The main goal of this paper is to present the free vibration and buckling of viscoelastic functionally graded porous(FGP)nanosheet based on nonlocal strain gradient(NSGT)and surface elasticity theories.The nanosheets ...The main goal of this paper is to present the free vibration and buckling of viscoelastic functionally graded porous(FGP)nanosheet based on nonlocal strain gradient(NSGT)and surface elasticity theories.The nanosheets are placed on a visco-Pasternak medium in a hygro-temperature environment with nonlinear rules.The viscoelastic material characteristics of nanosheets are based on Kelvin’s model.The unique point of this study is to consider the change of nonlocal and length-scale coefficients according to thickness,similar to the laws of the material properties.The Galerkin approach based on the Kirchhoff-love plate theory is applied to determine the natural frequency and critical buckling load of the viscoelastic FGP nanosheet with various boundary conditions.The accuracy of the proposed method is verified through reliable publications.The outcome of this study highlights the significant effects of the nonlocal and length-scale parameters on the vibration and buckling behaviors of viscoelastic FGP nanosheets.展开更多
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
Current studies on carbon nanotube (CNT) size effects predominantly employ Eringen’s differential nonlocal model, which is widely recognized as ill-suited for bounded domains. This paper investigates the free vibrati...Current studies on carbon nanotube (CNT) size effects predominantly employ Eringen’s differential nonlocal model, which is widely recognized as ill-suited for bounded domains. This paper investigates the free vibration of multi-walled CNTs (MWCNTs) with mathematically well-posed two-phase strain-driven and stress-driven nonlocal integral models incorporating the bi-Helmholtz kernel. The van der Waals (vdW) forces coupling MWCNT layers are similarly modeled as size-dependent via the bi-Helmholtz two-phase nonlocal integral framework. Critically, conventional pure strain-driven or stress-driven formulations become over-constrained when nonlocal vdW interactions are considered. The two-phase strategy resolves this limitation by enabling consistent coupling. Each bi-Helmholtz integral constitutive equation is equivalently transformed into a differential form requiring four additional constitutive boundary conditions (CBCs). The numerical solutions are obtained with the generalized differential quadrature method (GDQM) for these coupled higher-order equations. The parametric studies on double-walled CNTs (DWCNTs) and triple-walled CNTs (TWCNTs) elucidate the nonlocal effects predicted by both formulations. Additionally, the influence of nonlocal parameters within vdW forces is systematically evaluated to comprehensively characterize the size effects in MWCNTs.展开更多
Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the s...Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the static bending analysis of a piezoelectric sandwich functionally graded porous(FGP)double-curved shallow nanoshell based on the flexoelectric effect and nonlocal strain gradient theory.Two coefficients that reduce or increase the stiffness of the nanoshell,including nonlocal and length-scale parameters,are considered to change along the nanoshell thickness direction,and three different porosity rules are novel points in this study.The nanoshell structure is placed on a Pasternak elastic foundation and is made up of three separate layers of material.The outermost layers consist of piezoelectric smart material with flexoelectric effects,while the core layer is composed of FGP material.Hamilton’s principle was used in conjunction with a unique refined higher-order shear deformation theory to derive general equilibrium equations that provide more precise outcomes.The Navier and Galerkin-Vlasov methodology is used to get the static bending characteristics of nanoshells that have various boundary conditions.The program’s correctness is assessed by comparison with published dependable findings in specific instances of the model described in the article.In addition,the influence of parameters such as flexoelectric effect,nonlocal and length scale parameters,elastic foundation stiffness coefficient,porosity coefficient,and boundary conditions on the static bending response of the nanoshell is detected and comprehensively studied.The findings of this study have practical implications for the efficient design and control of comparable systems,such as micro-electromechanical and nano-electromechanical devices.展开更多
The incomplete understanding of nanoscale surface interactions arising from underlying atomistic long-range forces limits our ability to simulate and design their performance. In this paper, the surface elasticity is ...The incomplete understanding of nanoscale surface interactions arising from underlying atomistic long-range forces limits our ability to simulate and design their performance. In this paper, the surface elasticity is constructed from underlying atomistic nonlocal interactions in spherical nanoparticles. By introducing an intrinsic length scale,we quantify the surface region thickness, and demonstrate the progressive elastic modulus transition caused by asymmetric atomistic nonlocal interactions. The universal surface scaling law, relating the intrinsic length scale to the particle dimensions, is established, and a surface-dominated criterion is developed for quantifying the transition to the surfacedominated behaviors. The model is thoroughly validated through the molecular static simulations and experimental data with the material-specific intrinsic length constants.展开更多
