The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Xiaoqiang Wang - One of the best experts on this subject based on the ideXlab platform.
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efficient and stable exponential time differencing runge kutta methods for phase field Elastic Bending energy models
Journal of Computational Physics, 2016Co-Authors: Xiaoqiang WangAbstract:The Willmore flow formulated by phase field dynamics based on the Elastic Bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.
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modelling and simulations of multi component lipid membranes and open membranes via diffuse interface approaches
Journal of Mathematical Biology, 2007Co-Authors: Xiaoqiang WangAbstract:Diffuse interface (phase field) models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the Elastic Bending energy and the line tension energy with prescribed volume and surface area constraints. By comparing our numerical simulations with recent biological experiments, it is demonstrated that the diffuse interface models can effectively capture the rich phenomena associated with the multi-component vesicle transformation and thus offering great functionality in their simulation and modelling.
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Simulating the deformation of vesicle membranes under Elastic Bending energy in three dimensions
Journal of Computational Physics, 2006Co-Authors: Chun Liu, Xiaoqiang WangAbstract:In this paper, we study the three-dimensional deformation of a vesicle membrane under the Elastic Bending energy, with prescribed bulk volume and surface area. Both static and dynamic deformations are considered. A newly developed energetic variational formulation is employed to give an effective Eulerian description. Efficient time and spatial discretizations are considered and implemented. Numerical experiments illustrate some fascinating phenomena that are of interests in real applications.
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a phase field formulation of the willmore problem
Nonlinearity, 2005Co-Authors: Chun Liu, Rolf J Ryham, Xiaoqiang WangAbstract:In this paper, we demonstrate, through asymptotic expansions, the convergence of a phase field formulation to model surfaces minimizing the mean curvature energy with volume and surface area constraints. Under the assumption of the existence of a smooth limiting surface, it is shown that the interface of a phase field, which is a critical point of the Elastic Bending energy, converges to a critical point of the surface energy. Further, the Elastic Bending energy of the phase field converges to the surface energy and the Lagrange multipliers associated with the volume and surface area constraints remain uniformly bounded. This paper is a first step to analytically justify the numerical simulations performed by Du, Liu and Wang in 2004 to model equilibrium configurations of vesicle membranes.
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retrieving topological information for phase field models
Siam Journal on Applied Mathematics, 2005Co-Authors: Chun Liu, Xiaoqiang WangAbstract:The phase field approach has become a popular tool in modeling interface motion, microstructure evolution, and more recently the shape transformation of vesicle membranes under Elastic Bending energy. While it is advantageous to employ phase field models in numerical simu- lations to automatically handle topological changes to the microstructures or the configurations of vesicle membranes, detecting topological events may also become important for many applications such as those in the simulation of blood cells. Motivated by such considerations, a new quantity is formulated to retrieve some topological information based on the phase field formulation and to capture the occurrence of topological events. It can also be used as a control method to avoid unphys- ical changes of topology due to the numerical methods, should it become necessary for particular practical applications. Through numerical experiments, we demonstrate the effectiveness and the robustness of the new quantity in detecting the topology of fluid bubbles and vesicle membranes.
Xiaofeng Yang - One of the best experts on this subject based on the ideXlab platform.
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efficient energy stable scheme for volume conserved phase field Elastic Bending energy model of lipid vesicles
Journal of Computational and Applied Mathematics, 2021Co-Authors: Kejia Pan, Chuanjun Chen, Xiaofeng YangAbstract:Abstract In this paper, we consider numerical approximations of the volume-conserved phase-field Elastic Bending energy model for lipid vesicles where a nonlocal term is added to the model such that the total volume can be conserved precisely. We further develop two linear and unconditionally energy stable schemes by combining the recently developed IEQ and SAV approaches with the stabilization technique, where several extra stabilization terms are added to enhance the stability and keep the required accuracy while using large time steps. Through the comparisons with some other type numerical schemes for simulating numerous benchmarking numerical examples in 2D and 3D, we demonstrate the robustness of the new nonlocal volume-conserved model, as well as the stability and the accuracy of the developed schemes, numerically.
