We explain various facets of the THSR(Tohsaki-Horiuchi Schuck-Ropke)wave function.We first discuss the THSR,wave function as a wave function of cluster-gas state,since the THSR,wave function was originally introduced ...We explain various facets of the THSR(Tohsaki-Horiuchi Schuck-Ropke)wave function.We first discuss the THSR,wave function as a wave function of cluster-gas state,since the THSR,wave function was originally introduced to elucidate the 3a-condensate-like character of the Hoyle state(O2^+ state)of 12C.We briefly review the cluster-model studies of the Hoyle state in 1970’s in order to explain how there emerged the idea to assign the a condensate character to the Hoyle state.We then explain that the THSR wave function can describe very well also non-gaslike ordinary cluster states with spatial localization of clusters.This fact means that the dynamical motion of clusters is of nonlocalized nature just as in gas-like states of clusters and the localization of clusters is due to the inter-cluster Pauli principle which is against the close approach of two clusters.The nonlocalized cluster dynamics is formulated by the container model of cluster dynamics.The container model describes gas-like state and non-gaslike states as the solutions of the Hill Wheeler equation with respect to the size parameter of THSR wave function which is just the size parameter of the container.When we notice that fact that the THSR wave function with the smallest value of size parameter is equivalent to the shell-model wave function,we see that the container model describes the evolution of cluster structure from the ground state with shell-model structure up to the gas-like cluster state via ordinary non-gaslike cluster states.For the description of various cluster structure,more generation of THSR wave function have been introduced and we review some typical examples with their actual applications.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 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
This research utilizes analytical solutions to investigate the issue of nonlinear static bending in nanobeams affected by the flexomagnetic effect.The nanobeams are exposed to mechanical loads and put in a temperature...This research utilizes analytical solutions to investigate the issue of nonlinear static bending in nanobeams affected by the flexomagnetic effect.The nanobeams are exposed to mechanical loads and put in a temperature environment.The equilibrium equation of the beam is formulated based on the newly developed higher-order shear deformation theory.The flexomagnetic effect is explained by the presence of the strain gradient component,which also takes into consideration the impact of small-size effects.This study has used a flexible transformation to derive the equilibrium equation for a single variable,which significantly simplifies the process of determining the precise solution to the bending issue.This highlights the originality and significance of the present study,which is based on a newly developed shear deformation theory to clarify the distinctions between the nonlinear and linear problems.This study also presents the findings of numerical simulations that investigate the impact of various geometric,material,and temperature parameters on the nonlinear behavior of nanobeams.These discoveries are significant for designers to develop nanobeams that can function efficiently in many physical conditions,including mechanical,thermal,and magnetic mediums.展开更多
Nonlocal set of orthogonal product states(OPSs)can improve the confidentiality of information when it is used to design quantum cryptographic protocols.It is a difficult question how to construct a nonlocal set of OPS...Nonlocal set of orthogonal product states(OPSs)can improve the confidentiality of information when it is used to design quantum cryptographic protocols.It is a difficult question how to construct a nonlocal set of OPSs on general multipartite and high dimensional quantum systems.Different from the previous works,we first present a novel method for constructing a nonlocal product set with 3d-2 members on C^(d)■C^(d)■C^(d)quantum system for d≥3.Then,we extend this construction method to C^(d_(1))■C^(d_(2))■C^(d_(3))quantum system and■_(i=1)^(n)C^(di)quantum system respectively,where 3≤d_(1)≤d_(2)≤d_(3)≤…≤dC_(d_(i))and n≥3.The nonlocal set of OPSs constructed by our method contains fewer elements than those constructed by the existing methods,except for one special case.More importantly,the set of states constructed by our method has a completely different structure from those constructed by the existing methods since our nonlocal set does not contain a“stopper”state.Our result is helpful to further understand the different structures of nonlocal sets on multipartite systems.展开更多
Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nano...Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.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