This study aims to investigate the propagation of harmonic waves in nonlocal magneto-electro-elastic(MEE)laminated composites with interface stress imperfections using an analytical approach.The pseudo-Stroh formulati...This study aims to investigate the propagation of harmonic waves in nonlocal magneto-electro-elastic(MEE)laminated composites with interface stress imperfections using an analytical approach.The pseudo-Stroh formulation and nonlocal theory proposed by Eringen were adopted to derive the propagator matrix for each layer.Both the propagator and interface matrices were formulated to determine the recursive fields.Subsequently,the dispersion equation was obtained by imposing traction-free and magneto-electric circuit open boundary conditions on the top and bottom surfaces of the plate.Dispersion curves,mode shapes,and natural frequencies were calculated for sandwich plates composed of BaTiO3 and CoFe2O4.Numerical simulations revealed that both interface stress and the nonlocal effect influenced the tuning of the dispersion curve and mode shape for the given layup.The nonlocal effect caused a significant decrease in the dispersion curves,particularly in the high-frequency regions.Additionally,compared to the nonlocal effect,the interface stress exerted a greater influence on the mode shapes.The generalized analytical framework developed in this study provides an effective tool for both the theoretical analysis and practical design of MEE composite laminates.展开更多
In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reve...In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.展开更多
It is well-known that the propagation phenomena of nonlocal dispersal equations have been extensively studied,and the known results on the interface dynamics of this equation are under the compactly supported initial ...It is well-known that the propagation phenomena of nonlocal dispersal equations have been extensively studied,and the known results on the interface dynamics of this equation are under the compactly supported initial value.Moreover,there was no explicit formula regarding the interface due to the peculiarity of nonlocal dispersal operators.Anatural question is whether it is possible to provide a precise characterization of the interface with respect to small parameter for the general initial values(including exponentially bounded and unbounded).This paper is concerned with the interface dynamics of the nonlocal dispersal equation with scaling parameter.For the exponentially bounded initial value,by choosing the hyperbolic scaling,we show that at a very small time,the interface is confined within a generated layer whose thickness is at most O(√ɛ|ln ɛ|),,and subsequently,the interface propagates at a linear speed determined by the decay rate of initial value.For a class of exponentially unbounded initial value,by introducing the nonlinear scaling based on the decay of initial value,we deduce the corresponding Hamilton-Jacobi equation and describe precisely the propagation of the interface,which provides a superlinear speed of the interface.The investigation of the interface dynamics under different scaling reflects multiplex propagation modes in spatial dynamics and provides a new perspective on the wave propagation in nonlocal dispersal equations.展开更多
Based on the Timoshenko beam theory,this paper proposes a nonlocal bi-gyroscopic model for spinning functionally graded(FG)nanotubes conveying fluid,and the thermal–mechanical vibration and stability of such composit...Based on the Timoshenko beam theory,this paper proposes a nonlocal bi-gyroscopic model for spinning functionally graded(FG)nanotubes conveying fluid,and the thermal–mechanical vibration and stability of such composite nanostructures under small scale,rotor,and temperature coupling effects are investigated.The nanotube is composed of functionally graded materials(FGMs),and different volume fraction functions are utilized to control the distribution of material properties.Eringen’s nonlocal elasticity theory and Hamilton’s principle are applied for dynamical modeling,and the forward and backward precession frequencies as well as 3D mode configurations of the nanotube are obtained.By conducting dimensionless analysis,it is found that compared to the Timoshenko nano-beam model,the conventional Euler–Bernoulli(E-B)model holds the same flutter frequency in the supercritical region,while it usually overestimates the higher-order precession frequencies.The nonlocal,thermal,and flowing effects all can lead to buckling or different kinds of coupled flutter in the system.The material distribution of the P-type FGM nanotube can also induce coupled flutter,while that of the S-type FGM nanotube has no impact on the stability of the system.This paper is expected to provide a theoretical foundation for the design of motional composite nanodevices.展开更多
In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial s...In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.展开更多
