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Wigner Equations for Phonons Transport and Quantum Heat Flux 声子输运和量子热通量的Wigner方程
2区 数学
Journal of Nonlinear Science Pub Date : 2023-11-03 DOI: 10.1007/s00332-023-09993-z
V. D. Camiola, V. Romano, G. Vitanza
{"title":"Wigner Equations for Phonons Transport and Quantum Heat Flux","authors":"V. D. Camiola, V. Romano, G. Vitanza","doi":"10.1007/s00332-023-09993-z","DOIUrl":"https://doi.org/10.1007/s00332-023-09993-z","url":null,"abstract":"Abstract Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the acoustic, optical and Z phonons are deduced. The equations are valid for any solid, including 2D crystals like graphene. With the use of Moyal’s calculus and its properties, the pseudo-differential operators are expanded up to the second order in $$hbar $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ħ</mml:mi> </mml:math> . An energy transport model is obtained by using the moment method with closure relations based on a quantum version of the Maximum Entropy Principle by employing a relaxation time approximation for the production terms of energy and energy flux. An explicit form of the thermal conductivity with quantum correction up to $$hbar ^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>ħ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> order is obtained under a long-time scaling for the most relevant phonon branches.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"65 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Hamiltonian Mechanics and Lie Algebroid Connections 哈密顿力学与李代数连接
2区 数学
Journal of Nonlinear Science Pub Date : 2023-11-02 DOI: 10.1007/s00332-023-09986-y
Jiawei Hu, Ari Stern
{"title":"Hamiltonian Mechanics and Lie Algebroid Connections","authors":"Jiawei Hu, Ari Stern","doi":"10.1007/s00332-023-09986-y","DOIUrl":"https://doi.org/10.1007/s00332-023-09986-y","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"89 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Exponential Entropy Dissipation for Weakly Self-Consistent Vlasov–Fokker–Planck Equations 弱自洽Vlasov-Fokker-Planck方程的指数熵耗散
2区 数学
Journal of Nonlinear Science Pub Date : 2023-10-30 DOI: 10.1007/s00332-023-09984-0
Erhan Bayraktar, Qi Feng, Wuchen Li
{"title":"Exponential Entropy Dissipation for Weakly Self-Consistent Vlasov–Fokker–Planck Equations","authors":"Erhan Bayraktar, Qi Feng, Wuchen Li","doi":"10.1007/s00332-023-09984-0","DOIUrl":"https://doi.org/10.1007/s00332-023-09984-0","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136022984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 1
Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization 辅助函数作为库普曼观测值:基于多项式优化的动力系统数据驱动分析
2区 数学
Journal of Nonlinear Science Pub Date : 2023-10-30 DOI: 10.1007/s00332-023-09990-2
Jason J. Bramburger, Giovanni Fantuzzi
{"title":"Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization","authors":"Jason J. Bramburger, Giovanni Fantuzzi","doi":"10.1007/s00332-023-09990-2","DOIUrl":"https://doi.org/10.1007/s00332-023-09990-2","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"320 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136102995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 2
Blowup Analysis of a Hysteresis Model Based Upon Singular Perturbations 基于奇异摄动的迟滞模型爆破分析
2区 数学
Journal of Nonlinear Science Pub Date : 2023-10-26 DOI: 10.1007/s00332-023-09983-1
K. U. Kristiansen
{"title":"Blowup Analysis of a Hysteresis Model Based Upon Singular Perturbations","authors":"K. U. Kristiansen","doi":"10.1007/s00332-023-09983-1","DOIUrl":"https://doi.org/10.1007/s00332-023-09983-1","url":null,"abstract":"Abstract In this paper, we provide a geometric analysis of a new hysteresis model that is based upon singular perturbations. Here hysteresis refers to a type of regularization of piecewise smooth differential equations where the past of a trajectory, in a small neighborhood of the discontinuity set, determines the vector-field at present. In fact, in the limit where the neighborhood of the discontinuity vanishes, hysteresis converges in an appropriate sense to Filippov’s sliding vector-field. Recently (2022), however, Bonet and Seara showed that hysteresis, in contrast to regularization through smoothing, leads to chaos in the regularization of grazing bifurcations, even in two dimensions. The hysteresis model we analyze in the present paper—which was developed by Bonet et al in a paper from 2017 as an attempt to unify different regularizations of piecewise smooth systems—involves two singular