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numerical approximations of the navier stokes equation coupled with volume conserved multi phase field vesicles system fully decoupled linear unconditionally energy stable and second order time accurate numerical scheme
Computer Methods in Applied Mechanics and Engineering, 2021Co-Authors: Xiaofeng YangAbstract:Abstract We consider the numerical approximation of the flow-coupled multi-phase-field Elastic Bending energy model of lipid vesicles. Based on the classical model with approximate volume conservation only, this paper first establishes a new model that can accurately conserve volume by adding some nonlocal terms to the model equation. Then, for the system coupled with the incompressible flow, we propose a novel numerical method to construct an effective scheme that is fully-decoupled, linear, unconditionally energy stable, and second-order time-accurate. The key idea to achieve the full decoupling nature is to introduce an ordinary differential equation to deal with the nonlinear coupling term that satisfies the so-called “zero-energy-contribution” property. Thus, in actual calculations, this scheme only needs to solve several independent linear equations with constant coefficients at each time step. We strictly prove the solvability and unconditional energy stability, and perform numerical simulations in 2D and 3D to verify the accuracy and stability of the scheme numerically.
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a novel fully decoupled second order time accurate unconditionally energy stable scheme for a flow coupled volume conserved phase field Elastic Bending energy model
Journal of Computational Physics, 2021Co-Authors: Xiaofeng YangAbstract:Abstract Different from the classical phase-field Elastic Bending model of lipid vesicles that uses a penalty term to conserve volume approximately, in this paper, a new model with accurate volume conservation is first established. Then, for its coupling system with the incompressible flow, we design a highly efficient scheme which is linear and energy stable. More importantly, this scheme is second-order time-accurate and fully-decoupled and it only needs to solve several independent linear equations with constant coefficients at each time step to obtain a numerical solution with second-order time accuracy. The key idea is to introduce two types of nonlocal auxiliary variables, one of which is linearize the nonlinear potential, and the other is used to introduce an ordinary differential equation to deal with the nonlinear coupling terms that satisfy the “zero-energy-contribution” feature. We strictly prove the solvability and unconditional energy stability and conduct numerical simulations in 2D and 3D to demonstrate the accuracy and stability of the scheme numerically. To the best of the author's knowledge, the decoupling method developed in this paper is the first second-order fully-decoupled scheme for the flow-coupled phase-field model.
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efficient linear schemes with unconditional energy stability for the phase field Elastic Bending energy model
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Xiaofeng Yang, Lili JuAbstract:Abstract In this paper, we study efficient numerical schemes of the classical phase field Elastic Bending energy model that has been widely used to describe the shape deformation of biological lipid vesicles, in which the free energy of the system consists of an Elastic Bending energy, a surface area constraint and a volume constraint. One major challenge in solving such model numerically is how to design appropriate temporal discretizations in order to preserve energy stability with large time step sizes at the semi-discrete level. We develop a first order and a second order time stepping scheme for this highly nonlinear and stiff parabolic PDE system based on the “Invariant Energy Quadratization” approach. In particular, the resulted semi-discretizations lead to linear systems in space with symmetric positive definite operators at each time step, thus can be efficiently solved. In addition, the proposed schemes are rigorously proved to be unconditionally energy stable. Various numerical experiments in 2D and 3D are presented to demonstrate the stability and accuracy of the proposed schemes.
Chun Liu - One of the best experts on this subject based on the ideXlab platform.
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Simulating the deformation of vesicle membranes under Elastic Bending energy in three dimensions
Journal of Computational Physics, 2006Co-Authors: Chun Liu, Xiaoqiang WangAbstract:In this paper, we study the three-dimensional deformation of a vesicle membrane under the Elastic Bending energy, with prescribed bulk volume and surface area. Both static and dynamic deformations are considered. A newly developed energetic variational formulation is employed to give an effective Eulerian description. Efficient time and spatial discretizations are considered and implemented. Numerical experiments illustrate some fascinating phenomena that are of interests in real applications.
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a phase field formulation of the willmore problem
Nonlinearity, 2005Co-Authors: Chun Liu, Rolf J Ryham, Xiaoqiang WangAbstract:In this paper, we demonstrate, through asymptotic expansions, the convergence of a phase field formulation to model surfaces minimizing the mean curvature energy with volume and surface area constraints. Under the assumption of the existence of a smooth limiting surface, it is shown that the interface of a phase field, which is a critical point of the Elastic Bending energy, converges to a critical point of the surface energy. Further, the Elastic Bending energy of the phase field converges to the surface energy and the Lagrange multipliers associated with the volume and surface area constraints remain uniformly bounded. This paper is a first step to analytically justify the numerical simulations performed by Du, Liu and Wang in 2004 to model equilibrium configurations of vesicle membranes.
