In this paper, we prove the existence of forced waves for Leslie-Gower prey-predator model with nonlocal effects under shifting environment. By constructing a pair of upper and lower solutions with the method of monot...In this paper, we prove the existence of forced waves for Leslie-Gower prey-predator model with nonlocal effects under shifting environment. By constructing a pair of upper and lower solutions with the method of monotone iteration, we can obtain the existence of forced waves for any positive constant shifting speed. Finally, we show the asymptotical behavior of traveling wave fronts in two tails.展开更多
Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefo...Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.展开更多
The model of a locally resonant (LR) epoxy/PZT-4 phononic crystal (PC)nanobeam with “spring-mass” resonators periodically attached to epoxy is proposed. The corresponding band structures are calculated by coupling E...The model of a locally resonant (LR) epoxy/PZT-4 phononic crystal (PC)nanobeam with “spring-mass” resonators periodically attached to epoxy is proposed. The corresponding band structures are calculated by coupling Euler beam theory, nonlocal piezoelectricity theory and plane wave expansion (PWE) method. Three complete band gaps with the widest total width less than 10GHz can be formed in the proposed nanobeam by comprehensively comparing the band structures of three kinds of LR PC nanobeams with resonators attached or not. Furthermore, influencing rules of the coupling fields between electricity and mechanics,“spring-mass” resonator, nonlocal effect and different geometric parameters on the first three band gaps are discussed and summarized. All the investigations are expected to be applied to realize the active control of vibration in the region of ultrahigh frequency.展开更多
Transformation optics is a mathematical method that is based on the geometric interpretation of Maxwell’s equations.This technique enables a direct link between a desired electromagnetic(EM)phenomenon and the materia...Transformation optics is a mathematical method that is based on the geometric interpretation of Maxwell’s equations.This technique enables a direct link between a desired electromagnetic(EM)phenomenon and the material response required for its occurrence,providing a powerful and intuitive design tool for the control of EM fields on all length scales.With the unprecedented design flexibility offered by transformation optics(TO),researchers have demonstrated a host of interesting devices,such as invisibility cloaks,field concentrators,and optical illusion devices.Recently,the applications of TO have been extended to the subwavelength scale to study surface plasmon-assisted phenomena,where a general strategy has been suggested to design and study analytically various plasmonic devices and investigate the associated phenomena,such as nonlocal effects,Casimir interactions,and compact dimensions.We review the basic concept of TO and its advances from macroscopic to the nanoscale regimes.展开更多
文摘In this paper, we prove the existence of forced waves for Leslie-Gower prey-predator model with nonlocal effects under shifting environment. By constructing a pair of upper and lower solutions with the method of monotone iteration, we can obtain the existence of forced waves for any positive constant shifting speed. Finally, we show the asymptotical behavior of traveling wave fronts in two tails.
文摘Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.
基金supported by the National Natural Science Foundation of China(51979130,11847009)the Young Elite Scientists Sponsorship Program by CAST(2022QNRC001)+1 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China(22KJB580005)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(SJCX221961)。
文摘The model of a locally resonant (LR) epoxy/PZT-4 phononic crystal (PC)nanobeam with “spring-mass” resonators periodically attached to epoxy is proposed. The corresponding band structures are calculated by coupling Euler beam theory, nonlocal piezoelectricity theory and plane wave expansion (PWE) method. Three complete band gaps with the widest total width less than 10GHz can be formed in the proposed nanobeam by comprehensively comparing the band structures of three kinds of LR PC nanobeams with resonators attached or not. Furthermore, influencing rules of the coupling fields between electricity and mechanics,“spring-mass” resonator, nonlocal effect and different geometric parameters on the first three band gaps are discussed and summarized. All the investigations are expected to be applied to realize the active control of vibration in the region of ultrahigh frequency.
基金This work was supported in part by the Singapore Ministry of Education under Grant Nos.2017-T1-001-239(RG91/17(S))and MOE2015-T2-1-145, in part by the Gordon and Betty Moore Foundation.
文摘Transformation optics is a mathematical method that is based on the geometric interpretation of Maxwell’s equations.This technique enables a direct link between a desired electromagnetic(EM)phenomenon and the material response required for its occurrence,providing a powerful and intuitive design tool for the control of EM fields on all length scales.With the unprecedented design flexibility offered by transformation optics(TO),researchers have demonstrated a host of interesting devices,such as invisibility cloaks,field concentrators,and optical illusion devices.Recently,the applications of TO have been extended to the subwavelength scale to study surface plasmon-assisted phenomena,where a general strategy has been suggested to design and study analytically various plasmonic devices and investigate the associated phenomena,such as nonlocal effects,Casimir interactions,and compact dimensions.We review the basic concept of TO and its advances from macroscopic to the nanoscale regimes.
