Projects
Here are some of the projects I worked on during my Ph.D.
Simulations of Viscoelastic Waves
What is viscoelasticity? Viscoelasticity have been used to model deformation and stress in certain solids, including metals, polymers, and biological materials, when they are under external forces.
Goal The stress-strain relation of viscoelastic materials can be modeled using classical as well as fractional Zener models. Under external load and traction terms we study the stability and well-posedness of the viscoelastic wave problem in both the Laplace and time domains. We use our team’s computational package to test our theoretical results on a model and create three dimensional simulation of the solution.
Results. The figure on right is the result of one of our numerical simulations where the material is modeled by Fractional Zener model and the bottom of the solid is shaken but the rest of the boundary is free. The traveling viscoelastic waves from bottom to top as well as the dissipativity of the system are captured.
The video below the picture demonstrates the deformation of a viscoelastic solid when a hand press-like input is given. The material is assumed to be a light and viscoelastic with fractional Zener model.
More. The details of the numerical approximation algorithm and its error analysis can be found in this poster.
For the details of the model, and theory see our team paper.
To learn more about creating a simulation with our team's MATLAB software, check out my GitHub repository.
What is viscoelasticity? Viscoelasticity have been used to model deformation and stress in certain solids, including metals, polymers, and biological materials, when they are under external forces.
Goal The stress-strain relation of viscoelastic materials can be modeled using classical as well as fractional Zener models. Under external load and traction terms we study the stability and well-posedness of the viscoelastic wave problem in both the Laplace and time domains. We use our team’s computational package to test our theoretical results on a model and create three dimensional simulation of the solution.
Results. The figure on right is the result of one of our numerical simulations where the material is modeled by Fractional Zener model and the bottom of the solid is shaken but the rest of the boundary is free. The traveling viscoelastic waves from bottom to top as well as the dissipativity of the system are captured.
The video below the picture demonstrates the deformation of a viscoelastic solid when a hand press-like input is given. The material is assumed to be a light and viscoelastic with fractional Zener model.
More. The details of the numerical approximation algorithm and its error analysis can be found in this poster.
For the details of the model, and theory see our team paper.
To learn more about creating a simulation with our team's MATLAB software, check out my GitHub repository.
Surface segmentation of objects in 3D images
Goal. This is an ongoing project with Dr. Gunay Dogan at NIST. Our goal is to build a software with a python interface that extracts the boundary of a list of objects in a 3D image. Target images are microscale material images.
Method. We use an energy minimization with a FEM solver to iteratively converge to the target surface. Our energy functional takes advantage of a combination of edge-based and region-based models and achieves a fast convergence.
Simulation. Given a 3D array of pixel intensities, and approximation parameters, the user can obtain an approximation of the surfaces of the objects in terms of a mesh data format. The animation on the right is an example of capturing the surface of a 3D box-object. Red points correspond to high pixel intensities. We see that the evolving surface adaptively captures the sharp edges.
Software will be available on GitHub soon.
Goal. This is an ongoing project with Dr. Gunay Dogan at NIST. Our goal is to build a software with a python interface that extracts the boundary of a list of objects in a 3D image. Target images are microscale material images.
Method. We use an energy minimization with a FEM solver to iteratively converge to the target surface. Our energy functional takes advantage of a combination of edge-based and region-based models and achieves a fast convergence.
Simulation. Given a 3D array of pixel intensities, and approximation parameters, the user can obtain an approximation of the surfaces of the objects in terms of a mesh data format. The animation on the right is an example of capturing the surface of a 3D box-object. Red points correspond to high pixel intensities. We see that the evolving surface adaptively captures the sharp edges.
Software will be available on GitHub soon.