Physica D: Nonlinear Phenomena最新文献

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Impact of rectangular, half-elliptical, trapezoidal, and triangular tabs on the mixing behavior of circular sonic jets

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134557

Amit Krishnat Mali , Tamal Jana , Mrinal Kaushik , Gautam Choubey

This study investigates the mixing characteristics of sonic jets with and without control mechanisms. Specifically, passive controls in the form of tabs placed at the exit of a convergent nozzle are examined both computationally and experimentally. The research focuses on the jet decay characteristics and flow development of a plain nozzle compared to nozzles equipped with square, half-elliptical, triangular, and trapezoidal tabs. The realizable k-ε turbulence model is employed, as it effectively captures the structures of sonic jets in both correctly expanded and underexpanded states. The tabs were found to cause significant distortions in the jet structure, leading to increased mass entrainment and lateral spread of the jet. Notably, half-elliptical tabs were the most effective across all expansion levels compared to square, trapezoidal, and triangular tabs. Half-elliptical tabs had a maximum reduction of 69.2 % in sonic core length for underexpanded jets at a nozzle pressure ratio (NPR) of 4. Additionally, reductions in core lengths were 55.5 % for correctly expanded jets at NPR 2 and 66.6 % for underexpanded jets at NPR 3.

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引用次数: 0

Almost synchronization phenomena in the two and three coupled Brusselator systems

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134457

Ana Mayora-Cebollero , Jorge A. Jover-Galtier , Fátima Drubi , Santiago Ibáñez , Álvaro Lozano , Carmen Mayora-Cebollero , Roberto Barrio

We present a study of some temporal almost synchronization phenomena of systems of two and three coupled Brusselators: they are approximately synchronized during most of the dynamics, only losing synchronization for small times and quickly returning to an almost synchronized state. Here we show two situations where this phenomenon occurs, one related with codimension-two Hopf–pitchfork bifurcations, and the other one due to the existence of fast–slow dynamics. On the one hand, a detailed characterization of the codimension-two Hopf–pitchfork bifurcations in the model allows us to determine the regions of the parameter space in which this phenomenon occurs. On the other hand, a fast–slow analysis of the two coupled Brusselators, using singular perturbation theory, illustrates the second situation studied here. We next analyze this phenomenon numerically, by explicitly calculating the fraction of time during which different trajectories are almost synchronized. Our results are then extended to the case of three coupled Brusselators.

{"title":"Almost synchronization phenomena in the two and three coupled Brusselator systems","authors":"Ana Mayora-Cebollero , Jorge A. Jover-Galtier , Fátima Drubi , Santiago Ibáñez , Álvaro Lozano , Carmen Mayora-Cebollero , Roberto Barrio","doi":"10.1016/j.physd.2024.134457","DOIUrl":"10.1016/j.physd.2024.134457","url":null,"abstract":"<div><div>We present a study of some temporal almost synchronization phenomena of systems of two and three coupled Brusselators: they are approximately synchronized during most of the dynamics, only losing synchronization for small times and quickly returning to an almost synchronized state. Here we show two situations where this phenomenon occurs, one related with codimension-two Hopf–pitchfork bifurcations, and the other one due to the existence of fast–slow dynamics. On the one hand, a detailed characterization of the codimension-two Hopf–pitchfork bifurcations in the model allows us to determine the regions of the parameter space in which this phenomenon occurs. On the other hand, a fast–slow analysis of the two coupled Brusselators, using singular perturbation theory, illustrates the second situation studied here. We next analyze this phenomenon numerically, by explicitly calculating the fraction of time during which different trajectories are almost synchronized. Our results are then extended to the case of three coupled Brusselators.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134457"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Geometrically exact post-buckling and post-flutter of standing cantilevered pipe conveying fluid

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134478

Amir Mehdi Dehrouyeh-Semnani

Although the nonlinear dynamics of hanging cantilevered pipes conveying fluid have been extensively scrutinized, there is limited research on the nonlinear behavior of standing ones. Hence, the objective of this study is to examine the geometrically exact nonlinear static and dynamic responses of cantilevered pipes conveying fluid in a standing position. The geometrically exact rotation-based model, combined with the shooting method and the Galerkin technique, is applied to assess the nonlinear static behavior of system and its stability characteristics. Moreover, to compute the nonlinear dynamics of system, the geometrically exact quaternion-based model, together with the Galerkin technique, is employed. It is revealed that the system may undergo buckling through either a supercritical or subcritical pitchfork bifurcation, depending on the gravity parameter, which may give rise to extremely large-amplitude responses. The system may also experience flutter instability due to a supercritical Hopf bifurcation, which brings about self-excited periodic oscillations. The generic behavior of system for a specific range of the gravity parameter is investigated across four distinct scenarios, which vary based on the gravity parameter and mass ratio. Notably, only one of these scenarios is analogous to the situation that comes to pass for the hanging case.

