Pub Date : 2025-01-20DOI: 10.1016/j.cnsns.2025.108623
Yan Wang, Baoli Yin, Yang Liu, Hong Li
The paper focuses on numerically solving the nonlinear time fractional Schrödinger equations. The modified Crank–Nicolson scheme is used for the time discretization and the Galerkin finite element approximation is used in the spatial direction. Besides, we provide the proofs of stability by mathematical induction and unconditionally optimal error estimates by a discrete fractional Grönwall inequality derived in this paper, Sobolev embedding theorems and some other inequalities for the fully discrete linearized modified Galerkin finite element scheme. Furthermore, a transformed Crank–Nicolson Galerkin finite element method based on the change of variable is constructed on the uniform space–time mesh for solving the nonlinear time fractional Schrödinger equations with nonsmooth solutions. Finally, the numerical experiments clearly and accurately demonstrate the rationality of the numerical scheme and the correctness of the theoretical results.
{"title":"Modified L1 Crank–Nicolson finite element methods with unconditional convergence for nonlinear time-fractional Schrödinger equations","authors":"Yan Wang, Baoli Yin, Yang Liu, Hong Li","doi":"10.1016/j.cnsns.2025.108623","DOIUrl":"10.1016/j.cnsns.2025.108623","url":null,"abstract":"<div><div>The paper focuses on numerically solving the nonlinear time fractional Schrödinger equations. The modified <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span> Crank–Nicolson scheme is used for the time discretization and the Galerkin finite element approximation is used in the spatial direction. Besides, we provide the proofs of stability by mathematical induction and unconditionally optimal error estimates by a discrete fractional Grönwall inequality derived in this paper, Sobolev embedding theorems and some other inequalities for the fully discrete linearized modified <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span> Galerkin finite element scheme. Furthermore, a transformed <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span> Crank–Nicolson Galerkin finite element method based on the change of variable <span><math><mrow><mi>t</mi><mo>=</mo><msup><mrow><mi>s</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>α</mi></mrow></msup></mrow></math></span> is constructed on the uniform space–time mesh for solving the nonlinear time fractional Schrödinger equations with nonsmooth solutions. Finally, the numerical experiments clearly and accurately demonstrate the rationality of the numerical scheme and the correctness of the theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108623"},"PeriodicalIF":3.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057371","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 : 2025-01-20DOI: 10.1016/j.cnsns.2025.108618
Xiaolu Lin , Shenzhou Zheng
In this paper, we investigate the multiplicity and concentration of normalized solutions to a fractional logarithmic Schrödinger problem with the prescribed mass , where , is unknown and appears as a Lagrange multiplier. By the minimization method combined with penalization technique and Ljusternik–Schnirelmann theory, we prove the multiplicity of normalized solutions where the numbers of normalized solutions are linked to the topology of the set where potential attains its minimum. Moreover, the concentration and decay of normalized solutions are analyzed in the end. The above properties of our normalized solutions are also new, even for .