In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,where...In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.展开更多
The paper is devoted to establishing the long-time behavior of solutions to the extensible beam equation with rotational inertia and nonlocal strong damping.Within the theory of asymptotical smoothness,we investigate ...The paper is devoted to establishing the long-time behavior of solutions to the extensible beam equation with rotational inertia and nonlocal strong damping.Within the theory of asymptotical smoothness,we investigate the existence of the attractor by using the contractive function method and more detailed estimates.展开更多
In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured ...In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.展开更多
We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear...We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics.展开更多
This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated al...This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated along both the radial and circumferential directions.By transforming the proposed integral constitutive equations into the equivalent differential forms,complemented by the corresponding constitutive boundary conditions(CBCs),a well-posed mathematical formulation is established for analyzing the axisymmetric bending and buckling of annular/circular functionally graded(FG)sandwich nanoplates.The boundary conditions at the inner edge of a solid nanoplate are derived by L'H?spital's rule.The numerical solution is obtained by the generalized differential quadrature method(GDQM).The accuracy of the proposed model is validated through comparison with the data from the existing literature.A parameter study is conducted to demonstrate the effects of FG sandwich parameters,size parameters,and nonlocal gradient parameters.展开更多
Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton...Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions.In the present study,we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity.This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures.The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform.The results obtained have not been previously reported for this type of nonlinearity.Additionally,for the purpose of comparison,the numerical examination has taken into account some scenarios with fixed parameter values.Notably,the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson fromthis study.Furthermore,the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation,which includes error tables and graphs.It is important tomention that themethodology employed in this study does not involve any form of linearization,discretization,or perturbation.Consequently,the physical nature of the problem to be solved remains unaltered,which is one of the main advantages.展开更多
In this paper,we consider the Hopf lemma of the following mixed local and nonlocal weighted semilinear elliptic equations{-div(|x|^(-2α)■u)+(-△)_(α)^(s)u=0,x∈U,u(x^(^))=-u(x),x∈H,u(x)=0,x∈R^(N)\U,where H belong...In this paper,we consider the Hopf lemma of the following mixed local and nonlocal weighted semilinear elliptic equations{-div(|x|^(-2α)■u)+(-△)_(α)^(s)u=0,x∈U,u(x^(^))=-u(x),x∈H,u(x)=0,x∈R^(N)\U,where H belong to R^(N)with 0∈H is an open and affine half space,U belong to H is an open and bounded set,s∈(0,1),α∈[0,N-2s/2),(-△)_(α)^(s)is weighted fractional Laplacian with a weighted function.展开更多
If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t...If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.展开更多
In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the co...In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space, and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero. The expressions of the antisymmetric stress and the nonlocal residuals are given. The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached. In addition, the objectivity about the nonlocal residuals and the energy conservation law of nonlocal field is discussed briefly, and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived.展开更多
Nonlocal means filtering is a noise attenuation method based on redundancies in image information. It is also a nonlocal denoising method that uses the self-similarity of an image, assuming that the valid structures o...Nonlocal means filtering is a noise attenuation method based on redundancies in image information. It is also a nonlocal denoising method that uses the self-similarity of an image, assuming that the valid structures of the image have a certain degree of repeatability that the random noise lacks. In this paper, we use nonlocal means filtering in seismic random noise suppression. To overcome the problems caused by expensive computational costs and improper filter parameters, this paper proposes a block-wise implementation of the nonlocal means method with adaptive filter parameter estimation. Tests with synthetic data and real 2D post-stack seismic data demonstrate that the proposed algorithm better preserves valid seismic information and has a higher accuracy when compared with traditional seismic denoising methods （e.g., f-x deconvolution）, which is important for subsequent seismic processing and interpretation.展开更多
