Application Of Level Set Method Research Articles

Application of level-set method in simulation of normal and cancer cells deformability within a microfluidic device

Application of microfluidic systems for the study of cellular behaviors has been a flourishing area of research in the past decade. In the process of probing cell biomechanics the passage of a cell through a narrow microchannel or a small pore has attracted much attention during the recent years. And the study of cellular deformability and transportability using these systems with enhanced resolution and accuracy has opened a new paradigm for high-throughput characterization of both healthy and diseased cell populations.Here we use the level-set method to explore the relationship between the transit time and mechanical properties of normal white blood cells (WBCs) and breast cancer epithelial cells (MCF7) under different microenvironmental parameters (i.e., pressure difference, cell size, effective cell surface tension, constriction size and taper angle) in a 2-D computational domain by considering the cell as a viscous drop. The novel biomechanical relations are obtained for each cell type by the Response Surface Method (RSM), relating microenvironmental parameters to the dimensionless entry time of the normal and cancer cells. Our results revealed that MCF7 cells show asignificantly different behavior (a bifurcating behavior when the pressure difference of inlet/outlet increases) in regards to the dimensionless entry time as a function of microchannel taper angle in comparison with the WBC. These results suggest that the microenvironmental parameters have a significant effect on the transportability of the cells and different cells have different behaviors in response to a specific microenvironmental parameter. Finally, it can be claimed that this method can be also utilized to distinguish between benign and cancerous cells or even to probe tumor heterogeneity toward high throughput cell cytometry.

Topology Optimization of Free Damping Treatments on Plates Using Level Set Method

Application of level set method to optimize the topology of free damping treatments on plates is investigated. The objective function is defined as a combination of several desired modal loss factors solved by the finite element-modal strain energy method. The finite element model for the composite plate is described as combining the level set function. A clamped rectangle composite plate is numerically and experimentally analyzed. The optimized results for a single modal show that the proposed method has the possibility of nucleation of new holes inside the material domain, and the final design is insensitive to initial designs. The damping treatments are guided towards the areas with high modal strain energy. For the multimodal case, the optimized result matches the normalized modal strain energy of the base plate, which would provide a simple implementation way for industrial application. Experimental results show good agreements with the proposed method. The experimental results are in good agreement with the optimization results. It is very promising to see that the optimized result for each modal has almost the same damping effect as that of the full coverage case, and the result for multimodal gets moderate damping at each modal.

Application of Level Set Method for Shape and Topology Optimization in an Electromagnetic System

Level set methods(LSM) are conceptual methods for using level sets as tools for numerical analysis of surfaces and geometries. The advantage of the level set model is that you can perform numerical calculations involving curves and surfaces in a fixed grid without parameterizing these objects. In recent years, it has been applied to structural design optimization of mechanical engineering, and it has been actively studied as a new design technique overcoming the problems of existing shape sensitivity analysis method and phase optimization method. You can also use the level setting method to easily follow how the topology changes. In this study, we show the application of the level set method to the optimal design using sensitivity analysis. This paper presents applications of dielectric electrode design, moving objects and particle dynamics in magnetic field systems.

Application of level-set method for deposition in three-dimensional reconstructed porous media.

Three-dimensional (3D) porous structures which are usually discretized by voxels can also be discretized by the level-set method (LSM) and flow, reactive transport, and structure evolution can be modeled. The determination of the solid-liquid interface is detailed as well as the discretization of the governing equations. Comparisons between a one-dimensional analytical solution and LSM are conducted for validation. Deposition in 3D reconstructed media is studied under various flow and reaction conditions. The evolution of the structure is explored locally by means of the pore geometry and globally by means of the permeability and the porosity. The difference between the voxel method and LSM is discussed during the investigations.

Numerical and Experimental Analysis of the Growth of Gravitational Interfacial Instability Generated by Two Viscous Fluids of Different Densities

In the geophysical context, there are a wide variety of mechanisms which may lead to the formation of unstable density stratification, leading in turn to the development of the Rayleigh-Taylor instability and, more generally, interfacial gravity-driven instabilities, which involves moving boundaries and interfaces. The purpose of this work is to study the level set method and to apply the process to study the Rayleigh-Taylor instability experimentally and numerically. With the help of a simple, inexpensive experimental arrangement, the R-T instability has been visualized with moderate accuracy for real fluids. The same physical phenomenon has been investigated numerically to track the interface of two fluids of different densities to observe the gravitational instability with the application of level set method coupled with volume of fraction replacing the Heaviside function. Good agreement between theory and experimental results was found and growth of instability for both of the methods has been plotted.

Level Set Analysis of Two-fluid Interfacial Flows

In this study, application of Level Set method in modeling incompressible immiscible two-phase flows for some benchmark problems such as rising bubble and bursting bubble at the free surface is explained. Derivations of Level Set function and con- vective terms are done using fifth order Weighted Essentially Non-Oscillatory (WENO) scheme. It is observed that Level Set method is very successful in modeling two-phase flows, especially in handling topological changes like bubble skirt pinching off and merging of bubble with the free surface.