Developing lightweight lattice materials that possess exceptional strength,stiffness,and toughness(or energy absorption)simultaneously remains a significant challenge.In this study,we develop a novel design strategy:i...Developing lightweight lattice materials that possess exceptional strength,stiffness,and toughness(or energy absorption)simultaneously remains a significant challenge.In this study,we develop a novel design strategy:incorporating nonlocal interactions into lattice beams,creating“nonlocal lattices”.Utilizing simulation experiments,we investigated the bending behaviors of these lattices,with a particular focus on their damage evolution.Interestingly,these nonlocal lattices,categorized as stretch-dominated,exhibit extraordinary peak force(strength)and stiffness(modulus)comparable to traditional stretchdominated lattices,while maintaining superior energy absorption(toughness).Analysis of damage evolution within the lattice beams reveals a transition from localized to dispersed damage patterns.This transition delays strain localization,thereby improving material utilization efficiency.Furthermore,stronger nonlocal interaction leads to a more dispersed damage zone,further improving materials utilization efficiency.These findings demonstrate that nonlocal lattices achieve excellent energy dissipation(toughness)without compromising strength and stiffness.This highlights the crucial role of nonlocal interactions in governing strain localization within lattice materials.The design strategy here unlocks new inspirations for the development of strong and tough lightweight materials.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
The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behav...The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behavior.Classical continuum theories are inadequate at micro-and nanoscales,particularly concerning size effects,singularities,and phenomena like strain softening or phase transitions.This limitation follows from their lack of intrinsic length scale parameters,crucial for representingmicrostructural features.Theoretical and experimental findings emphasize the critical role of these parameters on small scales.This review thoroughly examines various strain gradient elasticity(SGE)theories commonly employed in literature to capture these size-dependent effects on the elastic response.Given the complexity arising from numerous SGE frameworks available in the literature,including first-and second-order gradient theories,we conduct a comprehensive and comparative analysis of common SGE models.This analysis highlights their unique physical interpretations and compares their effectiveness in modeling the size-dependent behavior of low-dimensional structures.A brief discussion on estimating additional material constants,such as intrinsic length scales,is also included to improve the practical relevance of SGE.Following this theoretical treatment,the review covers analytical and numerical methods for solving the associated higher-order governing differential equations.Finally,we present a detailed overview of strain gradient applications in multiscale andmultiphysics response of solids.Interesting research on exploring the relevance of SGE for reduced-order modeling of complex macrostructures,a universal multiphysics coupling in low-dimensional structures without being restricted to limited material symmetries(as in the case of microstructures),is also presented here for interested readers.Finally,we briefly discuss alternative nonlocal elasticity approaches(integral and integro-differential)for incorporating size effects,and conclude with some potential areas for future research on strain gradients.This review aims to provide a clear understanding of strain gradient theories and their broad applicability beyond classical elasticity.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
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
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
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
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
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
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
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
To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations.There are also some other methods that are based on integrable scala...To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations.There are also some other methods that are based on integrable scalar nonlinear partial differential equations.We show that some systems of integrable equations published recently are the M_(2)-extension of integrable such scalar equations.For illustration,we give Korteweg-de Vries,Kaup-Kupershmidt,and SawadaKotera equations as examples.By the use of such an extension of integrable scalar equations,we obtain some new integrable systems with recursion operators.We also give the soliton solutions of the systems and integrable standard nonlocal and shifted nonlocal reductions of these systems.展开更多
To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the infl...To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the influence of noise and extract the edge information of the image.The new edge extractor is used as the adaptive function and the weighting function of the l_(p) norm variational model to control the noise reduction ability of the model,and a new model 1 is obtained.Considering that the new model 1 only uses the gradient mode as the image feature operator,which is insufficient to express the image texture information,a new level set curvature gradient variational model 2 combined with the edge extractor is proposed.The new model 2 uses the idea of minimum curvature of the level set of clear images to obtain noise reduction images.By coupling new model 1 and new model 2 to smooth the noise and protect more textures,a new Non-local level set denoising model(NLSDM)for image noise reduction is obtained.The experimental results show that compared with the noise reduction model,the new model has significantly improved the peak signal-to-noise ratio and structural similarity,and the effect of noise reduction and edge preservation is better.展开更多
基金supported by JSPS KAKENHI Grant Nos.17K14262,JP16K05351,17K05440,and 18K03658.One of the authors(A.T.)was supported by the Ministry of Education and Science of the Republic of Kazakhstan,and the research grant number is IRN:AP05132476.
