Wen Chen

Wen Chen
Hohai University · Institute of Soft Matter Mechanics

PhD

About

462
Publications
126,410
Reads
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12,371
Citations
Introduction
Some original works are structural derivative model for extra-slow diffusion, Hausdorff derivative & fractal operators, positive fractional time derivative, physics models of frequency-dependent acoustic attenuation, power-law actual gas model, fractal quantum relationships, PDE-based RBF wavelets, nonlinear matrix product, singular boundary method and boundary knot method which are free of mesh, integration, fictitious boundary and especially efficient for high-frequency waves.
Additional affiliations
March 2006 - present
Hohai University
Position
  • Professor (Full)
Description
  • Director of Institute of Soft Matter Mechanics (2006-2015), Associate Dean of College of Civil Engineering (2007-2010), Assoicat Dean (2010-2013) and Dean (2013-2016) of College of Mechanics and Materials.
March 2006 - present
Hohai University
Position
  • Professor (Full)
January 2004 - January 2006
Institute of Applied Physics and Computational Mathematics
Position
  • Professor
Description
  • Basic research
Education
March 1994 - March 1997
Shanghai Jiao Tong University
Field of study
  • Mechanical Engineering
September 1991 - March 1994
Shanghai Jiao Tong University
Field of study
  • Mechanical Engineering
September 1984 - June 1988
Huazhong University of Science and Technology
Field of study
  • Engineering Mechanics

Publications

Publications (462)
Book
Full-text available
A few novel radial basis function (RBF) discretization schemes for partial differential equations are developed in this study. For boundary-type methods, we derive the indirect and direct symmetric boundary knot methods. Based on the multiple reciprocity principle, the boundary particle method is introduced for general inhomogeneous problems withou...
Article
This study unveils the time–space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time–space fabric on physical behaviors and accordingly derive fractional quantum relationships between energy and frequency, momentum and wavenumber which further give rise to fr...
Article
This paper proposes a new implicit definition of the fractional Laplacian. Compared with the existing explicit definitions in literature, this novel definition has clear physical significance and is mathematically simple and numerically easy to calculate for multidimensional problems. In stark contrast to a quick increasing and extensive applicatio...
Article
This paper proposes a novel structural derivative approach to tackle the perplexing modeling problem of ultraslow diffusion. The structural function plays a central role in this new strategy as a kernel transform of underlying time-space fabric of physical systems. Ultraslow diffusion has been observed in numerous lab experiments and field observat...
Article
This paper proposes a fractional biharmonic operator equation model in the time-space domain to describe scattering attenuation of acoustic waves in heterogeneous media. Compared with the existing models, the proposed fractional model is able to describe arbitrary frequency-dependent scattering attenuation, which typically obeys an empirical power...
Article
The 4E analysis is utilized on a bulky combined cycle power plant (CCPP) with a dual pressure recovery boiler and an additional duct burner. Multi-objective evolutionary optimizations have been applied to obtain the best state of the heat recovery steam generator (HRSG), saturated temperature, cost reduction, and carbon dioxide emission, simultaneo...
Article
Ultrafast diffusion process characterized by unusually large diffusivities is often occurs on porous media and the mean square displacement grows exponentially in time. This paper clarifies the characteristics of ultrafast diffusion and tackles this perplexing problem using the fractional Brownian motion run with a nonlinear clock model. We employ...
Article
In this paper, we present a meshless method of fundamental solutions using the analytical crack Green’s function to solve anti-plane crack problems. The proposed scheme is a simple, powerful and effective collocation method for crack problems since it only requires the boundary discretization without special treatments of the crack. Three typical n...
Article
Full-text available
This research paper analyzes the exergy of an absorption refrigeration cycle with a multi mixture working fluid selected as water and lithium-bromide. It relies on the fundamental thermodynamic principles, being chiefly the first and second laws. The exergy destructions have been obtained from different parts of the cycle; after which several compo...
