Pub Date : 2025-01-22DOI: 10.1016/j.cnsns.2025.108629
Debkumar Chakraborty, Biplab Maity, Samiran Ghosh
The rational breathers (Akhmediev, Kuznetsov-Ma, Peregrine) through the modulation instability (MI) are excited in positive ion - negative ion collisional plasmas by means of analytical and computation. The dynamics of the modulated waves are modeled by a nonlinear Schrödinger type equation with a linear damping term that arises due to the ion-ion weak collision. Both the low and high frequency waves undergo MI in a certain parameter space (that depends on the mass and temperature of both the ions). The computation on the basis of experimental parameters reveal the formation of rational breathers on a finite background in PINI plasmas. The weak collisional dissipation delays the wave focusing process of the rational breathers and also enhance the amplitude of the second wave focusing in the Akhmediev breather dynamics.
{"title":"Modulated wave dynamics and excitation of rational breathers in positive ion–negative ion collisional plasmas","authors":"Debkumar Chakraborty, Biplab Maity, Samiran Ghosh","doi":"10.1016/j.cnsns.2025.108629","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108629","url":null,"abstract":"The rational breathers (Akhmediev, Kuznetsov-Ma, Peregrine) through the modulation instability (MI) are excited in positive ion - negative ion collisional plasmas by means of analytical and computation. The dynamics of the modulated waves are modeled by a nonlinear Schrödinger type equation with a linear damping term that arises due to the ion-ion weak collision. Both the low and high frequency waves undergo MI in a certain parameter space (that depends on the mass and temperature of both the ions). The computation on the basis of experimental parameters reveal the formation of rational breathers on a finite background in PINI plasmas. The weak collisional dissipation delays the wave focusing process of the rational breathers and also enhance the amplitude of the second wave focusing in the Akhmediev breather dynamics.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"53 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057365","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 : 2025-01-21DOI: 10.1016/j.cnsns.2025.108616
Yifan Wang, Wei Sun
This study focuses on an adaptive decentralized control problem for second-order large-scale interconnected nonlinear systems with uncertainties. The proposed control method is the first study of second-order large-scale systems using fully actuated system approach, considering that most real physical systems are second-order, whereas the existing literature on large-scale systems primarily considers first-order systems. By integrating the fully actuated system approach, decentralized control and adaptive technology, a novel controller is devised to ensure that the signals of the closed-loop system remain semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero. Finally, a numerical simulation example is presented to validate the effectiveness of the proposed control method.
{"title":"Adaptive decentralized control for second-order large-scale nonlinear systems via fully actuated system approach","authors":"Yifan Wang, Wei Sun","doi":"10.1016/j.cnsns.2025.108616","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108616","url":null,"abstract":"This study focuses on an adaptive decentralized control problem for second-order large-scale interconnected nonlinear systems with uncertainties. The proposed control method is the first study of second-order large-scale systems using fully actuated system approach, considering that most real physical systems are second-order, whereas the existing literature on large-scale systems primarily considers first-order systems. By integrating the fully actuated system approach, decentralized control and adaptive technology, a novel controller is devised to ensure that the signals of the closed-loop system remain semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero. Finally, a numerical simulation example is presented to validate the effectiveness of the proposed control method.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"30 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057370","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 : 2025-01-21DOI: 10.1016/j.cnsns.2025.108624
Yanping Qiu, Jun Cheng, Zhidong Zhou, Jinde Cao
This paper focuses on the distributed filter issue for a class of nonlinear systems under hybrid cyber-attacks, encompassing both deception attacks and denial of service (DoS) attacks with uncertain attack probabilities. In the sensor network, each filter estimates the output signals of the systems by dealing with the output measurements from the systems and the information received from its neighbors and each filter may receive the state estimation information affected by outliers from its neighbors, which is propagated based on the communication topology. With the purpose of mitigating the effects from channel noise during the signal transmission on filtering error systems (FES) and the potential anomalies’ impact in signal transmission caused by the hybrid cyber-attacks, a dynamic saturation function-based distributed filter is designed during the filtering process, whose saturation level is adaptively varying based on previous measurement errors. Through this approach and by utilizing Lyapunov-Krasovskii theory, sufficient conditions are established to ensure the stochastic stability (SS) of the FES and to achieve the predefined H∞ performance objectives. Finally, a practical model is presented to demonstrate the effectiveness and practicality of the designed distributed filter methodology.