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retrieving topological information for phase field models
Siam Journal on Applied Mathematics, 2005Co-Authors: Chun Liu, Xiaoqiang WangAbstract:The phase field approach has become a popular tool in modeling interface motion, microstructure evolution, and more recently the shape transformation of vesicle membranes under Elastic Bending energy. While it is advantageous to employ phase field models in numerical simu- lations to automatically handle topological changes to the microstructures or the configurations of vesicle membranes, detecting topological events may also become important for many applications such as those in the simulation of blood cells. Motivated by such considerations, a new quantity is formulated to retrieve some topological information based on the phase field formulation and to capture the occurrence of topological events. It can also be used as a control method to avoid unphys- ical changes of topology due to the numerical methods, should it become necessary for particular practical applications. Through numerical experiments, we demonstrate the effectiveness and the robustness of the new quantity in detecting the topology of fluid bubbles and vesicle membranes.
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Retrieving topological information for phase field models
2005Co-Authors: Chun Liu, Xiaoqiang WangAbstract:Abstract. Phase field approach has becoming a popular tool in modeling interface motion, microstruture evolution and more recently the shape transformation of vesicle membrane under Elastic Bending energy. While it is advantageous to employ the phase field models in the numerical simulations to automatically handle the topological changes to the microstructures or the configurations of vesicle membranes, detecting topological events may also become important for many applications such as those in the simulation of blood cells. Motivated by such considerations, a new quantity is formulated to retrieve some topological information based on the phase field formulation and to capture the occurrence of topological events. It can also be used as a control method to avoid the unphysical changes of topology due to the numerical methods should it becomes necessary for particular practical applications. Through numerical experiments, we demonstrate the effectiveness and the robustness of the new quantity in detecting the topology of fluid bubbles and vesicle membranes. Key words. phase field, Elastic Bending energy, Gauss-Bonnet formula 1. Introduction. Phase-field modeling of the mezoscopic morphology and mi-crostructure evolution has become popular in recent years (see [6, 7, 8, 9, 12, 13, 20, 21, 32, 33, 36]) and the references therein). These phase field approach is usuall
Fan Yang - One of the best experts on this subject based on the ideXlab platform.
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experiments and theory in strain gradient Elasticity
Journal of The Mechanics and Physics of Solids, 2003Co-Authors: Arthur C.m. Chong, Fan Yang, Jianxun Wang, Pin TongAbstract:Abstract Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors. This set enables the application of the higher-order equilibrium conditions to strain gradient Elasticity theory and reduces the number of independent Elastic length scale parameters from five to three. On the basis of this new strain gradient theory, a strain gradient Elastic Bending theory for plane-strain beams is developed. Solutions for cantilever Bending with a moment and line force applied at the free end are constructed based on the new higher-order Bending theory. In classical Bending theory, the normalized Bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order Bending theory, the normalized higher-order Bending rigidity has a new dependence on the thickness of the beam and on a higher-order Bending parameter, bh. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted Bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beam's thickness as predicted by the strain gradient Elastic Bending theory, and that the higher-order Bending parameter, bh, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beam's Bending rigidity. The present results indicate that the Elastic strain gradient effect is significant in Elastic deformation of small-scale structures.
Bernd Ishaque - One of the best experts on this subject based on the ideXlab platform.
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analysis of the Elastic Bending characteristics of cementless short hip stems considering the valgus alignment of the prosthetic stem
Clinical Biomechanics, 2018Co-Authors: Alexander Jahnke, Carlos Alfonso Fonseca Ulloa, Jorn Bengt Seeger, Markus Rickert, Gerhard Walter Jahnke, Gafar Adam Ahmed, Bernd IshaqueAbstract:Abstract Background The resultant hip force causes a varus torque which must be compensated by a shear force couple depending on the stem alignment of the prosthesis. Since the prosthesis is substantially less flexible than the bone, the interior of the femur is stiffened over the entire prosthesis length. The present study thus aims at analyzing short-stem prostheses for its Elastic Bending characteristics, considering inappropriate valgus alignment of the prosthetic stem. Methods Five short stem prostheses were implanted each in synthetic femora in a standardized manner – in neutral and valgus stem alignments. Bending movements were recorded applying a tilting torque MX of ±3.5 Nm in medio-lateral direction. Variance analyses and Friedman tests were used. A P-value Findings Bending movements b1-b6 showed significant differences (P Interpretation Regarding the Elastic Bending behavior we see a relevant influence of the stems´ design. We conclude that the short-stem principle does not necessarily require the shortest possible prosthesis but rather a long and thin extending stem tip to optimize the lever ratios, ensuring a more physiological Bending behavior of the femur. In addition, without sufficient anchoring of the prosthesis, the valgus stem alignment could favor tilting of the implant and should therefore be avoided.