{"title":"Geometrically exact post-buckling and post-flutter of standing cantilevered pipe conveying fluid","authors":"Amir Mehdi Dehrouyeh-Semnani","doi":"10.1016/j.physd.2024.134478","DOIUrl":"10.1016/j.physd.2024.134478","url":null,"abstract":"<div><div>Although the nonlinear dynamics of hanging cantilevered pipes conveying fluid have been extensively scrutinized, there is limited research on the nonlinear behavior of standing ones. Hence, the objective of this study is to examine the geometrically exact nonlinear static and dynamic responses of cantilevered pipes conveying fluid in a standing position. The geometrically exact rotation-based model, combined with the shooting method and the Galerkin technique, is applied to assess the nonlinear static behavior of system and its stability characteristics. Moreover, to compute the nonlinear dynamics of system, the geometrically exact quaternion-based model, together with the Galerkin technique, is employed. It is revealed that the system may undergo buckling through either a supercritical or subcritical pitchfork bifurcation, depending on the gravity parameter, which may give rise to extremely large-amplitude responses. The system may also experience flutter instability due to a supercritical Hopf bifurcation, which brings about self-excited periodic oscillations. The generic behavior of system for a specific range of the gravity parameter is investigated across four distinct scenarios, which vary based on the gravity parameter and mass ratio. Notably, only one of these scenarios is analogous to the situation that comes to pass for the hanging case.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134478"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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-Hermitian gravitational effects on Bose–Einstein condensate

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134456

Tie-Fu Zhang , Chengxi Li , Yitong Pei , Kai Liu , Wu-Ming Liu

We investigated the impact of Non-Hermitian gravitational potentials on the spatial distribution of Bose–Einstein condensate (BEC) wave functions. Through numerical solutions of the Gross–Pitaevskii (GP) equation, we observed that the imaginary component of Non-Hermitian gravitational potentials affects the spatial periodicity of the BEC wave function phase, resulting in spatial displacement of the wave function’s peak. By formulating equations describing the momentum of the BEC wave function with respect to Non-Hermitian gravitational potential parameters and solving and analyzing them under specific conditions, we provided a reasoned interpretation of the numerical results. Our results also can be simulated experimentally with the help of electron beam technique. Our findings contribute to exploring the physical essence of Non-Hermitian gravitational potentials and their impact on BEC, offering theoretical guidance for potential related experiments.

引用次数: 0

Logarithmic lattice models for flows with boundaries

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134473

Ciro S. Campolina , Alexei A. Mailybaev

Many fundamental problems in fluid dynamics are related to the effects of solid boundaries. In general, they install sharp gradients and contribute to the development of small-scale structures, which are computationally expensive to resolve with numerical simulations. A way to access extremely fine scales with a reduced number of degrees of freedom is to consider the equations on logarithmic lattices in Fourier space. Here we introduce new toy models for flows with walls, by showing how to add boundaries to the logarithmic lattice framework. The resulting equations retain many important properties of the original systems, such as the conserved quantities, the symmetries and the boundary effects. We apply this technique to many flows, with emphasis on the inviscid limit of the Navier–Stokes equations. For this setup, simulations reach impressively large Reynolds numbers and disclose interesting insights about the original problem.

引用次数: 0

New frameworks of PFM for thermal fracturing in the linear thermoelasticity solids based on a microforce balance approach

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134498

Sayahdin Alfat

Crack propagation due to thermal expansion is one of the multi-physics problems which be a concern to many researchers. Therefore, we study thermal fracturing using the phase field model (or, PFM). Here, the new models to study thermal fracturing in linear thermoelasticity solids are proposed through PFM. Herein, the damage evolution equation is directly derived through the microforce balance approach or the Gurtin concept, while the heat evolution equation is derived through the first principle of thermodynamics. Furthermore, the thermodynamic consistency of the model is shown by Clausius–Duhem inequality. In particular, the Gurtin concept and the first principle of thermodynamics follow the entropy, internal energy, Helmholtz free energy, and energy dissipation functions which are based on the Biot of thermoelasticity model and the Ambrosio–Tortorelli regularization. Since our models are based on the microforce balance approach, we also derive the PFM for crack propagation which was proposed by Kimura and Takaishi via this approach. In the present study, we validate our proposed PFMs through several numerical experiments. Herein, we solve the numerical experiments using the adaptive finite element method. From these, good agreements are achieved between our models and the previous model.