{"title":"Distributed filtering for T-S fuzzy systems under cyber-attacks with time-varying saturation function","authors":"Yanping Qiu, Jun Cheng, Zhidong Zhou, Jinde Cao","doi":"10.1016/j.cnsns.2025.108624","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108624","url":null,"abstract":"This paper focuses on the distributed filter issue for a class of nonlinear systems under hybrid cyber-attacks, encompassing both deception attacks and denial of service (DoS) attacks with uncertain attack probabilities. In the sensor network, each filter estimates the output signals of the systems by dealing with the output measurements from the systems and the information received from its neighbors and each filter may receive the state estimation information affected by outliers from its neighbors, which is propagated based on the communication topology. With the purpose of mitigating the effects from channel noise during the signal transmission on filtering error systems (FES) and the potential anomalies’ impact in signal transmission caused by the hybrid cyber-attacks, a dynamic saturation function-based distributed filter is designed during the filtering process, whose saturation level is adaptively varying based on previous measurement errors. Through this approach and by utilizing Lyapunov-Krasovskii theory, sufficient conditions are established to ensure the stochastic stability (SS) of the FES and to achieve the predefined <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> performance objectives. Finally, a practical model is presented to demonstrate the effectiveness and practicality of the designed distributed filter methodology.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"35 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057369","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 : 2025-01-21DOI: 10.1016/j.cnsns.2025.108640
Yuan Wei, Jia Guo, Xiangyan Chen
The performance and efficiency of the mechanical system usually depend on the coordination between the rotor and other mechanical components. Due to the sliding motion between the coupling teeth, investigating the instability of the rotor is essential. The action of the coupling can cause changes in the seal performance. The article establishes a nonlinear dynamic rotor model that considers the coupling of internal friction and labyrinth seal, which is a dimensionless treatment and seeks to use the numerical method. The study investigated the impact of various parameters such as axial pressure drops, seal clearance, and seal length. Exploring the change of rotor system stability under the coupling effect of internal friction and labyrinth seal. By combining time history, bifurcation, and axis center trajectory analyze the dynamic characteristics, motion state, and seal force. The results indicate that the rotor system's stability decreases as speed increases with increased vibration amplitude. The increase in axial pressure drop causes the rotor system motion bifurcation point to advance, but it can suppress the offset at the first-critical speed. The increase in seal length can improve the seal effect, but the unstable speed becomes advanced, and the system stability is reduced. This study considers multiple factors and provides theoretical support for the dynamic design of the rotor system.
{"title":"Nonlinear dynamics analysis of labyrinth seal-rotor system considering internal friction in coupling","authors":"Yuan Wei, Jia Guo, Xiangyan Chen","doi":"10.1016/j.cnsns.2025.108640","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108640","url":null,"abstract":"The performance and efficiency of the mechanical system usually depend on the coordination between the rotor and other mechanical components. Due to the sliding motion between the coupling teeth, investigating the instability of the rotor is essential. The action of the coupling can cause changes in the seal performance. The article establishes a nonlinear dynamic rotor model that considers the coupling of internal friction and labyrinth seal, which is a dimensionless treatment and seeks to use the numerical method. The study investigated the impact of various parameters such as axial pressure drops, seal clearance, and seal length. Exploring the change of rotor system stability under the coupling effect of internal friction and labyrinth seal. By combining time history, bifurcation, and axis center trajectory analyze the dynamic characteristics, motion state, and seal force. The results indicate that the rotor system's stability decreases as speed increases with increased vibration amplitude. The increase in axial pressure drop causes the rotor system motion bifurcation point to advance, but it can suppress the offset at the first-critical speed. The increase in seal length can improve the seal effect, but the unstable speed becomes advanced, and the system stability is reduced. This study considers multiple factors and provides theoretical support for the dynamic design of the rotor system.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"36 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057366","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}
In this paper, a novel spring-based nonlinear energy sink (SNES) is proposed for suppressing torsional vibrations in long-shaft rotor systems. The SNES functions by employing a piecewise linear stiffness, which is generated through the extrusion of springs. This mechanism provides the long-shaft rotor system with a restoring torque that can be characterized as a cubic nonlinear force. The paper details the design of the SNES structure and formulates a dynamic model of the SNES-rotor system. Numerical investigations are conducted to assess the vibration damping capacity of the SNES under both transient and steady-state excitations, revealing the nonlinear dynamic behavior of the rotor-SNES system. Furthermore, the effects of various parameters on system performance are examined. Experimental studies on the integrated system demonstrate that the rotor system coupled with the SNES dissipates energy 1.47 times faster than a system without the SNES during transient responses. In terms of steady-state responses, the SNES achieves a vibration suppression rate of up to 52.60% in experiments. These results demonstrate the effective suppression of torsional vibrations in the rotor system by the proposed SNES.