{"title":"On the number of normalized solutions for a fractional Schrödinger problem with logarithmic nonlinearity","authors":"Xiaolu Lin , Shenzhou Zheng","doi":"10.1016/j.cnsns.2025.108618","DOIUrl":"10.1016/j.cnsns.2025.108618","url":null,"abstract":"<div><div>In this paper, we investigate the multiplicity and concentration of normalized solutions to a fractional logarithmic Schrödinger problem <span><math><mrow><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>2</mn><mi>s</mi></mrow></msup><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mi>λ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>log</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mspace></mspace><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> with the prescribed mass <span><math><mrow><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><mi>a</mi><msup><mrow><mi>ɛ</mi></mrow><mrow><mi>N</mi></mrow></msup><mspace></mspace><mtext>with</mtext><mspace></mspace><mi>a</mi><mo>></mo><mn>0</mn></mrow></math></span>, where <span><math><mrow><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span> is unknown and appears as a Lagrange multiplier. By the minimization method combined with penalization technique and Ljusternik–Schnirelmann theory, we prove the multiplicity of normalized solutions where the numbers of normalized solutions are linked to the topology of the set where potential <span><math><mi>V</mi></math></span> attains its minimum. Moreover, the concentration and decay of normalized solutions are analyzed in the end. The above properties of our normalized solutions are also new, even for <span><math><mrow><mi>s</mi><mo>=</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108618"},"PeriodicalIF":3.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021213","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 : 2025-01-19DOI: 10.1016/j.cnsns.2025.108638
Eunjung Lee , Uranchimeg Dorligjav , Richard James , Bowoon Kim , Hyung Uk Cho , Seungin Baek
The investigation of quantum dots, semiconductor structures renowned for their unique electronic and optical properties, has attracted considerable interest due to their diverse applications, spanning photovoltaics, optical communication, and quantum computing. However, the complex nature of multi-layered quantum dots, combined with their non-equilibrium behavior, presents a significant challenge in accurately describing their electronic properties. In response to this challenge, the Non-Equilibrium Green's Function method (NEGF) has emerged as a leading theoretical framework for studying electronic behavior in quantum devices, providing a robust approach to understanding non-equilibrium transport phenomena. While the NEGF method offers powerful insights into electronic transport in nanostructures, its computational requirements can be formidable, especially for large three-dimensional and complex geometries. This paper explores the application of the three-dimensional NEGF method to analyze multi-layered quantum dots, focusing on the complexities involved in simulating their electronic behavior. We propose a novel approach using low-rank approximation and pseudoinverse techniques to efficiently compute the nonequilibrium electron density matrix. This method relies on the block structure of the self-energy matrices and reduces the calculation time by a factor of 60 or more, while maintaining similar accuracy, as confirmed by the numerical results. We further discuss several strategies for handling these computational challenges, offering valuable insights into speeding up three-dimensional NEGF calculations.
{"title":"A new approach for efficient nonequilibrium quantum transport computation in electroluminescent quantum dots","authors":"Eunjung Lee , Uranchimeg Dorligjav , Richard James , Bowoon Kim , Hyung Uk Cho , Seungin Baek","doi":"10.1016/j.cnsns.2025.108638","DOIUrl":"10.1016/j.cnsns.2025.108638","url":null,"abstract":"<div><div>The investigation of quantum dots, semiconductor structures renowned for their unique electronic and optical properties, has attracted considerable interest due to their diverse applications, spanning photovoltaics, optical communication, and quantum computing. However, the complex nature of multi-layered quantum dots, combined with their non-equilibrium behavior, presents a significant challenge in accurately describing their electronic properties. In response to this challenge, the Non-Equilibrium Green's Function method (NEGF) has emerged as a leading theoretical framework for studying electronic behavior in quantum devices, providing a robust approach to understanding non-equilibrium transport phenomena. While the NEGF method offers powerful insights into electronic transport in nanostructures, its computational requirements can be formidable, especially for large three-dimensional and complex geometries. This paper explores the application of the three-dimensional NEGF method to analyze multi-layered quantum dots, focusing on the complexities involved in simulating their electronic behavior. We propose a novel approach using low-rank approximation and pseudoinverse techniques to efficiently compute the nonequilibrium electron density matrix. This method relies on the block structure of the self-energy matrices and reduces the calculation time by a factor of 60 or more, while maintaining similar accuracy, as confirmed by the numerical results. We further discuss several strategies for handling these computational challenges, offering valuable insights into speeding up three-dimensional NEGF calculations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108638"},"PeriodicalIF":3.4,"publicationDate":"2025-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-18DOI: 10.1016/j.cnsns.2025.108620
A. Murillo , A. Vieiro
The 2-jet normal form of the elliptic volume-preserving Hopf-zero bifurcation provides a one-parameter family of volume-preserving vector fields with a pair of saddle-foci points whose 2-dimensional invariant manifolds form a 2-sphere of spiralling heteroclinic orbits. We study the effect of an external periodic forcing on the splitting of these 2-dimensional invariant manifolds. The internal frequency (related to the foci and already presented in the unperturbed system) interacts with an external one (coming from the periodic forcing). If both frequencies are incommensurable, this interaction leads to quasi-periodicity in the splitting behaviour, which is exponentially small in (a suitable function of) the unfolding parameter of the Hopf-zero bifurcation. The corresponding behaviour is described by a Melnikov function. The changes of dominant harmonics correspond to primary quadratic tangencies between the invariant manifolds. Combining analytical and numerical results, we provide a detailed description of the asymptotic behaviour of the splitting under concrete arithmetic properties of the frequencies.