Application of level set method to optimal vibration control of plate structures

Vibration control plays a crucial role in many structures, especially in the lightweight ones. One of the most commonly practiced method to suppress the undesirable vibration of structures is to attach patches of the constrained layer damping (CLD) onto the surface of the structure. In order to consider the weight efficiency of a structure, the best shapes and locations of the CLD patches should be determined to achieve the optimum vibration suppression with minimum usage of the CLD patches. This paper proposes a novel topology optimization technique that can determine the best shape and location of the applied CLD patches, simultaneously. Passive vibration control is formulated in the context of the level set method, which is a numerical technique to track shapes and locations concurrently. The optimal damping set could be found in a structure, in its fundamental vibration mode, such that the maximum modal loss factor of the system is achieved. Two different plate structures will be considered and the damping patches will be optimally located on them. At the same time, the best shapes of the damping patches will be determined too. In one example, the numerical results will be compared with those obtained from the experimental tests to validate the accuracy of the proposed method. This comparison reveals the effectiveness of the level set approach in finding the optimum shape and location of the CLD patches.

Application of level set method for groundwater flow with moving boundary

A potential of level set methods for the numerical modeling of moving boundaries and interfaces in groundwater flow problems is shown by the application for a particular model of the flow with moving water table (the phreatic surface). The main ingredients of the level set methods like the advection of level set function, the computation of signed distance function and the extrapolation of missing data are explained for a class of possible applications. The numerical solution of the groundwater flow problem is proposed using the flux-based level set method and the immersed interface method that are based on a finite volume discretization on any fixed (unstructured) grid. Presented examples show good properties of the method concerning a small mass balance error and a good grid convergence even for an example with merging boundaries. An example with seepage boundary is computed using the locally adapted grids by refining and coarsening the mesh according to the position of moving water table.

Application of level set method to the design of mechanical components with a desired multi-dimensional stiffness

This article addresses an original algorithm in topology optimisation of mechanical components to achieve a desired multi-dimensional stiffness using the level set method. As opposed to the main application of topology optimisation to maximise stiffness while minimising weight, this article focuses on a general formulation to reach a desired multi-dimensional stiffness. It is shown that a simple extension of previous formulations is not able to lead the optimisation procedure to the desired multi-dimensional stiffness. To fulfil this aim, two different loadings – force and displacement – are applied to the component/structure at the point with a desired multi-dimensional stiffness. The finite-element solution for the force (displacement) loading results in displacement (reaction force) at the point of applied force (displacement). When the topology of the component media converges, the resultant strain field for the force and displacement loadings will be the same; i.e. force (displacement) loading results in displacement (reaction force) at the point of applied loading satisfying F=K Δ. Here F and Δ are external force and displacement vectors, respectively. In addition, a new and effective energy-based constraint is proposed to avoid discontinuity in the component media.

Application of level set method in simulation of surface roughness in nanotechnologies

One of the limiting factors in applications of plasma etching in nanotechnologies in general will be the control of plasma induced roughness or perhaps control of surface roughness by plasma etching. In this paper we consider roughening of nanocomposite materials during plasma etching for two etching modes (isotropic and anisotropic) by using a level set method. It was found that the presence of two phases with different etch rates (the ratio of the two etch rates is s and the abundance of one phase is p) affects the evolution of the surface roughness and that the etch rate is higher during the isotropic process as compared to the anisotropic process for all values of s and p. At the same time, in case of isotropic process, the higher s leads to a higher overall etch rate. The obtained results apart from their theoretical relevance, have practical implications for surface treatment of nanocomposite materials.

Finite Element-Based Level Set Methods for Higher Order Flows

In this paper we shall discuss the numerical simulation of geometric flows by level set methods. Main examples under considerations are higher order flows, such as surface diffusion and Willmore flow as well as variants of them with more complicated surface energies. Such problems find various applications, e.g. in materials science (thin film growth, grain boundary motion), biophysics (membrane shapes), and computer graphics (surface smoothing and restoration). We shall use spatial discretizations by finite element methods and semi-implicit time stepping based on local variational principles, which allows to maintain dissipation properties of the flows by the discretization. In order to compensate for the missing maximum principle, which is indeed a major hurdle for the application of level set methods to higher order flows, we employ frequent redistancing of the level set function. Finally we also discuss the solution of the arising discretized linear systems in each time step and some particular advantages of the finite element approach such as the variational formulation which allows to handle the higher order and various anisotropies efficiently and the possibility of local adaptivity around the zero level set.

Application of Level Set Method to the Simulation of Liquid-Gas Two-Phase Flow during Mold Filling

Level Set Method is an appropriate mathematical tool for solving two-phase flow problems. The main advantage of Level Set Method is its efficiency to deal with complex interfaces, even if topology changes. In this paper, the liquid-gas two-phase flow is simulated using a combination of Level Set Method and SOLA method. SOLA is used to compute the Navier-Stokes equation, and Level Set Method is used to track the interfaces between the liquid and the gas during mold filling process. The difficulty in the simulation of two-phase flow comes from great change of physical parameters (e.g., density and viscosity) across the interfaces. Level Set Method allows for large density ratio and jump in viscosity without reconstructing the numerical grid. In this work, the forming and moving of the gas bubbles in liquid were numerically simulated by Level Set approach. The numerical simulation results and experiments suggest that Level Set Method is quite reliable and effective for the simulation of liquid-gas two-phase flow during mold filling.

Conceptual design of compliant mechanisms using level set method

We propose a level set method-based framework for the conceptual design of compliant mechanisms. In this method, the compliant mechanism design problem is recast as an infinite dimensional optimization problem, where the design variable is the geometric shape of the compliant mechanism and the goal is to find a suitable shape in the admissible design space so that the objective functional can reach a minimum. The geometric shape of the compliant mechanism is represented as the zero level set of a one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobi partial differential equation. The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity field in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady-state solution of the partial differential equation. Besides the above-mentioned methodological issues, some numerical examples together with prototypes are presented to validate the performance of the method.