Pub Date : 2023-11-15DOI: 10.1007/s00332-023-09992-0
Stephan Wojtowytsch
{"title":"Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis","authors":"Stephan Wojtowytsch","doi":"10.1007/s00332-023-09992-0","DOIUrl":"https://doi.org/10.1007/s00332-023-09992-0","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136227753","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}
Pub Date : 2023-11-11DOI: 10.1007/s00332-023-09989-9
Kuan-Wei Chen, Chih-Wen Shih
{"title":"Phase-Locked Solutions of a Coupled Pair of Nonidentical Oscillators","authors":"Kuan-Wei Chen, Chih-Wen Shih","doi":"10.1007/s00332-023-09989-9","DOIUrl":"https://doi.org/10.1007/s00332-023-09989-9","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135041699","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}
Pub Date : 2023-11-11DOI: 10.1007/s00332-023-09994-y
Talha Ahmed, Dan Wilson
{"title":"Phase-Amplitude Coordinate-Based Neural Networks for Inferring Oscillatory Dynamics","authors":"Talha Ahmed, Dan Wilson","doi":"10.1007/s00332-023-09994-y","DOIUrl":"https://doi.org/10.1007/s00332-023-09994-y","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135042849","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}
Pub Date : 2023-11-07DOI: 10.1007/s00332-023-09985-z
Feng-Bin Wang, Ruiwen Wu, Xiao-Qiang Zhao
{"title":"A Nonlocal Reaction-Diffusion Model of West Nile Virus with Vertical Transmission","authors":"Feng-Bin Wang, Ruiwen Wu, Xiao-Qiang Zhao","doi":"10.1007/s00332-023-09985-z","DOIUrl":"https://doi.org/10.1007/s00332-023-09985-z","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432763","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}
Pub Date : 2023-11-07DOI: 10.1007/s00332-023-09988-w
Renato Calleja, Alessandra Celletti, Joan Gimeno, Rafael de la Llave
Abstract We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to maintain the accuracy and reliability of the computation of quasi-periodic attractors for parameter values extremely close to the breakdown and, therefore, it is possible to obtain information on the breakdown mechanism of these quasi-periodic attractors. The method uses at the same time numerical and rigorous improvements to provide (i) a very accurate computation of the time-1 map of the spin–orbit problem (which reduces the dimensionality of the problem); (ii) a very efficient KAM method for maps which computes the attractor and its tangent spaces (by quadratically convergent, low storage requirements, and low operation count); (iii) explicit algorithms backed by a rigorous a posteriori KAM theorem, which establishes that if the algorithm is successful and produces a small residual, then there is a true solution nearby; and (iv) guaranteed algorithms to reach arbitrarily close to the border of existence as long as there are enough computer resources. As a by-product of the accuracy that we maintain till breakdown, we study several scale-invariant observables of the tori used in the renormalization group of infinite-dimensional spaces. In contrast with previously studied simple models, the behavior at breakdown of the spin–orbit problem does not satisfy standard scaling relations which implies that the spin–orbit problem is not described by a hyperbolic fixed point of the renormalization operator.
{"title":"Accurate Computations up to Breakdown of Quasi-Periodic Attractors in the Dissipative Spin–Orbit Problem","authors":"Renato Calleja, Alessandra Celletti, Joan Gimeno, Rafael de la Llave","doi":"10.1007/s00332-023-09988-w","DOIUrl":"https://doi.org/10.1007/s00332-023-09988-w","url":null,"abstract":"Abstract We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to maintain the accuracy and reliability of the computation of quasi-periodic attractors for parameter values extremely close to the breakdown and, therefore, it is possible to obtain information on the breakdown mechanism of these quasi-periodic attractors. The method uses at the same time numerical and rigorous improvements to provide (i) a very accurate computation of the time-1 map of the spin–orbit problem (which reduces the dimensionality of the problem); (ii) a very efficient KAM method for maps which computes the attractor and its tangent spaces (by quadratically convergent, low storage requirements, and low operation count); (iii) explicit algorithms backed by a rigorous a posteriori KAM theorem, which establishes that if the algorithm is successful and produces a small residual, then there is a true solution nearby; and (iv) guaranteed algorithms to reach arbitrarily close to the border of existence as long as there are enough computer resources. As a by-product of the accuracy that we maintain till breakdown, we study several scale-invariant observables of the tori used in the renormalization group of infinite-dimensional spaces. In contrast with previously studied simple models, the behavior at breakdown of the spin–orbit problem does not satisfy standard scaling relations which implies that the spin–orbit problem is not described by a hyperbolic fixed point of the renormalization operator.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432120","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}
Pub Date : 2023-11-06DOI: 10.1007/s00332-023-09982-2
Riccardo Durastanti, Lorenzo Giacomelli
Abstract In the regime of lubrication approximation, we look at spreading phenomena under the action of singular potentials of the form $$P(h)approx h^{1-m}$$ P(h)≈h1-m as $$hrightarrow 0^+$$ h→0+ with $$m>1$$ m>1 , modeling repulsion between the liquid–gas interface and the substrate. We assume zero slippage at the contact line. Based on formal analysis arguments, we report that for any $$m>1$$ m>1 and any value of the speed (both positive and negative) there exists a three-parameter, hence generic, family of fronts (i.e., traveling-wave solutions with a contact line). A two-parameter family of advancing “linear-log” fronts also exists, having a logarithmically corrected linear behavior in the liquid bulk. All these fronts have finite rate of dissipation, indicating that singular potentials stand as an alternative solution to the contact-line paradox. In agreement with steady states, fronts have microscopic contact angle equal to $$pi /2$$ π/2 for all $$m>1$$ m>1 and finite energy for all $$m<3$$ m<3 . We also propose a selection criterion for the fronts, based on thermodynamically consistent contact-line conditions modeling friction at the contact line. So as contact-angle conditions do in the case of slippage models, this criterion selects a unique (up to translation) linear-log front for each positive speed. Numerical evidence suggests that, fixed the speed and the frictional coefficient, its shape depends on the spreading coefficient, with steeper fronts in partial wetting and a more prominent precursor region in dry complete wetting.