{"title":"Periodic perturbation of a 3D conservative flow with a heteroclinic connection to saddle-foci","authors":"A. Murillo , A. Vieiro","doi":"10.1016/j.cnsns.2025.108620","DOIUrl":"10.1016/j.cnsns.2025.108620","url":null,"abstract":"<div><div>The 2-jet normal form of the elliptic volume-preserving Hopf-zero bifurcation provides a one-parameter family of volume-preserving vector fields with a pair of saddle-foci points whose 2-dimensional invariant manifolds form a 2-sphere of spiralling heteroclinic orbits. We study the effect of an external periodic forcing on the splitting of these 2-dimensional invariant manifolds. The internal frequency (related to the foci and already presented in the unperturbed system) interacts with an external one (coming from the periodic forcing). If both frequencies are incommensurable, this interaction leads to quasi-periodicity in the splitting behaviour, which is exponentially small in (a suitable function of) the unfolding parameter of the Hopf-zero bifurcation. The corresponding behaviour is described by a Melnikov function. The changes of dominant harmonics correspond to primary quadratic tangencies between the invariant manifolds. Combining analytical and numerical results, we provide a detailed description of the asymptotic behaviour of the splitting under concrete arithmetic properties of the frequencies.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108620"},"PeriodicalIF":3.4,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021216","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 : 2025-01-18DOI: 10.1016/j.cnsns.2025.108636
Sandang Guo, Jing Jia, Xu Han, Shuaishuai Geng
As China modernizes its industries, predicting innovation performance in high-tech industries is essential for crafting innovation-driven strategies. However, the system output of high-tech industries is influenced by multiple input factors with interaction effects, often exhibiting non-linearity and uncertainty. To address this, a novel nonlinear multivariate grey Bernoulli model considering interaction effects, IENGBM(1,N), has been developed. This model identifies interaction effects between factors and the nonlinear features of the system, more flexibly capturing the fluctuating and nonlinear trend of innovation performance. This paper conducts a quantitative selection of modeling data instead of the former, which is a more rigorous way. Moreover, a comprehensive framework integrating particle swarm optimization (PSO), Monte Carlo simulation, and probability density analysis (PDA) is designed to enhance and validate the model's predictive accuracy. The model's solution is optimized, effectively eliminating jump errors. Experimental results show that the IENGBM(1,N) model with strong robustness outperforms five compare models in two cases, with fitting MAPE of 1.97 % and 2.97 %, and testing MAPE of 1.61 % and 1.44 %, respectively, and this verifies the absence of overfitting in the model. Lastly, the proposed model has been utilized to forecast the innovation performance of high-tech industries and their sub-industries in the feature, providing a practical and effective prediction tool.