文摘The main goal of this paper is to present the free vibration and buckling of viscoelastic functionally graded porous(FGP)nanosheet based on nonlocal strain gradient(NSGT)and surface elasticity theories.The nanosheets are placed on a visco-Pasternak medium in a hygro-temperature environment with nonlinear rules.The viscoelastic material characteristics of nanosheets are based on Kelvin’s model.The unique point of this study is to consider the change of nonlocal and length-scale coefficients according to thickness,similar to the laws of the material properties.The Galerkin approach based on the Kirchhoff-love plate theory is applied to determine the natural frequency and critical buckling load of the viscoelastic FGP nanosheet with various boundary conditions.The accuracy of the proposed method is verified through reliable publications.The outcome of this study highlights the significant effects of the nonlocal and length-scale parameters on the vibration and buckling behaviors of viscoelastic FGP nanosheets.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
基金Project supported by the National Natural Science Foundation of China(Nos.12172169 and 12272064)the Natural Science Foundation of Jiangsu Province of China(No.BK20241773)the Priority Academic Program Development of Jiangsu Higher Education Institutions of China。
文摘Current studies on carbon nanotube (CNT) size effects predominantly employ Eringen’s differential nonlocal model, which is widely recognized as ill-suited for bounded domains. This paper investigates the free vibration of multi-walled CNTs (MWCNTs) with mathematically well-posed two-phase strain-driven and stress-driven nonlocal integral models incorporating the bi-Helmholtz kernel. The van der Waals (vdW) forces coupling MWCNT layers are similarly modeled as size-dependent via the bi-Helmholtz two-phase nonlocal integral framework. Critically, conventional pure strain-driven or stress-driven formulations become over-constrained when nonlocal vdW interactions are considered. The two-phase strategy resolves this limitation by enabling consistent coupling. Each bi-Helmholtz integral constitutive equation is equivalently transformed into a differential form requiring four additional constitutive boundary conditions (CBCs). The numerical solutions are obtained with the generalized differential quadrature method (GDQM) for these coupled higher-order equations. The parametric studies on double-walled CNTs (DWCNTs) and triple-walled CNTs (TWCNTs) elucidate the nonlocal effects predicted by both formulations. Additionally, the influence of nonlocal parameters within vdW forces is systematically evaluated to comprehensively characterize the size effects in MWCNTs.
基金This work was supported by the Le Quy Don Technical University Research Fund(Grant No.23.1.11).
文摘Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the static bending analysis of a piezoelectric sandwich functionally graded porous(FGP)double-curved shallow nanoshell based on the flexoelectric effect and nonlocal strain gradient theory.Two coefficients that reduce or increase the stiffness of the nanoshell,including nonlocal and length-scale parameters,are considered to change along the nanoshell thickness direction,and three different porosity rules are novel points in this study.The nanoshell structure is placed on a Pasternak elastic foundation and is made up of three separate layers of material.The outermost layers consist of piezoelectric smart material with flexoelectric effects,while the core layer is composed of FGP material.Hamilton’s principle was used in conjunction with a unique refined higher-order shear deformation theory to derive general equilibrium equations that provide more precise outcomes.The Navier and Galerkin-Vlasov methodology is used to get the static bending characteristics of nanoshells that have various boundary conditions.The program’s correctness is assessed by comparison with published dependable findings in specific instances of the model described in the article.In addition,the influence of parameters such as flexoelectric effect,nonlocal and length scale parameters,elastic foundation stiffness coefficient,porosity coefficient,and boundary conditions on the static bending response of the nanoshell is detected and comprehensively studied.The findings of this study have practical implications for the efficient design and control of comparable systems,such as micro-electromechanical and nano-electromechanical devices.
基金Project supported by the National Natural Science Foundation of China (No.52175095)。
文摘The incomplete understanding of nanoscale surface interactions arising from underlying atomistic long-range forces limits our ability to simulate and design their performance. In this paper, the surface elasticity is constructed from underlying atomistic nonlocal interactions in spherical nanoparticles. By introducing an intrinsic length scale,we quantify the surface region thickness, and demonstrate the progressive elastic modulus transition caused by asymmetric atomistic nonlocal interactions. The universal surface scaling law, relating the intrinsic length scale to the particle dimensions, is established, and a surface-dominated criterion is developed for quantifying the transition to the surfacedominated behaviors. The model is thoroughly validated through the molecular static simulations and experimental data with the material-specific intrinsic length constants.
基金supported by the Ministry of Science and Technology Taiwan under Grant No.MOST 109-2628-E-009-002-MY3.