Article
This paper summarizes the latest advances of the third author’s research group on stretched Gaussian distribution underlying the Hausdorff fractal theory and its applications in fitting stretched Gaussian noise. Firstly, the Hausdorff fractal metrics are introduced as an extension of non-Euclidean distance. Based on the fractal scaling, the Hausdor...
Article
Full-text available
Image edge extraction based on the differential equations is an important branch of image processing. This paper makes the first attempt to employ the Hausdorff derivative gradient method (HDHM) to extract the image edge. In terms of the visual quality of details, contours, edge integrity, and continuity, the original images and noisy images were e...
Article
Fractional viscoelastic models have been confirmed to achieve good agreement with experimental data using only a few parameters, in contrast to the classical viscoelastic models in previous studies. With an increasing number of applications, the physical meaning of fractional viscoelastic models has been attracting more attention. This work establi...
Article
Full-text available
The memristor is of great application and significance in the integrated circuit design, the realization of large-capacity non-volatile memories and the neuromorphic systems. This paper firstly proposes the non-local structural derivative memristor model with two-degree-of-freedom increased to portray the memory effect of memristor. Actually, the d...
Article
Roughness induces the complex transport of fluid on interfacial flow. The intrinsic asperities of surfaces involve fractal trait. A fractal roughness model for the transport of fractional non-Newtonian fluid is proposed in this work. In the present analysis, the effective local radius is characterized by means of the algebraic superposition of the...
Article
Flow problem for non-Newtonian fluid has drawn considerable attention over past decades. In this study, we theoretically and numerically investigate the unsteady Stokes’ flow problem of the viscoelastic fluid. The constitutive equation of the viscoelastic fluid is modified from the Newtonian fluid by introducing the Hausdorff derivative, called the...
Book
复杂介质的力学行为经常表现出“反常”现象,因此不能采用传统的力学模型描述。豪斯道夫导数作为一种新型的建模工具,可以用来模拟复杂介质的流变、扩散等现象。本书主要介绍豪斯道夫导数的建模方法和工程应用。在理论研究方面,本书介绍了豪斯道夫导数的定义及其理论基础,并给出了统计力学解释;在实际应用方面,概述了豪斯道夫导数模型在流体力学、黏弹性力学、振动力学等方面的应用。此外,本书还介绍了求解豪斯道夫导数方程的计算方法和豪斯道夫导数模型的广义形式。本书涵盖了豪斯道夫导数的基本知识、建模方法、统计力学解释、工程应用和数值计算方法。 本书可供从事水文工程、土木工程、交通工程、采矿工程等研究的科技人员参考,亦可作为高等学校工程力学、环境力学、岩土力学等专业的研究生选修课教材或教学参考书。
Preprint
Stretched Gaussian distribution is the fundamental solution of the Hausdorff derivative diffusion equation and its corresponding stretched Gaussian noise is a widely encountered non-Gaussian noise in science and engineering. The least square method is a standard regression approach to fit Gaussian noisy data, but has distinct limits for non-Gaussia...
Article
Full-text available
This study intends to present a general formulation for the hybrid Jacobi and block pulse operational matrix of fractional integral operator in order to solve fractional differential and integro-differential equations. First, we define hybrid Jacobi polynomials and block pulse functions as an orthogonal basis for function approximation. Then, we co...
Article
This paper proposes a general time-space metric by an extension of the power-function-based fractal concept to the structural function fabric. The structural function can be an arbitrary-function to describe complex metric underlying physical systems. We call such a metric “structal”, and the fractal metric is its special case. This work is inspire...
Article
Efficient evaluation of near-boundary and boundary solutions for the Helmholtz equation with wideband wavenumbers by the boundary collocation method has been a difficult task for a long time. This study provides a regularized approach to bypass this limitation. The singular boundary method avoids the near singularity by using the nearly singular fa...
Article
Image sharpening based on the partial differential equations plays an important role in the fields of image processing. It is an effective technique to clear and sharpen image features, and provides a higher resolution for the subsequent processing. This paper makes the first attempt to employ the Hausdorff derivative Laplacian operator to sharpen...
