Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of t...Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a gen- eral theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived： （a） Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. （b） On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. （c） Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradi- ents form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. （d） The direction of the driving force induced by the hard curved surface is independent of the hydrophilieity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.展开更多
Thermocapillary migration in lubrication systems is a phenomenon in which the lubricant migrates via the interfacial tension difference caused by the nonuniform temperature generated by the wear behavior,which leads t...Thermocapillary migration in lubrication systems is a phenomenon in which the lubricant migrates via the interfacial tension difference caused by the nonuniform temperature generated by the wear behavior,which leads to lubricant starvation and results in severe damage.This paper proposes a novel method to eliminate the thermocapillary migration phenomenon,in which we successfully fabricate a surface that combines a shape gradient and wettability pattern on 316 L stainless steel,and the results prove that the prepared surface can not only effectively obstruct liquid paraffin droplet migration but also directionally transport liquid paraffin to the center of the wear track under the thermocapillary migration effect.The results of the wear tests further demonstrated that only the surface combination of a shape gradient and wettability pattern can achieve a decrease in the friction coefficient by means of external lubricant feeding in the state of lubricant starvation,which provides a strategy for improving and developing new types of lubrication enhancement for mitigating starvation lubrication.展开更多
We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is...We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H^(1) shape gradient flows.Convergence analysis with a priori error estimates is provided under general and different regularity assumptions.We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow.Numerical comparisons in 2D and 3D show that the distributed H1 shape gradient flow is more accurate than the popular boundary type.The corresponding distributed shape gradient algorithm is more effective.展开更多
Shape gradient flows are widely used in numerical shape optimization algorithms.We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems.We present...Shape gradient flows are widely used in numerical shape optimization algorithms.We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems.We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative.Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.展开更多
This paper describes a simple method of generating concentration gradients with linear and parabolic profiles by using a Christmas tree-shaped microfluidic network.The microfluidic gradient generator consists of two p...This paper describes a simple method of generating concentration gradients with linear and parabolic profiles by using a Christmas tree-shaped microfluidic network.The microfluidic gradient generator consists of two parts：a Christmas tree-shaped network for gradient generation and a broad microchannel for detection.A two-dimensional model was built to analyze the flow field and the mass transfer in the microfluidic network.The simulating results show that a series of linear and parabolic gradient profiles were generated via adjusting relative flow rate ratios of the two source solutions（R_L^2≥0.995 and _PR^2≥0.999）,which could match well with the experimental results（R_L^2≥0.987 and _PR^2≥0.996）.The proposed method is promising for the generation of linear and parabolic concentration gradient profiles,with the potential in chemical and biological applications such as combinatorial chemistry synthesis,stem cell differentiation or cytotoxicity assays.展开更多
For better controllability in actuations,it is desirable to create Functionally Graded Shape Memory Alloys（FG-SMAs）in the actuation direction.It can be achieved by applying different heat treatment processes to crea...For better controllability in actuations,it is desirable to create Functionally Graded Shape Memory Alloys（FG-SMAs）in the actuation direction.It can be achieved by applying different heat treatment processes to create the gradient along the radius of a SMA cylinder.Analytical solutions are derived to predict the macroscopic behaviors of such a functionally graded SMA cylinder.The Tresca yield criterion and linear hardening are used to describe the different phase transformations with different gradient parameters.The numerical results for an example of the model exhibit different pseudo-elastic behaviors from the non-gradient case,as well as a variational hysteresis loop for the transformation,providing a mechanism for easy actuation control.When the gradient disappears,the model can degenerate to the non-gradient case.展开更多
This paper is concerned with the optimal design of an obstacle located in the viscous and incompressible fluid which is driven by the steady-state Oseen equations with thermal effects. The structure of shape gradient ...This paper is concerned with the optimal design of an obstacle located in the viscous and incompressible fluid which is driven by the steady-state Oseen equations with thermal effects. The structure of shape gradient of the cost functional is derived by applying the differentiability of a minimax formulation involving a Lagrange functional with a space parametrization technique. A gradient type algorithm is employed to the shape optimization problem. Numerical examples indicate that our theory is useful for practical purpose and the proposed algorithm is feasible.展开更多
The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void...The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void shape effect and the Fleck-Hutchinson phenomenological strain gradient plasticity theory is employed to capture the size effects. It is found that the combined effects of void size and void shape are mainly controlled by the remote stress triaxiality. Based on this, a new size-dependent void growth model similar to the Rice-Tracey model is proposed and an important conclusion about the size-dependent void growth is drawn： the growth rate of the void with radius smaller than a critical radius rc may be ignored. It is interesting that rc. is a material constant independent of the initial void shape and the remote stress triaxiality.展开更多
A gyrokinetic model with integral eigenmode equations is developed based on the local equilibrium of shaped tokamak plasmas. Effects of main geometric parameters （finite aspect ratio, elongation, triangularity, and S...A gyrokinetic model with integral eigenmode equations is developed based on the local equilibrium of shaped tokamak plasmas. Effects of main geometric parameters （finite aspect ratio, elongation, triangularity, and Shafranov shift gradient） on the electrostatic electron temper- ature gradient （ETG） driven modes are investigated numerically. It is found that the finite aspect ratio has a general stabilizing effect, while the elongation can be either stabilizing or destabilizing, depending on the poloidal wavelength of the mode and other parameters. It is shown that a low aspect ratio enhances the stabilizing effect of elongation, and weakens its destabilizing effect as well.展开更多
基金supported by the National Natural Science Foundation of China(Nos.10872114,10672089, 10832005,and 11072125)
文摘Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a gen- eral theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived： （a） Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. （b） On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. （c） Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradi- ents form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. （d） The direction of the driving force induced by the hard curved surface is independent of the hydrophilieity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.