文摘We explain various facets of the THSR(Tohsaki-Horiuchi Schuck-Ropke)wave function.We first discuss the THSR,wave function as a wave function of cluster-gas state,since the THSR,wave function was originally introduced to elucidate the 3a-condensate-like character of the Hoyle state(O2^+ state)of 12C.We briefly review the cluster-model studies of the Hoyle state in 1970’s in order to explain how there emerged the idea to assign the a condensate character to the Hoyle state.We then explain that the THSR wave function can describe very well also non-gaslike ordinary cluster states with spatial localization of clusters.This fact means that the dynamical motion of clusters is of nonlocalized nature just as in gas-like states of clusters and the localization of clusters is due to the inter-cluster Pauli principle which is against the close approach of two clusters.The nonlocalized cluster dynamics is formulated by the container model of cluster dynamics.The container model describes gas-like state and non-gaslike states as the solutions of the Hill Wheeler equation with respect to the size parameter of THSR wave function which is just the size parameter of the container.When we notice that fact that the THSR wave function with the smallest value of size parameter is equivalent to the shell-model wave function,we see that the container model describes the evolution of cluster structure from the ground state with shell-model structure up to the gas-like cluster state via ordinary non-gaslike cluster states.For the description of various cluster structure,more generation of THSR wave function have been introduced and we review some typical examples with their actual applications.
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.
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.
文摘This research utilizes analytical solutions to investigate the issue of nonlinear static bending in nanobeams affected by the flexomagnetic effect.The nanobeams are exposed to mechanical loads and put in a temperature environment.The equilibrium equation of the beam is formulated based on the newly developed higher-order shear deformation theory.The flexomagnetic effect is explained by the presence of the strain gradient component,which also takes into consideration the impact of small-size effects.This study has used a flexible transformation to derive the equilibrium equation for a single variable,which significantly simplifies the process of determining the precise solution to the bending issue.This highlights the originality and significance of the present study,which is based on a newly developed shear deformation theory to clarify the distinctions between the nonlinear and linear problems.This study also presents the findings of numerical simulations that investigate the impact of various geometric,material,and temperature parameters on the nonlinear behavior of nanobeams.These discoveries are significant for designers to develop nanobeams that can function efficiently in many physical conditions,including mechanical,thermal,and magnetic mediums.
基金supported by the National Natural Science Foundation of China(Grant No.62171264)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2023MF080)the Natural Science Foundation of Beijing(Grant No.4252014).
文摘Nonlocal set of orthogonal product states(OPSs)can improve the confidentiality of information when it is used to design quantum cryptographic protocols.It is a difficult question how to construct a nonlocal set of OPSs on general multipartite and high dimensional quantum systems.Different from the previous works,we first present a novel method for constructing a nonlocal product set with 3d-2 members on C^(d)■C^(d)■C^(d)quantum system for d≥3.Then,we extend this construction method to C^(d_(1))■C^(d_(2))■C^(d_(3))quantum system and■_(i=1)^(n)C^(di)quantum system respectively,where 3≤d_(1)≤d_(2)≤d_(3)≤…≤dC_(d_(i))and n≥3.The nonlocal set of OPSs constructed by our method contains fewer elements than those constructed by the existing methods,except for one special case.More importantly,the set of states constructed by our method has a completely different structure from those constructed by the existing methods since our nonlocal set does not contain a“stopper”state.Our result is helpful to further understand the different structures of nonlocal sets on multipartite systems.
基金supported by Scientific Research Projects Department of Istanbul Technical University.Project Number:MGA-2018-41546.Grant receiver:E.T.
文摘Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11932002 and 11902004).
