In this paper, we consider a non-local PDE model with delay for population dynamics in Rn. First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term at in...In this paper, we consider a non-local PDE model with delay for population dynamics in Rn. First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term at infinity. Then, we obtain the global attractor by proving w-limit compactness property of the solution operator semigroup.展开更多
Significant progress has been made in computational imaging(CI),in which deep convolutional neural networks(CNNs)have demonstrated that sparse speckle patterns can be reconstructed.However,due to the limited“local”k...Significant progress has been made in computational imaging(CI),in which deep convolutional neural networks(CNNs)have demonstrated that sparse speckle patterns can be reconstructed.However,due to the limited“local”kernel size of the convolutional operator,for the spatially dense patterns,such as the generic face images,the performance of CNNs is limited.Here,we propose a“non-local”model,termed the Speckle-Transformer(SpT)UNet,for speckle feature extraction of generic face images.It is worth noting that the lightweight SpT UNet reveals a high efficiency and strong comparative performance with Pearson Correlation Coefficient(PCC),and structural similarity measure(SSIM)exceeding 0.989,and 0.950,respectively.展开更多
Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational...Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.展开更多
In view of the non-local phenomena appearing in the rock and concrete-like materials, the non-local damage and fracture model of rock and concrete-like materials was established through non-local method of Gaussian we...In view of the non-local phenomena appearing in the rock and concrete-like materials, the non-local damage and fracture model of rock and concrete-like materials was established through non-local method of Gaussian weighting function. The result indicates that, the stress of one point in the material is correlated not only to its strain history, but also to the interaction of the points in its certain adjacent region of the material. Based on the established non-local model, the numerical simulation of notch containing three-point bending beam was carried out. The results show that the grid sensitivities have been avoided and the fracture direction of the material has not been influenced by the grid shape, and the model proposed can be used to better simulate the damage developing process of the rock and concrete-like materials.展开更多
A non-local continuum model for strain-softening simply takingplastic strain or damage vari- able as a non-local variable isderived by using the additive decomposition principle of finitedeformation gra- dient. At the...A non-local continuum model for strain-softening simply takingplastic strain or damage vari- able as a non-local variable isderived by using the additive decomposition principle of finitedeformation gra- dient. At the same time, variational equations,their finite element formulations and numerical convolutedintegration algorithm of the model in current configuration usuallycalled co-moving coordinate system are given. stability andconvergence of the model are proven by means of the weak convergencetheorem of gen- eral function and the convoluted integration theory.展开更多
In this paper a new approach for PBL simulation, the non-local closure scheme based on the transient turbulence theory has been used. It was set up as an alternative to local closure schemes which physical concept is ...In this paper a new approach for PBL simulation, the non-local closure scheme based on the transient turbulence theory has been used. It was set up as an alternative to local closure schemes which physical concept is reasonable and distinct. A 2-D non-local closure model was developed in order to study the PBL structure and simulatesome interesting atmospheric processes over non-ulliform underlying surface, especially under the convective and unique weather conditions, such as sea-land circulation and the TIBL structure. The modelled results show good agreement with field measurement.展开更多
We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m2n-2R□-nRto the Einstein-Hilbert action. Moreover, to obtain s...We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m2n-2R□-nRto the Einstein-Hilbert action. Moreover, to obtain some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter ε for different n. By analysis we give the constraints on the model parameters ε.展开更多
Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical...Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.展开更多
A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structu...A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional （2D） electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thick- ness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.展开更多
For random noise suppression of seismic data, we present a non-local Bayes （NL- Bayes） filtering algorithm. The NL-Bayes algorithm uses the Gaussian model instead of the weighted average of all similar patches in th...For random noise suppression of seismic data, we present a non-local Bayes （NL- Bayes） filtering algorithm. The NL-Bayes algorithm uses the Gaussian model instead of the weighted average of all similar patches in the NL-means algorithm to reduce the fuzzy of structural details, thereby improving the denoising performance. In the denoising process of seismic data, the size and the number of patches in the Gaussian model are adaptively calculated according to the standard deviation of noise. The NL-Bayes algorithm requires two iterations to complete seismic data denoising, but the second iteration makes use of denoised seismic data from the first iteration to calculate the better mean and covariance of the patch Gaussian model for improving the similarity of patches and achieving the purpose of denoising. Tests with synthetic and real data sets demonstrate that the NL-Bayes algorithm can effectively improve the SNR and preserve the fidelity of seismic data.展开更多
The purpose of this study is to present an application of a novel enhancement technique for enhancing medical images generated from X-rays. The method presented in this study is based on a nonlinear partial differenti...The purpose of this study is to present an application of a novel enhancement technique for enhancing medical images generated from X-rays. The method presented in this study is based on a nonlinear partial differential equation （PDE） model, Kramer＇s PDE model. The usefulness of this method is investigated by experimental results. We apply this method to a medical X-ray image. For comparison, the X-ray image is also processed using classic Perona-Malik PDE model and Catte PDE model. Although the Perona-Malik model and Catte PDE model could also enhance the image, the quality of the enhanced images is considerably inferior compared with the enhanced image using Kramer＇s PDE model. The study suggests that the Kramer＇s PDE model is capable of enhancing medical X-ray images, which will make the X-ray images more reliable.展开更多
A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this...A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this paper is to propose some efficient and accurate numerical methods for the computational solution of one-dimensional continuous basic models for the growth and control of brain tumors. After computing the analytical solution, we construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization. Then, we investigate the convergence behavior of Conjugate gradient and generalized minimum residual as Krylov subspace methods to solve the tridiagonal toeplitz matrix system derived.展开更多
文摘In this paper, we consider a non-local PDE model with delay for population dynamics in Rn. First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term at infinity. Then, we obtain the global attractor by proving w-limit compactness property of the solution operator semigroup.