基金supported by the National Natural Science Foundation of China(No.52205204)the Outstanding Youth Innovation Team in Universities of Shandong Province(No.2023KJ116).
文摘Thermocapillary migration in lubrication systems is a phenomenon in which the lubricant migrates via the interfacial tension difference caused by the nonuniform temperature generated by the wear behavior,which leads to lubricant starvation and results in severe damage.This paper proposes a novel method to eliminate the thermocapillary migration phenomenon,in which we successfully fabricate a surface that combines a shape gradient and wettability pattern on 316 L stainless steel,and the results prove that the prepared surface can not only effectively obstruct liquid paraffin droplet migration but also directionally transport liquid paraffin to the center of the wear track under the thermocapillary migration effect.The results of the wear tests further demonstrated that only the surface combination of a shape gradient and wettability pattern can achieve a decrease in the friction coefficient by means of external lubricant feeding in the state of lubricant starvation,which provides a strategy for improving and developing new types of lubrication enhancement for mitigating starvation lubrication.
基金This work was supported in part by the National Natural Science Foundation of China under grants(No.11571115 and No.12071149)Natural Science Foundation of Shanghai(No.19ZR1414100)Science and Technology Commission of Shanghai Municipality(No.18dz2271000).
文摘We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H^(1) shape gradient flows.Convergence analysis with a priori error estimates is provided under general and different regularity assumptions.We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow.Numerical comparisons in 2D and 3D show that the distributed H1 shape gradient flow is more accurate than the popular boundary type.The corresponding distributed shape gradient algorithm is more effective.
基金supported in part by the National Key Basic Research Program under grant 2022YFA1004402the Science and Technology Commission of Shanghai Municipality(Nos.21JC1402500,22ZR1421900,and 22DZ2229014)the National Natural Science Foundation of China under grant(No.12071149).
文摘Shape gradient flows are widely used in numerical shape optimization algorithms.We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems.We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative.Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.
基金Supported by the National Natural Science Foundation of China(81372358,81527801,51303140,and 81602489)the Natural Science Foundation of Hubei Province(2014CFA029)+1 种基金the Colleges of Hubei Province Outstanding Youth Science and Technology Innovation Team(T201305)the Applied Foundational Research Program of Wuhan Municipal Science and Technology Bureau(2015060101010056)
文摘This paper describes a simple method of generating concentration gradients with linear and parabolic profiles by using a Christmas tree-shaped microfluidic network.The microfluidic gradient generator consists of two parts：a Christmas tree-shaped network for gradient generation and a broad microchannel for detection.A two-dimensional model was built to analyze the flow field and the mass transfer in the microfluidic network.The simulating results show that a series of linear and parabolic gradient profiles were generated via adjusting relative flow rate ratios of the two source solutions（R_L^2≥0.995 and _PR^2≥0.999）,which could match well with the experimental results（R_L^2≥0.987 and _PR^2≥0.996）.The proposed method is promising for the generation of linear and parabolic concentration gradient profiles,with the potential in chemical and biological applications such as combinatorial chemistry synthesis,stem cell differentiation or cytotoxicity assays.
基金the financial support of National Natural Science Foundation of China (no.11502284, 51505483, 11772041)the Fundamental Research Funds for the Central Universities (3122016C006) of China
文摘For better controllability in actuations,it is desirable to create Functionally Graded Shape Memory Alloys（FG-SMAs）in the actuation direction.It can be achieved by applying different heat treatment processes to create the gradient along the radius of a SMA cylinder.Analytical solutions are derived to predict the macroscopic behaviors of such a functionally graded SMA cylinder.The Tresca yield criterion and linear hardening are used to describe the different phase transformations with different gradient parameters.The numerical results for an example of the model exhibit different pseudo-elastic behaviors from the non-gradient case,as well as a variational hysteresis loop for the transformation,providing a mechanism for easy actuation control.When the gradient disappears,the model can degenerate to the non-gradient case.
文摘This paper is concerned with the optimal design of an obstacle located in the viscous and incompressible fluid which is driven by the steady-state Oseen equations with thermal effects. The structure of shape gradient of the cost functional is derived by applying the differentiability of a minimax formulation involving a Lagrange functional with a space parametrization technique. A gradient type algorithm is employed to the shape optimization problem. Numerical examples indicate that our theory is useful for practical purpose and the proposed algorithm is feasible.
基金The project supported by the National Natural Science Foundation of China(A10102006)the New Century Excellent Talents in Universities of China.
文摘The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void shape effect and the Fleck-Hutchinson phenomenological strain gradient plasticity theory is employed to capture the size effects. It is found that the combined effects of void size and void shape are mainly controlled by the remote stress triaxiality. Based on this, a new size-dependent void growth model similar to the Rice-Tracey model is proposed and an important conclusion about the size-dependent void growth is drawn： the growth rate of the void with radius smaller than a critical radius rc may be ignored. It is interesting that rc. is a material constant independent of the initial void shape and the remote stress triaxiality.
基金National Natural Science Foundation of China(No.10405014)
文摘A gyrokinetic model with integral eigenmode equations is developed based on the local equilibrium of shaped tokamak plasmas. Effects of main geometric parameters （finite aspect ratio, elongation, triangularity, and Shafranov shift gradient） on the electrostatic electron temper- ature gradient （ETG） driven modes are investigated numerically. It is found that the finite aspect ratio has a general stabilizing effect, while the elongation can be either stabilizing or destabilizing, depending on the poloidal wavelength of the mode and other parameters. It is shown that a low aspect ratio enhances the stabilizing effect of elongation, and weakens its destabilizing effect as well.