文摘Developing lightweight lattice materials that possess exceptional strength,stiffness,and toughness(or energy absorption)simultaneously remains a significant challenge.In this study,we develop a novel design strategy:incorporating nonlocal interactions into lattice beams,creating“nonlocal lattices”.Utilizing simulation experiments,we investigated the bending behaviors of these lattices,with a particular focus on their damage evolution.Interestingly,these nonlocal lattices,categorized as stretch-dominated,exhibit extraordinary peak force(strength)and stiffness(modulus)comparable to traditional stretchdominated lattices,while maintaining superior energy absorption(toughness).Analysis of damage evolution within the lattice beams reveals a transition from localized to dispersed damage patterns.This transition delays strain localization,thereby improving material utilization efficiency.Furthermore,stronger nonlocal interaction leads to a more dispersed damage zone,further improving materials utilization efficiency.These findings demonstrate that nonlocal lattices achieve excellent energy dissipation(toughness)without compromising strength and stiffness.This highlights the crucial role of nonlocal interactions in governing strain localization within lattice materials.The design strategy here unlocks new inspirations for the development of strong and tough lightweight materials.
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support from the Anusandhan National Research Foundation(ANRF),erstwhile Science and Engineering Research Board(SERB),India,under the startup research grant program(SRG/2022/000566).
文摘The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behavior.Classical continuum theories are inadequate at micro-and nanoscales,particularly concerning size effects,singularities,and phenomena like strain softening or phase transitions.This limitation follows from their lack of intrinsic length scale parameters,crucial for representingmicrostructural features.Theoretical and experimental findings emphasize the critical role of these parameters on small scales.This review thoroughly examines various strain gradient elasticity(SGE)theories commonly employed in literature to capture these size-dependent effects on the elastic response.Given the complexity arising from numerous SGE frameworks available in the literature,including first-and second-order gradient theories,we conduct a comprehensive and comparative analysis of common SGE models.This analysis highlights their unique physical interpretations and compares their effectiveness in modeling the size-dependent behavior of low-dimensional structures.A brief discussion on estimating additional material constants,such as intrinsic length scales,is also included to improve the practical relevance of SGE.Following this theoretical treatment,the review covers analytical and numerical methods for solving the associated higher-order governing differential equations.Finally,we present a detailed overview of strain gradient applications in multiscale andmultiphysics response of solids.Interesting research on exploring the relevance of SGE for reduced-order modeling of complex macrostructures,a universal multiphysics coupling in low-dimensional structures without being restricted to limited material symmetries(as in the case of microstructures),is also presented here for interested readers.Finally,we briefly discuss alternative nonlocal elasticity approaches(integral and integro-differential)for incorporating size effects,and conclude with some potential areas for future research on strain gradients.This review aims to provide a clear understanding of strain gradient theories and their broad applicability beyond classical elasticity.
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.
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 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 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partially supported by the Scientific and Technological Research Council of Turkey(TüBITAK)。
文摘To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations.There are also some other methods that are based on integrable scalar nonlinear partial differential equations.We show that some systems of integrable equations published recently are the M_(2)-extension of integrable such scalar equations.For illustration,we give Korteweg-de Vries,Kaup-Kupershmidt,and SawadaKotera equations as examples.By the use of such an extension of integrable scalar equations,we obtain some new integrable systems with recursion operators.We also give the soliton solutions of the systems and integrable standard nonlocal and shifted nonlocal reductions of these systems.
基金funded by National Nature Science Foundation of China,grant number 61302188.
文摘To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the influence of noise and extract the edge information of the image.The new edge extractor is used as the adaptive function and the weighting function of the l_(p) norm variational model to control the noise reduction ability of the model,and a new model 1 is obtained.Considering that the new model 1 only uses the gradient mode as the image feature operator,which is insufficient to express the image texture information,a new level set curvature gradient variational model 2 combined with the edge extractor is proposed.The new model 2 uses the idea of minimum curvature of the level set of clear images to obtain noise reduction images.By coupling new model 1 and new model 2 to smooth the noise and protect more textures,a new Non-local level set denoising model(NLSDM)for image noise reduction is obtained.The experimental results show that compared with the noise reduction model,the new model has significantly improved the peak signal-to-noise ratio and structural similarity,and the effect of noise reduction and edge preservation is better.