Article
A modified multilevel algorithm for solving the excessive storage requirements and ill-conditioning encountered in the boundary-type discretization method is proposed. The modified multilevel algorithm is an extension of the modified dual-level algorithm from dual levels to multiple levels. The method is a kernel-independent method. The core idea i...
Article
Full-text available
A dual-level method of fundamental solutions in conjunction with kernel-independent fast multipole method is proposed in this study. The competitive attributes of the method are that it inherits high accuracy of the method of fundamental solutions, yet avoids producing the resulting ill-conditioned linear system of equations. In contrast to the met...
Article
The main purpose of this work is to present an impressive numerical scheme to solve two-dimensional multi-term time fractional mixed diffusion-wave differential equations (TFMDWE). The proposed method is based on the compact dual reciprocity method and the meshless improved singular boundary method (ISBM). The most significant privilege of the prop...
Preprint
Full-text available
The aim of this paper is to propose a fast meshless numerical scheme for the simulation of non-linear SchrödingerSchr¨Schrödinger equations. In the proposed scheme, the implicit-Euler scheme is used for the temporal discretization and the localized method of approximate particular solution (LMAPS) is utilized for the spatial discretization. The mul...
Article
Full-text available
In this study, a new framework for the efficient and accurate solutions of three-dimensional (3D) dynamic coupled thermoelasticity problems is presented. In our computations, the Krylov deferred correction (KDC) method, a pseudo-spectral type collocation technique, is introduced to perform the large-scale and long-time temporal simulations. The gen...
Article
Full-text available
In this article, by using nonlinear Leray–Schauder-type alternative and Banach’s fixed point theorem, we investigate existence and uniqueness of solutions. We also prove Hyers–Ulam stability for the proposed coupled system of fractional differential equations (FDEs) with the nonlinear p-Laplacian operator and Riemann–Liouville integral boundary con...
Article
Full-text available
The difficulty in the description of thixotropic behaviors in semisolid foodstuffs is the time dependent nature of apparent viscosity under constant shear rate. In this study, we propose a novel theoretical model via fractional derivative to address the high demand by industries. The present model adopts the critical parameter of fractional derivat...
Article
A thorough understanding of the flow behavior of non⁃Newtonian fluid is the first step for analyzing, predicting and controlling of pipe flow. Experiments indicate that non⁃Newtonian fluid is historically dependent on the procedure of shear flow. The constitutive model for fractional non⁃Newtonian fluid was established via the spatial fractional ca...
Article
A thorough understanding of the flow behavior of non⁃Newtonian fluid is the first step for analyzing, predicting and controlling of pipe flow. Experiments indicate that non⁃Newtonian fluid is historically dependent on the procedure of shear flow. The constitutive model for fractional non⁃Newtonian fluid was established via the spatial fractional ca...
Article
Full-text available
A modified dual-level algorithm is proposed in the article. By the help of the dual level structure, the fully-populated interpolation matrix on the fine level is transformed to a local supported sparse matrix to solve the highly ill-conditioning and excessive storage requirement resulting from fully-populated interpolation matrix. The kernel-indep...
Article
Full-text available
Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other variables dependent order have been successfully applied to investigate time and/or space dependent dynamics. This study aims to provide a survey of the recent relevant literature and findings in primary definitions, models, numerical methods and their...
Article
Full-text available
Minimization functionals related to Euler's elastica energy has a broad range of applications in computer vision and image processing. This paper proposes a novel Euler's elastica and curvature-based variational model for image restoration corrupted with multiplicative noise. It combines Euler's elastica curvature with a Weberized total variation (...
Article
Full-text available
In this study, an absorption refrigeration cycle with the working fluid of water-lithium bromide is considered. The needful energy for generator is supplied by the steam at 100°C and in one atmospheric pressure. The exergy analysis is conducted on the whole cycle and it is calculated based on the first and the second laws of thermodynamics. Various...
