Wen Chen

Hohai University · Institute of Soft Matter Mechanics

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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。

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 (...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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],...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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+

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...

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...

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...

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...

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...

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...

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...

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...

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...

Based on the implicit calculus equation modeling approach, this paper proposes a speculative concept of the potential and wave operators on negative dimensionality. Unlike the standard partial differential equation (PDE) modeling, the implicit calculus modeling approach does not require the explicit expression of the PDE governing equation. Instead...

In the present paper, the nanoindentation of an elastic half-space by a conical indenter is investigated with the influence of surface tension. Based on the solution of a point force acting on an elastic half-space with surface tension, the singular integral equation of this problem is formulated and is then solved numerically by using the Gauss–Ch...

Based on the fractal derivative, a robust viscoelastic element—fractal dashpot—is proposed to characterize the rheological behaviors of non-Newtonian fluid. The mechanical responses of the fractal dashpot are investigated with different strains and stresses, which are compared with the existing dashpot models, including the Newton dashpot and the A...

This paper firstly employs the fast multipole method (FMM) to accelerate the singular boundary method (SBM) solution of the Stokes equation. We present a fast multipole singular boundary method (FMSBM) based on the combination of the SBM and the FMM. The proposed FMSBM scheme reduces CPU operations and memory requirements by one order of magnitude,...

This study investigates the combined Rankine power and the absorption cooling cycles. The working fluid used in this cycle is the binary liquid mixture of water and ammonia. It produces both refrigeration and power simultaneously via a single heat source. Parametric analysis has been adopted to evaluate the thermodynamic parameters effects on the o...

Non-Newtonian fluid has complex rheological characteristics. It is very helpful to reveal these characteristics for the applications of non-Newtonian fluid in industry and agriculture. The classical rheological models of non-Newtonian fluid usually have sophisticated forms and the limitations of specific materials or rheological situations. Fractio...

This paper proposes a novel variational model to remove either independent additive or multiplicative noise from synthetic and natural digital images via the fractional-order derivative operator. The non-local characteristics of fractional derivatives can help preserve textures and eliminate the “blocky effect”. The proposed strategy uses the fract...

The generalized finite difference method (GFDM) is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems. The method involves a coupling between the Taylor series expansions and weighted moving least-squares method. The main idea here is to fully inherit the high-accuracy advantage of the former...

In this paper, an advanced boundary element method (BEM) is developed for solving three-dimensional (3D) anisotropic heat conduction problems in thin-walled structures. The troublesome nearly singular integrals, which are crucial in the applications of the BEM to thin structures, are calculated efficiently by using a nonlinear coordinate transforma...

The singular boundary method (SBM) is a recent strong-form boundary collocation method which uses a linear combination of the fundamental solution of the governing equation to approximate the field variables. Due to its full interpolation matrix, the SBM solution encounters the high computational complexity and storage requirement that limit its ap...