{"title":"A novel spring-based nonlinear energy sink for torsional vibration suppression of long-shafting rotor system","authors":"Zhengqiu Xie, Kun Xie, Shuaishuai Ge, Zhigang Zhang, Ruizhi Shu, Rulong Tan, Wenbin Huang","doi":"10.1016/j.cnsns.2025.108639","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108639","url":null,"abstract":"In this paper, a novel spring-based nonlinear energy sink (SNES) is proposed for suppressing torsional vibrations in long-shaft rotor systems. The SNES functions by employing a piecewise linear stiffness, which is generated through the extrusion of springs. This mechanism provides the long-shaft rotor system with a restoring torque that can be characterized as a cubic nonlinear force. The paper details the design of the SNES structure and formulates a dynamic model of the SNES-rotor system. Numerical investigations are conducted to assess the vibration damping capacity of the SNES under both transient and steady-state excitations, revealing the nonlinear dynamic behavior of the rotor-SNES system. Furthermore, the effects of various parameters on system performance are examined. Experimental studies on the integrated system demonstrate that the rotor system coupled with the SNES dissipates energy 1.47 times faster than a system without the SNES during transient responses. In terms of steady-state responses, the SNES achieves a vibration suppression rate of up to 52.60% in experiments. These results demonstrate the effective suppression of torsional vibrations in the rotor system by the proposed SNES.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"74 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057368","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.2025.108627
Xiaochen Chu, Xiangyu Shi, Dongyang Shi
In this paper, we propose a backward Euler semi-implicit full discrete scheme for the time-dependent incompressible MHD equations and study the superconvergence behavior of the scheme. The spatial discretization is based on the bilinear-constant-bilinear elements for the velocity, pressure and magnetic fields, respectively, while the time discretization is based on the first-order backward Euler scheme. Firstly, we prove a new high accuracy estimation lemma related to the magnetic field, and prove the unconditional boundedness of numerical solutions in L∞-norm by introducing a time-discrete auxiliary system. Then we derive the superclose estimates rigorously, which lead to the corresponding superconvergence results with assistance from interpolation post-processing techniques. In the end, we provide some numerical examples to verify the correctness of our theoretical analysis.
{"title":"Unconditional superconvergence analysis of low-order conforming mixed finite element method for time-dependent incompressible MHD equations","authors":"Xiaochen Chu, Xiangyu Shi, Dongyang Shi","doi":"10.1016/j.cnsns.2025.108627","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108627","url":null,"abstract":"In this paper, we propose a backward Euler semi-implicit full discrete scheme for the time-dependent incompressible MHD equations and study the superconvergence behavior of the scheme. The spatial discretization is based on the bilinear-constant-bilinear elements for the velocity, pressure and magnetic fields, respectively, while the time discretization is based on the first-order backward Euler scheme. Firstly, we prove a new high accuracy estimation lemma related to the magnetic field, and prove the unconditional boundedness of numerical solutions in <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math>-norm by introducing a time-discrete auxiliary system. Then we derive the superclose estimates rigorously, which lead to the corresponding superconvergence results with assistance from interpolation post-processing techniques. In the end, we provide some numerical examples to verify the correctness of our theoretical analysis.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"53 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057372","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.2025.108622
Sun-Ho Choi, Dohyun Kwon, Hyowon Seo
We present a sufficient condition for asymptotic rendezvous of a Cucker-Smale type model on the unit sphere with an inter-particle bonding force. This second-order dynamical system includes a rotation operator defined on the surface of the three-dimensional unit sphere, and we derive an exponential decay estimate for the diameter of agent positions and demonstrate time-asymptotic flocking for a class of initial data. The sufficient condition for the initial data depends only on the communication rate and inter-particle bonding parameter, independent of the number of agents. The lack of momentum conservation and the presence of a curved space domain pose challenges in applying standard methodologies used in the original Cucker-Smale model. To address this and obtain a uniform position alignment estimate, we employ an energy dissipation property of this system and a transformation from the Cucker-Smale type flocking model into an inhomogeneous system in which the solution contains the position and velocity diameters. The coefficients of the transformed system are controlled by the communication rate and a uniform upper bound of velocities obtained by the energy dissipation.