Article
Full-text available
The main difficulty of the singular boundary method (SBM) is the calculation of the origin intensity factors introduced to remove the singularity of fundamental solution. This work presents an extension of the previous SBM formation. The new contribution of the present method is that the origin intensity factors for potential field gradients are de...
Article
In this paper, the generalized finite difference method (GFDM) combined with the Newton–Raphson method is proposed to accurately and efficiently simulate the steady-state double-diffusive natural convection in parallel- ogrammic enclosures filled with fluid-saturated porous media. The natural convection in fluid-saturated porous media, which is int...
Article
Full-text available
Granular materials as typical soft matter, their transport properties play significant roles in durability and service life in relevant practical engineering structures. Physico-mechanical properties of materials are generally dependent of their microstructures including interfacial and porous characteristics. The formation of such microstructures...
Article
A modified dual-level fast multipole boundary element method is proposed in this article. The core idea of the method is to use a dual-level structure to handle the excessive storage requirement and ill-conditioned problems resulting from the fully-populated interpolation matrix of the boundary element method. On one hand, the fully-populated matri...
Conference Paper
Full-text available
In this study, an absorption refrigeration cycle with the working fluid of water-lithium bromide is considered. The needful energy for generator is supplied by the steam at 100°C and in one atmospheric pressure. The exergy analysis is conducted on the whole cycle and it is calculated based on the first and the second laws of thermodynamics. Various...
Article
This paper aims at presenting a survey of the fractional derivative acoustic wave equations, which have been developed in recent decades to describe the observed frequencydependent attenuation and scattering of acoustic wave propagating through complex media. The derivation of these models and their underlying elastoviscous constitutive relationshi...
Article
Large-scale sound field analysis is a difficult task for numerical simulations. In this study, a modified dual-level fast multipole boundary element method is proposed for analyzing this challenging problem. The proposed method is based on the Burton–Miller formulation to overcome the non-uniqueness issues in exterior acoustic problems. By transfor...
Article
This paper presents a novel meshless method for the simulation of Helmholtz equations in arbitrary 2D domains. In the proposed method, the boundary conditions are approximated in advance to given the primary approximation of the solution. Then the final approximation is given by the summation of the primary approximation, the radial basis functions...
Article
The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we i...
Article
Full-text available
This paper deals with 2 core aspects of fractional calculus including existence of positive solution and Hyers‐Ulam stability for a class of singular fractional differential equations with nonlinear p‐Laplacian operator in Caputo sense. For these aims, the suggested problem is converted into an integral equation via Green function , for ε∈(n−1,n],...
Article
Full-text available
Active noise control is an efficient strategy of noise control. A numerical wave shielding model to inhibit wave propagation , which can be considered as an extension of traditional active noise control, is established using the singular boundary method using time-dependent fundamental solutions in this study. Two empirical formulas to evaluate the...
Article
In this paper, we apply the novel singular boundary method for the simulation of heat conduction problems in layered materials. The singular boundary method is a recently developed boundary-type meshless collocation method. While inheriting the merits of conventional boundary-type methods, mesh and singularity of fundamental solutions are also circ...
Article
This paper proposes a dissipative acoustic wave equation in which the fractal derivative is employed to represent dissipation. The proposed model is derived from the viscoelastic constitutive relationship via the fractal derivative. It is noted that the fractal derivative is a local operator and avoids the expensive computational costs of non-local...
Article
Full-text available
The local radial basis function (RBF) method is a promising solver for variable-order time fractional diffusion equation (TFDE) since it overcomes the computational burden of the traditional global method. Application of the local RBF method however is limited to Fickian diffusion, while real-world diffusion is usually non-Fickian in multiple dimen...
Article
Full-text available
To characterize the visco–elasto-plastic behavior of metals and alloys we propose a new constitutive equation based on a time–space fractional derivative. The rheological representative of the model can be analogous to that of the Bingham–Maxwell model, while the dashpot element and sliding friction element are replaced by the corresponding fractio...
Article
Surface tension plays a significant role in micro- and nanoindentation tests. Based on the solution of a concentrated force acting on an elastic half-plane with surface tension, the two-dimensional indentations of an elastic half-plane by a cylindrical indenter, a wedge indenter and a flat-ended indenter are formulated, and by employing the Gauss–C...