基金funding support from the Science and Technology Commission of Shanghai Municipality(Grant No.21DZ1100500)the Shanghai Frontiers Science Center Program(2021-2025 No.20)+2 种基金the Zhangjiang National Innovation Demonstration Zone(Grant No.ZJ2019ZD-005)supported by a fellowship from the China Postdoctoral Science Foundation(2020M671169)the International Postdoctoral Exchange Program from the Administrative Committee of Post-Doctoral Researchers of China([2020]33)。
文摘Significant progress has been made in computational imaging(CI),in which deep convolutional neural networks(CNNs)have demonstrated that sparse speckle patterns can be reconstructed.However,due to the limited“local”kernel size of the convolutional operator,for the spatially dense patterns,such as the generic face images,the performance of CNNs is limited.Here,we propose a“non-local”model,termed the Speckle-Transformer(SpT)UNet,for speckle feature extraction of generic face images.It is worth noting that the lightweight SpT UNet reveals a high efficiency and strong comparative performance with Pearson Correlation Coefficient(PCC),and structural similarity measure(SSIM)exceeding 0.989,and 0.950,respectively.
基金supported by the National Key R&D Program of China under Grant No.2021ZD0110400.
文摘Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.
基金Project(50904036) supported by the National Natural Science Foundation of ChinaProject (20090450421) supported China Postdoctoral Science Foundation
文摘In view of the non-local phenomena appearing in the rock and concrete-like materials, the non-local damage and fracture model of rock and concrete-like materials was established through non-local method of Gaussian weighting function. The result indicates that, the stress of one point in the material is correlated not only to its strain history, but also to the interaction of the points in its certain adjacent region of the material. Based on the established non-local model, the numerical simulation of notch containing three-point bending beam was carried out. The results show that the grid sensitivities have been avoided and the fracture direction of the material has not been influenced by the grid shape, and the model proposed can be used to better simulate the damage developing process of the rock and concrete-like materials.
基金the National Natural Science Foundation of China(No.19632030)
文摘A non-local continuum model for strain-softening simply takingplastic strain or damage vari- able as a non-local variable isderived by using the additive decomposition principle of finitedeformation gra- dient. At the same time, variational equations,their finite element formulations and numerical convolutedintegration algorithm of the model in current configuration usuallycalled co-moving coordinate system are given. stability andconvergence of the model are proven by means of the weak convergencetheorem of gen- eral function and the convoluted integration theory.
文摘In this paper a new approach for PBL simulation, the non-local closure scheme based on the transient turbulence theory has been used. It was set up as an alternative to local closure schemes which physical concept is reasonable and distinct. A 2-D non-local closure model was developed in order to study the PBL structure and simulatesome interesting atmospheric processes over non-ulliform underlying surface, especially under the convective and unique weather conditions, such as sea-land circulation and the TIBL structure. The modelled results show good agreement with field measurement.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11175077 and 11575075the Natural Science Foundation of Liaoning Province under Grant No L201683666
文摘We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m2n-2R□-nRto the Einstein-Hilbert action. Moreover, to obtain some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter ε for different n. By analysis we give the constraints on the model parameters ε.
基金Project supported by the National Natural Science Foundation of China(No.10272070)and the Development Foun-dation of the Education Commission of Shanghai,China.
文摘Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.
基金supported by the University of Kashan(No.463865/13)the Iranian Nanotechnology Development Committee
文摘A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional （2D） electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thick- ness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.
基金financially sponsored by Research Institute of Petroleum Exploration&Development(PETROCHINA)Scientific Research And Technology Development Projects(No.2016ycq02)China National Petroleum Corporation Science&Technology Development Projects(No.2015B-3712)Ministry of National Science&Technique(No.2016ZX05007-006)
文摘For random noise suppression of seismic data, we present a non-local Bayes （NL- Bayes） filtering algorithm. The NL-Bayes algorithm uses the Gaussian model instead of the weighted average of all similar patches in the NL-means algorithm to reduce the fuzzy of structural details, thereby improving the denoising performance. In the denoising process of seismic data, the size and the number of patches in the Gaussian model are adaptively calculated according to the standard deviation of noise. The NL-Bayes algorithm requires two iterations to complete seismic data denoising, but the second iteration makes use of denoised seismic data from the first iteration to calculate the better mean and covariance of the patch Gaussian model for improving the similarity of patches and achieving the purpose of denoising. Tests with synthetic and real data sets demonstrate that the NL-Bayes algorithm can effectively improve the SNR and preserve the fidelity of seismic data.
文摘The purpose of this study is to present an application of a novel enhancement technique for enhancing medical images generated from X-rays. The method presented in this study is based on a nonlinear partial differential equation （PDE） model, Kramer＇s PDE model. The usefulness of this method is investigated by experimental results. We apply this method to a medical X-ray image. For comparison, the X-ray image is also processed using classic Perona-Malik PDE model and Catte PDE model. Although the Perona-Malik model and Catte PDE model could also enhance the image, the quality of the enhanced images is considerably inferior compared with the enhanced image using Kramer＇s PDE model. The study suggests that the Kramer＇s PDE model is capable of enhancing medical X-ray images, which will make the X-ray images more reliable.
文摘A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this paper is to propose some efficient and accurate numerical methods for the computational solution of one-dimensional continuous basic models for the growth and control of brain tumors. After computing the analytical solution, we construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization. Then, we investigate the convergence behavior of Conjugate gradient and generalized minimum residual as Krylov subspace methods to solve the tridiagonal toeplitz matrix system derived.