{"title":"A nonlinear multivariate grey Bernoulli model for predicting innovation performance in high-tech industries","authors":"Sandang Guo, Jing Jia, Xu Han, Shuaishuai Geng","doi":"10.1016/j.cnsns.2025.108636","DOIUrl":"10.1016/j.cnsns.2025.108636","url":null,"abstract":"<div><div>As China modernizes its industries, predicting innovation performance in high-tech industries is essential for crafting innovation-driven strategies. However, the system output of high-tech industries is influenced by multiple input factors with interaction effects, often exhibiting non-linearity and uncertainty. To address this, a novel nonlinear multivariate grey Bernoulli model considering interaction effects, IENGBM(1,N), has been developed. This model identifies interaction effects between factors and the nonlinear features of the system, more flexibly capturing the fluctuating and nonlinear trend of innovation performance. This paper conducts a quantitative selection of modeling data instead of the former, which is a more rigorous way. Moreover, a comprehensive framework integrating particle swarm optimization (PSO), Monte Carlo simulation, and probability density analysis (PDA) is designed to enhance and validate the model's predictive accuracy. The model's solution is optimized, effectively eliminating jump errors. Experimental results show that the IENGBM(1,N) model with strong robustness outperforms five compare models in two cases, with fitting MAPE of 1.97 % and 2.97 %, and testing MAPE of 1.61 % and 1.44 %, respectively, and this verifies the absence of overfitting in the model. Lastly, the proposed model has been utilized to forecast the innovation performance of high-tech industries and their sub-industries in the feature, providing a practical and effective prediction tool.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108636"},"PeriodicalIF":3.4,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057374","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 : 2025-01-18DOI: 10.1016/j.cnsns.2025.108603
Wei Hu , Jihao Long , Yaohua Zang , Weinan E , Jiequn Han
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for the optimal control problem of such hybrid dynamical systems based on solving the equations derived from the hybrid minimum principle (HMP). The algorithm is an iterative scheme following the spirit of the method of successive approximations (MSA), and it is robust to undesired collisions observed in the initial guesses. We propose several techniques to address the additional numerical challenges introduced by the presence of discontinuities. The algorithm is tested on disc collision problems whose optimal solutions exhibit one or multiple collisions. Linear convergence in terms of iteration steps and asymptotic first-order accuracy in terms of time discretization are observed when the algorithm is implemented with the forward-Euler scheme. The numerical results demonstrate that the proposed algorithm has better accuracy and convergence than direct methods based on gradient descent. Furthermore, the algorithm is also simpler, more accurate, and more stable than a deep reinforcement learning method.
{"title":"Solving optimal control problems of rigid-body dynamics with collisions using the hybrid minimum principle","authors":"Wei Hu , Jihao Long , Yaohua Zang , Weinan E , Jiequn Han","doi":"10.1016/j.cnsns.2025.108603","DOIUrl":"10.1016/j.cnsns.2025.108603","url":null,"abstract":"<div><div>Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for the optimal control problem of such hybrid dynamical systems based on solving the equations derived from the hybrid minimum principle (HMP). The algorithm is an iterative scheme following the spirit of the method of successive approximations (MSA), and it is robust to undesired collisions observed in the initial guesses. We propose several techniques to address the additional numerical challenges introduced by the presence of discontinuities. The algorithm is tested on disc collision problems whose optimal solutions exhibit one or multiple collisions. Linear convergence in terms of iteration steps and asymptotic first-order accuracy in terms of time discretization are observed when the algorithm is implemented with the forward-Euler scheme. The numerical results demonstrate that the proposed algorithm has better accuracy and convergence than direct methods based on gradient descent. Furthermore, the algorithm is also simpler, more accurate, and more stable than a deep reinforcement learning method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108603"},"PeriodicalIF":3.4,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057376","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 : 2025-01-18DOI: 10.1016/j.cnsns.2025.108621
Jiaojiao Sun, Zhiqiang Luo, Bo Yan
Mechanical metamaterials are a class of artificially designed structures usually modeled as high degree-of-freedom (DOF) systems. They, particularly nonlinear mechanical metamaterials, are widely applied in vibration suppression. This manuscript proposes a method to study the stochastic stability of nonlinear mechanical metamaterial systems under combined Gaussian and Poisson white noises. The mathematical model of a nonlinear mechanical metamaterial with coupled elements is established, and its governing equation, which is a high-DOF nonlinear stochastic differential equation, is derived. To bypass the challenge of calculating multiple Lyapunov exponents, the governing equation is reduced as a one-dimensional averaged stochastic differential equation by applying the stochastic averaging method. The specific expression of the Lyapunov exponent of the one-dimensional equation is derived by using the two-step generalized elliptic coordinate transformations, and its sign yields the necessary and sufficient condition of stochastic stability. A nonlinear mechanical metamaterial with 10 coupled elements is taken as an example to illustrate the effectiveness of the proposed procedure and to investigate the effect of system parameters on the stochastic stability of nonlinear mechanical metamaterials.