Article
The Kansa method with the Multiquadric-radial basis function (MQ-RBF) is inherently meshfree and can achieve an exponential convergence rate if the optimal shape parameter is available. However, it is not an easy task to obtain the optimal shape parameter for complex problems whose analytical solution is often a priori unknown. This has long been a...
Article
Full-text available
Non-Newtonian fluid flow can be driven by spatially nonlocal velocity, the dynamics of which can be described by promising fractional derivative models. This study reports a left-side, Caputo type, space fractional-order constitutive equation (FCE) using a nonlocal, fractional velocity gradient and then interprets physical properties of non-Newtoni...
Article
Full-text available
Many theoretical and experimental results show that solute transport in heterogeneous porous media exhibits multi-scaling behaviors. To describe such non-Fickian diffusions, this work provides a distributed order Hausdorff diffusion model to describe the tracer transport in porous media. This model is proved to be equivalent with the diffusion equa...
Code
The Singularity toolbox is to solve the singularity at origin of the fundamental solution for 2-D and 3-D problems. The toolbox will be continually updated by Junpu Li (junpu.li@foxmail.com) at Hohai University. Requirements: Matlab 2016b+
Article
The time-dependent soil infiltration rate was derived based on the Hausdorff fractal derivative Richards equation. This model requires only 2 parameters, among which the Hausdorff derivative order characterizes the underlying water transport environment property in hetero-geneous soil, while the pore size distribution index categorizes different hy...
Article
We propose a novel Trefftz method for the numerical solution of the direct problem as well as the Cauchy problem of the multi-dimensional Laplace equation in an arbitrary domain. In the multiple/scale/direction Trefftz method (MSDTM) the directions are hyper-spherical unit vectors given explicitly, and the scales are determined by the collocation p...
Article
Full-text available
It has been long observed that cumbersome parameters are required for the traditional viscoelastic models to describe complex rheological behaviors. Inspired by the relationship between normal and anomalous diffusions, this paper tentatively employs tα to replace t, called as the scaling transformation, in the traditional creep compliance and relax...
Article
Full-text available
The Digital Total Variation (DTV) filtering is a digitized energy method used to denoise the measured image data. Different from the traditional variation method, this technique applies to arbitrarily located data points and also has the built-in edge detective property. This paper introduces a novel meshfree algorithm (Kansa technique) using DTV m...
Article
The main purpose of this article is to propose a modified singular boundary method using the modified fundamental solution of Helmholtz equation for simulation of three-dimensional high frequency acoustic wave problems. Compared with the standard second-order discretization methods which usually need to place more than 10-12 grid points in one wave...
Article
Full-text available
In this paper, a new formulation is proposed to evaluate the origin intensity factors (OIFs) in the singular boundary method (SBM) for solving 3D potential problems with Dirichlet boundary condition. The SBM is a strong-form boundary discretization collocation technique and is mathematically simple, easy-to-program, and free of mesh. The crucial st...
Article
This paper derives the time-dependent fundamental solution of the transient convection-diffusion problem by employing the exponential variable and Fourier transformations. A singular boundary method (SBM) formulation using this time-dependent fundamental solution is first applied in the simulation of the transient convection-diffusion problems. Acc...
Article
The Hausdorff derivative partial differential equations have in recent years been found to be capable of describing complex mechanics and physics behaviors such as anomalous diffusion, creep and relaxation in fractal media. But most research is concerned with time Hausdorff derivative models, and little has been reported on the numerical solution o...
Article
Full-text available
In this paper, we study the existence and uniqueness of solution (EUS) as well as Hyers-Ulam stability for a coupled system of FDEs in Caputo’s sense with nonlinear p-Laplacian operator. For this purpose, the suggested coupled system is transferred to an integral system with the help of four Green functions Gα1(t,s), Gβ1(t,s), Gα2(t,s), Gβ2(t,s). T...