perturbation parameters and includes a combination of slow–fast and nonsmooth effects. The description of this model is therefore—from the perspective of singular perturbation theory—challenging, even in two dimensions. Using blowup as our main technical tool, we prove existence of an invariant cylinder carrying fast dynamics in the azimuthal direction and a slow drift in the axial direction. We find that the slow drift is given by Filippov’s sliding vector-field to leading order. Moreover, in the case of grazing, we identify two important parameter regimes that relate the model to smoothing (through a saddle-node bifurcation of limit cycles) and hysteresis (through chaotic dynamics, due to a folded saddle and a novel return mechanism).","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"26 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A Hydrodynamical Model of Nematic Liquid Crystal Films with a General State of Orientational Order 具有一般定向有序状态的向列型液晶膜的流体动力学模型
2区 数学
Journal of Nonlinear Science Pub Date : 2023-10-21 DOI: 10.1007/s00332-023-09970-6
Lucas Bouck, Ricardo H. Nochetto, Vladimir Yushutin
{"title":"A Hydrodynamical Model of Nematic Liquid Crystal Films with a General State of Orientational Order","authors":"Lucas Bouck, Ricardo H. Nochetto, Vladimir Yushutin","doi":"10.1007/s00332-023-09970-6","DOIUrl":"https://doi.org/10.1007/s00332-023-09970-6","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"67 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135511593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 1
Pulsating Fronts of Spatially Periodic Bistable Reaction–Diffusion Equations Around an Obstacle 围绕障碍物的空间周期双稳态反应扩散方程的脉动锋
2区 数学
Journal of Nonlinear Science Pub Date : 2023-10-17 DOI: 10.1007/s00332-023-09981-3
Fu-Jie Jia, Wei-Jie Sheng, Zhi-Cheng Wang
{"title":"Pulsating Fronts of Spatially Periodic Bistable Reaction–Diffusion Equations Around an Obstacle","authors":"Fu-Jie Jia, Wei-Jie Sheng, Zhi-Cheng Wang","doi":"10.1007/s00332-023-09981-3","DOIUrl":"https://doi.org/10.1007/s00332-023-09981-3","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Non-existence of Mean-Field Models for Particle Orientations in Suspensions 悬架中粒子取向的平均场模型的不存在性
2区 数学
Journal of Nonlinear Science Pub Date : 2023-10-16 DOI: 10.1007/s00332-023-09959-1
Richard M. Höfer, Amina Mecherbet, Richard Schubert
{"title":"Non-existence of Mean-Field Models for Particle Orientations in Suspensions","authors":"Richard M. Höfer, Amina Mecherbet, Richard Schubert","doi":"10.1007/s00332-023-09959-1","DOIUrl":"https://doi.org/10.1007/s00332-023-09959-1","url":null,"abstract":"Abstract We consider a suspension of spherical inertialess particles in a Stokes flow on the torus $$mathbb {T}^3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . The particles perturb a linear extensional flow due to their rigidity constraint. Due to the singular nature of this perturbation, no mean-field limit for the behavior of the particle orientation can be valid. This contrasts with widely used models in the literature such as the FENE and Doi models and similar models for active suspensions. The proof of this result is based on the study of the mobility problem of a single particle in a non-cubic torus, which we prove to exhibit a nontrivial coupling between the angular velocity and a prescribed strain.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"37 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 3
Incompressible Limit of the Ericksen–Leslie Parabolic–Hyperbolic Liquid Crystal Model Ericksen-Leslie抛物-双曲液晶模型的不可压缩极限
2区 数学
Journal of Nonlinear Science Pub Date : 2023-10-14 DOI: 10.1007/s00332-023-09972-4
Liang Guo, Ning Jiang, Fucai Li, Yi-Long Luo, Shaojun Tang
{"title":"Incompressible Limit of the Ericksen–Leslie Parabolic–Hyperbolic Liquid Crystal Model","authors":"Liang Guo, Ning Jiang, Fucai Li, Yi-Long Luo, Shaojun Tang","doi":"10.1007/s00332-023-09972-4","DOIUrl":"https://doi.org/10.1007/s00332-023-09972-4","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 2
Publisher Correction: The Regularized Visible Fold Revisited 出版商更正:重新审视了正则化的可见折叠
2区 数学
Journal of Nonlinear Science Pub Date : 2023-10-13 DOI: 10.1007/s00332-023-09980-4
K. Uldall Kristiansen
{"title":"Publisher Correction: The Regularized Visible Fold Revisited","authors":"K. Uldall Kristiansen","doi":"10.1007/s00332-023-09980-4","DOIUrl":"https://doi.org/10.1007/s00332-023-09980-4","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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