl":"https://doi.org/10.1137/23m1548451","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1746-1774, December 2023. <br/> Abstract. This work presents a systematic methodology for describing the transient dynamics of coarse-grained molecular systems inferred from all-atom simulated data. We suggest Langevin-type dynamics where the coarse-grained interaction potential depends explicitly on time to efficiently approximate the transient coarse-grained dynamics. We apply the path-space force matching approach at the transient dynamics regime to learn the proposed model parameters. In particular, we parameterize the coarse-grained potential both with respect to the pair distance of the coarse-grained particles and the time, and we obtain an evolution model that is explicitly time dependent. Moreover, we follow a data-driven approach to estimate the friction kernel, given by appropriate correlation functions directly from the underlying all-atom molecular dynamics simulations. To explore and validate the proposed methodology we study a benchmark system of a moving particle in a box. We examine the suggested model’s effectiveness in terms of the system’s correlation time and find that the model can well approximate the transient time regime of the system, depending on the correlation time of the system. As a result, in the less correlated case, it can represent the dynamics for a longer time interval. We present an extensive study of our approach to a realistic high-dimensional water molecular system. Posing the water system initially out of thermal equilibrium we collect trajectories of all-atom data for the, empirically estimated, transient time regime. Then, we infer the suggested model and strengthen the model’s validity by comparing it with simplified Markovian models.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138546065","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}
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1717-1745, December 2023. Abstract. The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as [math]-limits of three-dimensional atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness [math] and interatomic distance [math]. First, we set up a novel theory for ultrathin rods composed of finitely many atomic fibers ([math]), which incorporates surface energy and new discrete terms in the limiting functional. This can be thought of as a contribution to the mechanical modelling of nanowires. Second, we treat the case where [math] and recover a nonlinear rod model—the modern version of Kirchhoff’s rod theory.
{"title":"A Bending-Torsion Theory for Thin and Ultrathin Rods as a [math]-Limit of Atomistic Models","authors":"Bernd Schmidt, Jiří Zeman","doi":"10.1137/22m1517640","DOIUrl":"https://doi.org/10.1137/22m1517640","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1717-1745, December 2023. <br/> Abstract. The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as [math]-limits of three-dimensional atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness [math] and interatomic distance [math]. First, we set up a novel theory for ultrathin rods composed of finitely many atomic fibers ([math]), which incorporates surface energy and new discrete terms in the limiting functional. This can be thought of as a contribution to the mechanical modelling of nanowires. Second, we treat the case where [math] and recover a nonlinear rod model—the modern version of Kirchhoff’s rod theory.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"171 2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138546026","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}
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1690-1716, December 2023. Abstract. We investigate an optimal control model with pointwise constraints governed by a two-time-scale time-fractional advection-diffusion-reaction equation with space-time-dependent fractional order and coefficients, which describes, e.g., the contaminant in groundwater under various transport scales or miscible displacement of hydrocarbon by injected fluid through heterogeneous porous media. To accommodate for the effects of complex fractional order and coefficients, an auxiliary equation method is proposed, along with the Fredholm alternative for compact operators, to analyze the well-posedness of the state equation. Additionally, a bootstrapping argument is utilized to progressively improve the solution regularity through a carefully designed pathway, leading to the maximal regularity estimates. Subsequently, we analyze the adjoint equation derived from the first-order optimality condition, which requires more subtle treatments due to the presence of hidden-memory variable-order fractional operators. Based on these findings, we ultimately analyze the well-posedness, first-order optimality conditions and maximal regularity estimates for the optimal control problem, and we conduct numerical experiments to investigate its behavior in potential applications.