{"title":"New frameworks of PFM for thermal fracturing in the linear thermoelasticity solids based on a microforce balance approach","authors":"Sayahdin Alfat","doi":"10.1016/j.physd.2024.134498","DOIUrl":"10.1016/j.physd.2024.134498","url":null,"abstract":"<div><div>Crack propagation due to thermal expansion is one of the multi-physics problems which be a concern to many researchers. Therefore, we study thermal fracturing using the phase field model (or, PFM). Here, the new models to study thermal fracturing in linear thermoelasticity solids are proposed through PFM. Herein, the damage evolution equation is directly derived through the microforce balance approach or the Gurtin concept, while the heat evolution equation is derived through the first principle of thermodynamics. Furthermore, the thermodynamic consistency of the model is shown by Clausius–Duhem inequality. In particular, the Gurtin concept and the first principle of thermodynamics follow the entropy, internal energy, Helmholtz free energy, and energy dissipation functions which are based on the Biot of thermoelasticity model and the Ambrosio–Tortorelli regularization. Since our models are based on the microforce balance approach, we also derive the PFM for crack propagation which was proposed by Kimura and Takaishi via this approach. In the present study, we validate our proposed PFMs through several numerical experiments. Herein, we solve the numerical experiments using the adaptive finite element method. From these, good agreements are achieved between our models and the previous model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134498"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Full Lyapunov exponents spectrum with Deep Learning from single-variable time series

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134510

Carmen Mayora-Cebollero , Ana Mayora-Cebollero , Álvaro Lozano , Roberto Barrio

In this article we study if a Deep Learning technique can be used to obtain an approximate value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide the full Lyapunov exponents spectrum with just single-variable time series. We train a Convolutional Neural Network and use the resulting network to approximate the full spectrum using the time series of just one variable from the studied systems (Lorenz system and coupled Lorenz system). The results are quite surprising since all the values are well approximated with only partial data. This strategy allows to speed up the complete analysis of the systems and also to study the hyperchaotic dynamics in the coupled Lorenz system.

引用次数: 0

Flow time history deep learning for feature decomposition and disentanglement

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134470

Qingliang Zhan , Xin Liu , Chunjin Bai , Yang Chao , Dongming Bao , Zhiyong Wang , Xiannian Sun

Machine intelligence has recently played an increasingly important role in the study of fluids. It would be a promising way to use machine intelligence to decompose and disentangle the massive flow data to mine the underlying flow knowledge. In this study, by extracting and disentangling the temporal features hidden in the flow time history (FTH) data, the flow feature is decomposed and disentangled in a deep learning manner. To preserve the spatial information of data, observed sampling at each position is compressed into a low dimensional latent code by the encoder, and then the decoder acts as a mapping from the latent space to the high dimensional FTH space, forming an unsupervised FTH feature decomposition algorithm. The laminar and turbulent flow around circular cylinder at Re=100 and Re=3900 are analyzed using FTH deep learning. Results of laminar case show that the code parameters of each FTH sample represent the weight of basic temporal features at that particular flow position, whereas the distribution of the latent code represents the corresponding spatial feature. Additionally, the turbulence results indicate that the proposed method achieves more accurate reconstruction outcomes than conventional linear-theory-based methods while maintaining independence of decomposed feature. This work shows that the FTH deep learning models are high accuracy approaches to learn the disentangled flow knowledge directly from the raw point-based data.