{"title":"Stochastic stability of nonlinear mechanical metamaterial systems under combined Gaussian and Poisson white noises","authors":"Jiaojiao Sun, Zhiqiang Luo, Bo Yan","doi":"10.1016/j.cnsns.2025.108621","DOIUrl":"10.1016/j.cnsns.2025.108621","url":null,"abstract":"<div><div>Mechanical metamaterials are a class of artificially designed structures usually modeled as high degree-of-freedom (DOF) systems. They, particularly nonlinear mechanical metamaterials, are widely applied in vibration suppression. This manuscript proposes a method to study the stochastic stability of nonlinear mechanical metamaterial systems under combined Gaussian and Poisson white noises. The mathematical model of a nonlinear mechanical metamaterial with <span><math><mi>n</mi></math></span> coupled elements is established, and its governing equation, which is a high-DOF nonlinear stochastic differential equation, is derived. To bypass the challenge of calculating multiple Lyapunov exponents, the governing equation is reduced as a one-dimensional averaged stochastic differential equation by applying the stochastic averaging method. The specific expression of the Lyapunov exponent of the one-dimensional equation is derived by using the two-step generalized elliptic coordinate transformations, and its sign yields the necessary and sufficient condition of stochastic stability. A nonlinear mechanical metamaterial with 10 coupled elements is taken as an example to illustrate the effectiveness of the proposed procedure and to investigate the effect of system parameters on the stochastic stability of nonlinear mechanical metamaterials.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108621"},"PeriodicalIF":3.4,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021215","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}
The viscosity of the cytosol plays a crucial role in the biology of microtubules (MTs), affecting their architecture and dynamics function. Understanding the overall functionality of this parameter is essential. The effect of viscosity on MT dynamics is studied when modelling longitudinal and angular displacements. The rotating wave approximation is used to derive two uncoupled complex Ginzburg–Landau (CGL) equations for the longitudinal and angular displacements, respectively. Then, analytical two solitary wave solution types are constructed using the modified Hirota bilinear method. Its appears that the viscosity dampens the longitudinal displacements of MTs by significantly reducing the magnitude of longitudinal waves. In the case of angular displacements, the influence of viscosity is negligible, such that MTs angular displacements are transparent to viscosity. Our analytical predictions are confirmed by numerical solutions with pretty much high accuracy. The solutions obtained offer promising prospects for regulating the viscosity of the cytosol in order to control the assembly, disassembly and stability of MTs.
{"title":"Nonlinear dynamics effect of viscosity of cytosol into the microtubules and exact solutions","authors":"Tabapsi Kamdem Rostand , Belobo Belobo Didier , Bansi Kamdem Christel Delphin , Dang Koko Adamou , Tabi Conrad Bertrand , Kofané Timoléon Crépin","doi":"10.1016/j.cnsns.2025.108615","DOIUrl":"10.1016/j.cnsns.2025.108615","url":null,"abstract":"<div><div>The viscosity of the cytosol plays a crucial role in the biology of microtubules (MTs), affecting their architecture and dynamics function. Understanding the overall functionality of this parameter is essential. The effect of viscosity on MT dynamics is studied when modelling longitudinal and angular displacements. The rotating wave approximation is used to derive two uncoupled complex Ginzburg–Landau (CGL) equations for the longitudinal and angular displacements, respectively. Then, analytical two solitary wave solution types are constructed using the modified Hirota bilinear method. Its appears that the viscosity dampens the longitudinal displacements of MTs by significantly reducing the magnitude of longitudinal waves. In the case of angular displacements, the influence of viscosity is negligible, such that MTs angular displacements are transparent to viscosity. Our analytical predictions are confirmed by numerical solutions with pretty much high accuracy. The solutions obtained offer promising prospects for regulating the viscosity of the cytosol in order to control the assembly, disassembly and stability of MTs.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108615"},"PeriodicalIF":3.4,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021218","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 : 2025-01-17DOI: 10.1016/j.cnsns.2025.108607
Ying Jing, Youguo Wang, Qiqing Zhai
The processes and control of information diffusion have received significant attention in the information age. Considering the prevalent environmental noise and individual memory, this paper constructs a variable-order fractional information diffusion model on heterogeneous networks, incorporating internal Gaussian white noise and external Lévy noise. Since the introduction of noise leading to stochastic resonance, we define a metric of generalized signal-to-noise ratio (GSNR) to measure the gain effect of noise on the system. To effectively suppress the spread of negative information and promote the dissemination of positive information within the constraints of limited resources, the dynamic event-triggered impulsive control (DETIC) is designed to the variable-order fractional negative–positive information diffusion model with short memory induced by internal and external noise, where it successfully prevent impulse signals from disrupting the non-locality of the fractional-order operator. Besides, the exclusion of Zeno behavior and the stability of the controlled system are proved and it is demonstrated that the minimum execution interval are not less than the corresponding static event-triggered mechanism. Employing the particle swarm optimization (PSO) algorithm, we determine the optimal noise intensities based on the GSNR, along with the optimal DETIC. Comparative experiments and the instance show that the combination of optimal noise intensities and optimal DETIC achieve the best results in suppressing the diffusion of negative information and promoting the dissemination of positive information, which provides valuable guidance for controlling the information diffusion.