{"title":"Analysis and Simulation of Optimal Control for a Two-Time-Scale Fractional Advection-Diffusion-Reaction Equation with Space-Time-Dependent Order and Coefficients","authors":"Yiqun Li, Hong Wang, Xiangcheng Zheng","doi":"10.1137/23m1573537","DOIUrl":"https://doi.org/10.1137/23m1573537","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1690-1716, December 2023. <br/> Abstract. We investigate an optimal control model with pointwise constraints governed by a two-time-scale time-fractional advection-diffusion-reaction equation with space-time-dependent fractional order and coefficients, which describes, e.g., the contaminant in groundwater under various transport scales or miscible displacement of hydrocarbon by injected fluid through heterogeneous porous media. To accommodate for the effects of complex fractional order and coefficients, an auxiliary equation method is proposed, along with the Fredholm alternative for compact operators, to analyze the well-posedness of the state equation. Additionally, a bootstrapping argument is utilized to progressively improve the solution regularity through a carefully designed pathway, leading to the maximal regularity estimates. Subsequently, we analyze the adjoint equation derived from the first-order optimality condition, which requires more subtle treatments due to the presence of hidden-memory variable-order fractional operators. Based on these findings, we ultimately analyze the well-posedness, first-order optimality conditions and maximal regularity estimates for the optimal control problem, and we conduct numerical experiments to investigate its behavior in potential applications.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138546032","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}
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1667-1689, December 2023. Abstract. In this work, we propose and study a preconditioned framework with a graphic Ginzburg–Landau functional for image segmentation and data clustering by parallel computing. Solving nonlocal models is usually challenging due to the huge computation burden. For the nonconvex and nonlocal variational functional, we propose several damped Jacobi and generalized Richardson preconditioners for the large-scale linear systems within a difference of convex functions algorithm framework. These preconditioners are efficient for parallel computing with GPU and can leverage the computational cost. Our framework also provides flexible step sizes with a global convergence guarantee. Numerical experiments show the proposed algorithms are very competitive compared to the singular value decomposition based spectral method.
{"title":"Preconditioned Algorithm for Difference of Convex Functions with Applications to Graph Ginzburg–Landau Model","authors":"Xinhua Shen, Hongpeng Sun, Xuecheng Tai","doi":"10.1137/23m1561270","DOIUrl":"https://doi.org/10.1137/23m1561270","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1667-1689, December 2023. <br/> Abstract. In this work, we propose and study a preconditioned framework with a graphic Ginzburg–Landau functional for image segmentation and data clustering by parallel computing. Solving nonlocal models is usually challenging due to the huge computation burden. For the nonconvex and nonlocal variational functional, we propose several damped Jacobi and generalized Richardson preconditioners for the large-scale linear systems within a difference of convex functions algorithm framework. These preconditioners are efficient for parallel computing with GPU and can leverage the computational cost. Our framework also provides flexible step sizes with a global convergence guarantee. Numerical experiments show the proposed algorithms are very competitive compared to the singular value decomposition based spectral method.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":" 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138493194","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}
Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1644-1666, December 2023. Abstract. The constructive theory of analytical higher-order contrast bounds for the effective constants of dispersed conducting and piezoelectric fibrous composites is developed. The lower-order bounds, e.g., Wiener and Hashin–Shtrikman bounds, are universal for composites but do not take into account interactions among inclusions corresponding to their location. To study the variety of dispersed random composites, we use computationally effective structural sums directly relating the location of inclusions to the effective constants. The present paper is the first report where the structural sums are applied to higher-order contrast bounds instead of the virtually impossible in computation multipoint correlation functions. We concentrate our attention on two-phase conducting fibrous composites. Rylko’s matrix decomposition is used for the higher-order contrast bounds to extend the obtained analytical bounds to piezoelectric fibrous composites. The supplementary materials contain the results of numerical-symbolic computations, the long analytical formulas for the effective constants and bounds up to [math], where [math] stands for concentration.
{"title":"High-order Contrast Bounds for Piezoelectric Constants of Two-phase Fibrous Composites","authors":"Vladimir Mityushev","doi":"10.1137/23m1559907","DOIUrl":"https://doi.org/10.1137/23m1559907","url":null,"abstract":"Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1644-1666, December 2023. <br/> Abstract. The constructive theory of analytical higher-order contrast bounds for the effective constants of dispersed conducting and piezoelectric fibrous composites is developed. The lower-order bounds, e.g., Wiener and Hashin–Shtrikman bounds, are universal for composites but do not take into account interactions among inclusions corresponding to their location. To study the variety of dispersed random composites, we use computationally effective structural sums directly relating the location of inclusions to the effective constants. The present paper is the first report where the structural sums are applied to higher-order contrast bounds instead of the virtually impossible in computation multipoint correlation functions. We concentrate our attention on two-phase conducting fibrous composites. Rylko’s matrix decomposition is used for the higher-order contrast bounds to extend the obtained analytical bounds to piezoelectric fibrous composites. The supplementary materials contain the results of numerical-symbolic computations, the long analytical formulas for the effective constants and bounds up to [math], where [math] stands for concentration.","PeriodicalId":501053,"journal":{"name":"Multiscale Modeling and Simulation","volume":"13 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494516","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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