文摘This study aims to investigate the propagation of harmonic waves in nonlocal magneto-electro-elastic(MEE)laminated composites with interface stress imperfections using an analytical approach.The pseudo-Stroh formulation and nonlocal theory proposed by Eringen were adopted to derive the propagator matrix for each layer.Both the propagator and interface matrices were formulated to determine the recursive fields.Subsequently,the dispersion equation was obtained by imposing traction-free and magneto-electric circuit open boundary conditions on the top and bottom surfaces of the plate.Dispersion curves,mode shapes,and natural frequencies were calculated for sandwich plates composed of BaTiO3 and CoFe2O4.Numerical simulations revealed that both interface stress and the nonlocal effect influenced the tuning of the dispersion curve and mode shape for the given layup.The nonlocal effect caused a significant decrease in the dispersion curves,particularly in the high-frequency regions.Additionally,compared to the nonlocal effect,the interface stress exerted a greater influence on the mode shapes.The generalized analytical framework developed in this study provides an effective tool for both the theoretical analysis and practical design of MEE composite laminates.
文摘In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.
基金partially supported by the NSF of China(12271226)partially supported by the NSF of China(12201434)+4 种基金the NSF of Gansu Province of China(21JR7RA537)the NSF of Gansu Province of China(21JR7RA535)the Fundamental Research Funds for the Central Universities(lzujbky-2021-kb15)partially supported by the NSF of China(12371170)the R&D Program of Beijing Municipal Education Commission(KM202310028017)。
文摘It is well-known that the propagation phenomena of nonlocal dispersal equations have been extensively studied,and the known results on the interface dynamics of this equation are under the compactly supported initial value.Moreover,there was no explicit formula regarding the interface due to the peculiarity of nonlocal dispersal operators.Anatural question is whether it is possible to provide a precise characterization of the interface with respect to small parameter for the general initial values(including exponentially bounded and unbounded).This paper is concerned with the interface dynamics of the nonlocal dispersal equation with scaling parameter.For the exponentially bounded initial value,by choosing the hyperbolic scaling,we show that at a very small time,the interface is confined within a generated layer whose thickness is at most O(√ɛ|ln ɛ|),,and subsequently,the interface propagates at a linear speed determined by the decay rate of initial value.For a class of exponentially unbounded initial value,by introducing the nonlinear scaling based on the decay of initial value,we deduce the corresponding Hamilton-Jacobi equation and describe precisely the propagation of the interface,which provides a superlinear speed of the interface.The investigation of the interface dynamics under different scaling reflects multiplex propagation modes in spatial dynamics and provides a new perspective on the wave propagation in nonlocal dispersal equations.
基金National Natural Science Foundation of China,12372025,Feng Liang,12072311,Feng Liang.
文摘Based on the Timoshenko beam theory,this paper proposes a nonlocal bi-gyroscopic model for spinning functionally graded(FG)nanotubes conveying fluid,and the thermal–mechanical vibration and stability of such composite nanostructures under small scale,rotor,and temperature coupling effects are investigated.The nanotube is composed of functionally graded materials(FGMs),and different volume fraction functions are utilized to control the distribution of material properties.Eringen’s nonlocal elasticity theory and Hamilton’s principle are applied for dynamical modeling,and the forward and backward precession frequencies as well as 3D mode configurations of the nanotube are obtained.By conducting dimensionless analysis,it is found that compared to the Timoshenko nano-beam model,the conventional Euler–Bernoulli(E-B)model holds the same flutter frequency in the supercritical region,while it usually overestimates the higher-order precession frequencies.The nonlocal,thermal,and flowing effects all can lead to buckling or different kinds of coupled flutter in the system.The material distribution of the P-type FGM nanotube can also induce coupled flutter,while that of the S-type FGM nanotube has no impact on the stability of the system.This paper is expected to provide a theoretical foundation for the design of motional composite nanodevices.
基金supported by the National Natural Sciences Foundation of China(No.62363005)。
文摘In this paper,we investigate the blow-up phenomenon for a class of logarithmic viscoelastic equations with delay and nonlocal terms under acoustic boundary conditions.Using the energy method,we prove that nontrivial solutions with negative initial energy will blow up in finite time,and provide an upper bound estimate for the blow-up time.Additionally,we also derive a lower bound estimate for the blow-up time.