在润滑近似下，我们研究了奇异势作用下的扩散现象，其形式为$$P(h)approx h^{1-m}$$ P (h)≈h1 - m: $$hrightarrow 0^+$$ h→0 +，$$m>1$$ m ＆gt;1、模拟液气界面与衬底之间的斥力。我们假设接触线上的滑动为零。基于形式分析论证，我们报告了对于任意$$m>1$$ m ＆gt;1和速度的任何值(正负)都存在一个三参数，因此，一般的锋面族(即具有接触线的行波解)。一个推进的“线性-对数”锋面的双参数族也存在，在液体体中具有对数校正的线性行为。所有这些锋面的耗散率都是有限的，这表明奇异势可以作为接触线悖论的另一种解决办法。与稳态一致，对于所有$$m>1$$ m ＆gt，锋面的微观接触角等于$$pi /2$$ π / 2;1和有限能量的所有$$m<3$$ m ＆lt;3 .我们还提出了一个选择标准的锋面，基于热力学一致的接触线条件，模拟在接触线上的摩擦。因此，就像滑移模型中的接触角条件一样，该准则为每个正速度选择一个唯一的(直到平移)线性对数前。数值证据表明，在一定的速度和摩擦系数下，其形状取决于扩散系数，部分润湿时锋面更陡，干燥完全润湿时前驱区更突出。
{"title":"Thin-Film Equations with Singular Potentials: An Alternative Solution to the Contact-Line Paradox","authors":"Riccardo Durastanti, Lorenzo Giacomelli","doi":"10.1007/s00332-023-09982-2","DOIUrl":"https://doi.org/10.1007/s00332-023-09982-2","url":null,"abstract":"Abstract In the regime of lubrication approximation, we look at spreading phenomena under the action of singular potentials of the form $$P(h)approx h^{1-m}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>h</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>≈</mml:mo> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> as $$hrightarrow 0^+$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>→</mml:mo> <mml:msup> <mml:mn>0</mml:mn> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> with $$m>1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , modeling repulsion between the liquid–gas interface and the substrate. We assume zero slippage at the contact line. Based on formal analysis arguments, we report that for any $$m>1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and any value of the speed (both positive and negative) there exists a three-parameter, hence generic, family of fronts (i.e., traveling-wave solutions with a contact line). A two-parameter family of advancing “linear-log” fronts also exists, having a logarithmically corrected linear behavior in the liquid bulk. All these fronts have finite rate of dissipation, indicating that singular potentials stand as an alternative solution to the contact-line paradox. In agreement with steady states, fronts have microscopic contact angle equal to $$pi /2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> for all $$m>1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and finite energy for all $$m<3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo><</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . We also propose a selection criterion for the fronts, based on thermodynamically consistent contact-line conditions modeling friction at the contact line. So as contact-angle conditions do in the case of slippage models, this criterion selects a unique (up to translation) linear-log front for each positive speed. Numerical evidence suggests that, fixed the speed and the frictional coefficient, its shape depends on the spreading coefficient, with steeper fronts in partial wetting and a more prominent precursor region in dry complete wetting.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634194","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}
Pub Date : 2023-11-03DOI: 10.1007/s00332-023-09993-z
V. D. Camiola, V. Romano, G. Vitanza
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 $$hbar $$ ħ . 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 $$hbar ^2$$ ħ2 order is obtained under a long-time scaling for the most relevant phonon branches.
{"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":null,"pages":null},"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}
Pub Date : 2023-11-02DOI: 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":null,"pages":null},"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}
Pub Date : 2023-10-30DOI: 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":null,"pages":null},"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}
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