{"title":"Flow time history deep learning for feature decomposition and disentanglement","authors":"Qingliang Zhan , Xin Liu , Chunjin Bai , Yang Chao , Dongming Bao , Zhiyong Wang , Xiannian Sun","doi":"10.1016/j.physd.2024.134470","DOIUrl":"10.1016/j.physd.2024.134470","url":null,"abstract":"<div><div>Machine intelligence has recently played an increasingly important role in the study of fluids. It would be a promising way to use machine intelligence to decompose and disentangle the massive flow data to mine the underlying flow knowledge. In this study, by extracting and disentangling the temporal features hidden in the flow time history (FTH) data, the flow feature is decomposed and disentangled in a deep learning manner. To preserve the spatial information of data, observed sampling at each position is compressed into a low dimensional latent code by the encoder, and then the decoder acts as a mapping from the latent space to the high dimensional FTH space, forming an unsupervised FTH feature decomposition algorithm. The laminar and turbulent flow around circular cylinder at <em>Re</em>=100 and <em>Re</em>=3900 are analyzed using FTH deep learning. Results of laminar case show that the code parameters of each FTH sample represent the weight of basic temporal features at that particular flow position, whereas the distribution of the latent code represents the corresponding spatial feature. Additionally, the turbulence results indicate that the proposed method achieves more accurate reconstruction outcomes than conventional linear-theory-based methods while maintaining independence of decomposed feature. This work shows that the FTH deep learning models are high accuracy approaches to learn the disentangled flow knowledge directly from the raw point-based data.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134470"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Analytical results for chromatin polymer models with enhancer-promoter interactions

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134511

Zihang Huang, Haowen Chen, Wenjie Cao, Jiaqi Teng, Tianshou Zhou

Complex chromosomal organizations can be currently measured by experimental technologies, but spatiotemporal dynamics of the chromatin remain elusive. Here we analyze a chromatin polymer model with long-range interactions that account for the communications between multiple enhancer and promoter (E-P) pairs. We analytically show that the relaxation times of the nucleosomes emerges in hierarchy and the mean square displacement of every nucleosome grows over time in a power law. We find that more E-P pairs change neither the relaxation time hierarchy nor the diffusion mode of the nucleosomes. We also derive the analytical expressions for the joint probability distribution of nucleosome spatial positions and for the distribution of the spatial distance between any two loci, finding that the latter is a Maxwell-Boltzmann distribution rather than the previously assumed Gauss distribution. In addition, we present a method for calculating the encounter probability between any two nucleosomes, and numerically verify that this probability is approximately inversely proportional to the mean spatial distance between the two nucleosomes. These analytical results reveal the essence of chromatin organization and lay a solid foundation for further studying transcriptional dynamics regulated by E-P communications.

{"title":"Analytical results for chromatin polymer models with enhancer-promoter interactions","authors":"Zihang Huang, Haowen Chen, Wenjie Cao, Jiaqi Teng, Tianshou Zhou","doi":"10.1016/j.physd.2024.134511","DOIUrl":"10.1016/j.physd.2024.134511","url":null,"abstract":"<div><div>Complex chromosomal organizations can be currently measured by experimental technologies, but spatiotemporal dynamics of the chromatin remain elusive. Here we analyze a chromatin polymer model with long-range interactions that account for the communications between multiple enhancer and promoter (E-P) pairs. We analytically show that the relaxation times of the nucleosomes emerges in hierarchy and the mean square displacement of every nucleosome grows over time in a power law. We find that more E-P pairs change neither the relaxation time hierarchy nor the diffusion mode of the nucleosomes. We also derive the analytical expressions for the joint probability distribution of nucleosome spatial positions and for the distribution of the spatial distance between any two loci, finding that the latter is a Maxwell-Boltzmann distribution rather than the previously assumed Gauss distribution. In addition, we present a method for calculating the encounter probability between any two nucleosomes, and numerically verify that this probability is approximately inversely proportional to the mean spatial distance between the two nucleosomes. These analytical results reveal the essence of chromatin organization and lay a solid foundation for further studying transcriptional dynamics regulated by E-P communications.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134511"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Variable coefficient-informed neural network for PDE inverse problem in fluid dynamics

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134362

Che Han , Xing Lü

Variable-coefficient equations are crucial in the field of fluid dynamics as they accurately capture the spatial and temporal properties of fluid. In many cases, there exist some constraints among the coefficients and embedding these constraints into neural networks poses a challenge. In this paper, we design a variable coefficient-informed neural network (VCINN) to address the inverse problem of variable-coefficient partial differential equation in fluid dynamics. The VCINN framework integrates the physics-informed neural network (PINN) with the constraints among multiple coefficients, encoding both constraints and physics information into the neural networks. Compared to classical PINN, VCINN enjoys such advantages as parallelization capacity, embedding constraint information and efficient hyperparameter adjustment. Through a series of examples, the capability of the approach to recover coefficients from observations has been validated. Numerical results indicate that the present method achieves higher accuracy and lower training error compared to classical PINN.

引用次数: 0

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