基金supported by the National Natural Science Foundation of China under Grant No.12147115the Discipline(Subject)Leader Cultivation Project of Universities in Anhui Province under Grant Nos.DTR2023052 and DTR2024046+2 种基金the Natural Science Research Project of Universities in Anhui Province under Grant No.2024AH040202the Young Top Notch Talents and Young Scholars of High End Talent Introduction and Cultivation Action Project in Anhui Provincethe Scientific Research Foundation Funded Project of Chuzhou University under Grant Nos.2022qd022 and 2022qd038。
文摘In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1210150211961059)the University Innovation Project of Gansu Province(Grant No.2023B-062).
文摘The paper is devoted to establishing the long-time behavior of solutions to the extensible beam equation with rotational inertia and nonlocal strong damping.Within the theory of asymptotical smoothness,we investigate the existence of the attractor by using the contractive function method and more detailed estimates.
基金supported by the NSF of Ningxia(2022AAC03234)the NSF of China(11761004),the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09)the Postgraduate Innovation Project of North Minzu University(YCX23074).
文摘In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.
基金supported by the National Natural Science Foundation of China(Grant Nos.12261131495 and 12475008)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009)。
文摘We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated along both the radial and circumferential directions.By transforming the proposed integral constitutive equations into the equivalent differential forms,complemented by the corresponding constitutive boundary conditions(CBCs),a well-posed mathematical formulation is established for analyzing the axisymmetric bending and buckling of annular/circular functionally graded(FG)sandwich nanoplates.The boundary conditions at the inner edge of a solid nanoplate are derived by L'H?spital's rule.The numerical solution is obtained by the generalized differential quadrature method(GDQM).The accuracy of the proposed model is validated through comparison with the data from the existing literature.A parameter study is conducted to demonstrate the effects of FG sandwich parameters,size parameters,and nonlocal gradient parameters.
文摘Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions.In the present study,we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity.This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures.The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform.The results obtained have not been previously reported for this type of nonlinearity.Additionally,for the purpose of comparison,the numerical examination has taken into account some scenarios with fixed parameter values.Notably,the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson fromthis study.Furthermore,the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation,which includes error tables and graphs.It is important tomention that themethodology employed in this study does not involve any form of linearization,discretization,or perturbation.Consequently,the physical nature of the problem to be solved remains unaltered,which is one of the main advantages.
基金Supported by the National Natural Science Foundation of China(Grant No.12361026)Fundamental Research Funds for the Central Universities(Grant No.31920240069)Innovation Team Project of Northwest Minzu University.
文摘In this paper,we consider the Hopf lemma of the following mixed local and nonlocal weighted semilinear elliptic equations{-div(|x|^(-2α)■u)+(-△)_(α)^(s)u=0,x∈U,u(x^(^))=-u(x),x∈H,u(x)=0,x∈R^(N)\U,where H belong to R^(N)with 0∈H is an open and affine half space,U belong to H is an open and bounded set,s∈(0,1),α∈[0,N-2s/2),(-△)_(α)^(s)is weighted fractional Laplacian with a weighted function.
基金the National Natural Science Foundation of China(No.10674024)
文摘If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.
文摘In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space, and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero. The expressions of the antisymmetric stress and the nonlocal residuals are given. The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached. In addition, the objectivity about the nonlocal residuals and the energy conservation law of nonlocal field is discussed briefly, and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived.
基金supported by the National Natural Science Foundation of China(No.41074075)National Science and Technology Project(SinoProbe-03)+1 种基金National public industry special subject(No. 201011047-02)Graduate Innovation Fund of Jilin University(No. 20121070)
文摘Nonlocal means filtering is a noise attenuation method based on redundancies in image information. It is also a nonlocal denoising method that uses the self-similarity of an image, assuming that the valid structures of the image have a certain degree of repeatability that the random noise lacks. In this paper, we use nonlocal means filtering in seismic random noise suppression. To overcome the problems caused by expensive computational costs and improper filter parameters, this paper proposes a block-wise implementation of the nonlocal means method with adaptive filter parameter estimation. Tests with synthetic data and real 2D post-stack seismic data demonstrate that the proposed algorithm better preserves valid seismic information and has a higher accuracy when compared with traditional seismic denoising methods （e.g., f-x deconvolution）, which is important for subsequent seismic processing and interpretation.