{"title":"Stochastic resonance and dynamic event-triggered impulsive control of a variable-order fractional information diffusion system with hybrid noise","authors":"Ying Jing, Youguo Wang, Qiqing Zhai","doi":"10.1016/j.cnsns.2025.108607","DOIUrl":"10.1016/j.cnsns.2025.108607","url":null,"abstract":"<div><div>The processes and control of information diffusion have received significant attention in the information age. Considering the prevalent environmental noise and individual memory, this paper constructs a variable-order fractional information diffusion model on heterogeneous networks, incorporating internal Gaussian white noise and external Lévy noise. Since the introduction of noise leading to stochastic resonance, we define a metric of generalized signal-to-noise ratio (GSNR) to measure the gain effect of noise on the system. To effectively suppress the spread of negative information and promote the dissemination of positive information within the constraints of limited resources, the dynamic event-triggered impulsive control (DETIC) is designed to the variable-order fractional negative–positive information diffusion model with short memory induced by internal and external noise, where it successfully prevent impulse signals from disrupting the non-locality of the fractional-order operator. Besides, the exclusion of Zeno behavior and the stability of the controlled system are proved and it is demonstrated that the minimum execution interval are not less than the corresponding static event-triggered mechanism. Employing the particle swarm optimization (PSO) algorithm, we determine the optimal noise intensities based on the GSNR, along with the optimal DETIC. Comparative experiments and the instance show that the combination of optimal noise intensities and optimal DETIC achieve the best results in suppressing the diffusion of negative information and promoting the dissemination of positive information, which provides valuable guidance for controlling the information diffusion.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108607"},"PeriodicalIF":3.4,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021244","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 : 2025-01-17DOI: 10.1016/j.cnsns.2025.108609
Fei Zhu
In this paper, we study the expansion of Noble-Abel gas into the vacuum around a convex corner for the two-dimensional compressible magnetohydrodynamic system. Unlike previous studies, we study the incoming flow at sound speed, a discontinuous boundary value problem for a two-dimensional set of magnetohydrodynamic equations. When , the technical difficulty of the point being a singularity arises. To overcome this difficulty, we initially set up consistent “interior” , calculations for various solutions to the regularized boundary value issue, followed by applying the Arzela–Ascoli theorem and conventional diagonalization methods to develop universal Lipschitz continuous solutions.
{"title":"Expansion of magnetic fluid around a convex corner into vacuum","authors":"Fei Zhu","doi":"10.1016/j.cnsns.2025.108609","DOIUrl":"10.1016/j.cnsns.2025.108609","url":null,"abstract":"<div><div>In this paper, we study the expansion of Noble-Abel gas into the vacuum around a convex corner for the two-dimensional compressible magnetohydrodynamic system. Unlike previous studies, we study the incoming flow at sound speed, a discontinuous boundary value problem for a two-dimensional set of magnetohydrodynamic equations. When <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>, the technical difficulty of the <span><math><mi>O</mi></math></span> point being a singularity arises. To overcome this difficulty, we initially set up consistent “interior” <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> calculations for various solutions to the regularized boundary value issue, followed by applying the Arzela–Ascoli theorem and conventional diagonalization methods to develop universal Lipschitz continuous solutions.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108609"},"PeriodicalIF":3.4,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021247","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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