{"title":"Uniform position alignment estimate of a spherical flocking model with inter-particle bonding forces","authors":"Sun-Ho Choi, Dohyun Kwon, Hyowon Seo","doi":"10.1016/j.cnsns.2025.108622","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108622","url":null,"abstract":"We present a sufficient condition for asymptotic rendezvous of a Cucker-Smale type model on the unit sphere with an inter-particle bonding force. This second-order dynamical system includes a rotation operator defined on the surface of the three-dimensional unit sphere, and we derive an exponential decay estimate for the diameter of agent positions and demonstrate time-asymptotic flocking for a class of initial data. The sufficient condition for the initial data depends only on the communication rate and inter-particle bonding parameter, independent of the number of agents. The lack of momentum conservation and the presence of a curved space domain pose challenges in applying standard methodologies used in the original Cucker-Smale model. To address this and obtain a uniform position alignment estimate, we employ an energy dissipation property of this system and a transformation from the Cucker-Smale type flocking model into an inhomogeneous system in which the solution contains the position and velocity diameters. The coefficients of the transformed system are controlled by the communication rate and a uniform upper bound of velocities obtained by the energy dissipation.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"54 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057373","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.2025.108623
Yan Wang, Baoli Yin, Yang Liu, Hong Li
The paper focuses on numerically solving the nonlinear time fractional Schrödinger equations. The modified L1 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 L1 Galerkin finite element scheme. Furthermore, a transformed L1 Crank–Nicolson Galerkin finite element method based on the change of variable t=s1/α 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 [formula omitted] 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":"https://doi.org/10.1016/j.cnsns.2025.108623","url":null,"abstract":"The paper focuses on numerically solving the nonlinear time fractional Schrödinger equations. The modified <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:mrow><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:math> 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 <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:mrow><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:math> Galerkin finite element scheme. Furthermore, a transformed <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:mrow><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:math> Crank–Nicolson Galerkin finite element method based on the change of variable <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:mrow><mml:mi>t</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:msup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>α</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math> 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.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"39 1","pages":""},"PeriodicalIF":3.9,"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 <mml:math altimg="si1.svg" display="block"><mml:mrow><mml:msup><mml:mrow><mml:mi>ɛ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>−</mml:mo><mml:mi>Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">+</mml:mo><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>u</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo><mml:mi>λ</mml:mi><mml:mi>u</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">+</mml:mo><mml:mi>u</mml:mi><mml:mo>log</mml:mo><mml:msup><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mspace width="1em"></mml:mspace><mml:mtext>in</mml:mtext><mml:mspace width="1em"></mml:mspace><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math> with the prescribed mass <mml:math altimg="si2.svg" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mo>∫</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>u</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mi>x</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo><mml:mi>a</mml:mi><mml:msup><mml:mrow><mml:mi>ɛ</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup><mml:mspace width="1em"></mml:mspace><mml:mtext>with</mml:mtext><mml:mspace width="1em"></mml:mspace><mml:mi>a</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, where <mml:math altimg="si3.svg" display="inline"><mml:mrow><mml:mi>ɛ</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, <mml:math altimg="si4.svg" display="inline"><mml:mrow><mml:mi>λ</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">∈</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:math> 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 <mml:math altimg="si5.svg" display="inline"><mml:mi>V</mml:mi></mml:math> attains its minimum. Moreover, the concentration and decay of normalized solutions are analyzed in the end. The a
{"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":"https://doi.org/10.1016/j.cnsns.2025.108618","url":null,"abstract":"In this paper, we investigate the multiplicity and concentration of normalized solutions to a fractional logarithmic Schrödinger problem <mml:math altimg=\"si1.svg\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:mi>ɛ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>−</mml:mo><mml:mi>Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">+</mml:mo><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>u</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mi>λ</mml:mi><mml:mi>u</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">+</mml:mo><mml:mi>u</mml:mi><mml:mo>log</mml:mo><mml:msup><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mspace width=\"1em\"></mml:mspace><mml:mtext>in</mml:mtext><mml:mspace width=\"1em\"></mml:mspace><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math> with the prescribed mass <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mo>∫</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>u</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi>x</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mi>a</mml:mi><mml:msup><mml:mrow><mml:mi>ɛ</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup><mml:mspace width=\"1em\"></mml:mspace><mml:mtext>with</mml:mtext><mml:mspace width=\"1em\"></mml:mspace><mml:mi>a</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, where <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mrow><mml:mi>ɛ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">∈</mml:mo><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow></mml:math> 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 <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mi>V</mml:mi></mml:math> attains its minimum. Moreover, the concentration and decay of normalized solutions are analyzed in the end. The a","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"1 1","pages":""},"PeriodicalIF":3.9,"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":"https://doi.org/10.1016/j.cnsns.2025.108638","url":null,"abstract":"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.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"11 1","pages":""},"PeriodicalIF":3.9,"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":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：