Currently, I am working with Dr. Robert Lipton as a Postdoc. Our project work involves numerical analysis of nonlocal models. I finished my Ph.D. in August 2016 and my adviser was Dr. Kaushik Dayal. My research interests lie in numerical methods, multiscale modeling, and computational mechanics. If you have any question, feel free to get in touch.

## Short Bio

Name:
Prashant Kumar Jha
Position:
Postdoc
Degree Credentials:
B.E., Mechanical Engineering, Govt. Engineering College, Raipur, India
M.E., Mechanical Engineering, Indian Institute of Science, Bangalore, India
Ph.D., Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, USA
Reserach Interests:
Multiscale modeling, Computational mechanics, Peridynamics, Numerical analysis
Office Location and Phone:
145 Lockett Hall, +1-225-249-9456
prashant.j16o@gmail.com, jha@math.lsu.edu

## Curriculum Vitae

• My C.V. can be found here.

• ## Ph.D. Thesis

• My Ph.D. thesis can be found in this link: thesis link.

• ## Research Publications

Below are research publications which are either submitted to the journal or are published.

[2017-1] Numerical analysis of nonlocal fracture models in H\"{o}lder space. Prashant K. Jha and Robert Lipton. Preprint, to appear in SIAM Journal on Numerical Analysis. Submitted on January 18, 2017. Link to Arxiv: arxiv_preprint

[2017-2] Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics. Prashant K. Jha and Robert Lipton. Preprint, submitted for review in International Journal for Numerical Methods in Engineering. Submitted on July 1, 2017. Link to Arxiv: arxiv_preprint.

[2017-3] Free damage propagation with memory. Robert Lipton, Eyad Said and Prashant K. Jha. Submitted for review in Journal of Elasticity on July 15, 2017.

[2017-4] Finite element approximation of nonlinear nonlocal models. Prashant K. Jha and Robert Lipton. Preprint, submitted for review in Mathematical Models and Methods in Applied Sciences on October 20, 2017. Link to Arxiv: arxiv_preprint.

## Work in Progress

List of projects on which I am currently working on.

• Stability and consistency of finite element approximation of linear peridynamics. Prashant K. Jha and Robert Lipton. Estimated time to complete: November-December 2017.
• In this work, we consider finite element approximation of linear peridynamics. We show the stability and convergence of numerical approximation. We present numerical results to verify the convergence rate. We also show with the help of numerical results that similar stability condition on time step holds for nonlinear peridynamics when displacement field is nice.

• Overivew of peridynamics theory, numerical analysis, and implementation. Prashant K. Jha, Patrick Diehl and Robert Lipton. Estimated time to complete: November-December 2017.
• In this work, we give overview of peridynamics theory and discuss convergence and stability results for numerical approximation of peridynamics theory. We present numerical results for quasistatic problems and dynamics problem using finite difference method and finite element method. The results are obtained from our computational code. Code is based on parallel API called HPX.
• Continuum Limits of Geometrically-Complex Nanostructures with Electrical Interactions. Prashant K. Jha and Kaushik Dayal. Expecting to finalize the draft by December 2017.
• In this work, we consider the electrical interactions in nanostructures like nanorods, nanohelix, and nanofilms. We find that in the limit the energy is short range. We show that the results in this work agrees with the work of Gioia and James on thin film magnetics.
• Numerical analysis of state-based peridynamics model with damage. Prashant K. Jha and Robert Lipton. Estimated time to complete: January-February 2018.
• We consider nonlinear state-based peridynamics model with time history dependent potential. Our goal is to consider the numerical approximation of such model and show convergence and stability of the approximation.
• Dynamic brittle fracture from non-local double well potentials. Robert Lipton, Eyad Said and Prashant K. Jha. Estimated time to complete: October-November 2017.
• In this work, we introduce regularized state-based peridynamics model for free fracture propagation. We show that the model is well posed and solution exists in $L^\infty$.
• Book Chapter: Finite differences in Nonlinear Nonlocal Continuum Models. Prashant K. Jha and Robert Lipton. Book: Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Estimated time to complete: November 2017.
• Book Chapter: Numerical Convergence Studies of Peridynamics Based Nonlocal Continuum Models. Prashant K. Jha and Robert Lipton. Book: Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Estimated time to complete: November 2017.

• ## Professional Activity

• Presented my work with co-author Dr. Robert Lipton at 14th US National Congress on Computational Mechanics on 19th July 2017. See Title-abstract and presentation pdf.

• AEM Mechanics Research Seminar, Aerospace Engineering and Mechanics, University of Minnesota. Title: Coarse Graining of Electric Field Interactions with Materials. Date: March 21, 2017. Read abstract here and presentation here.

• IMA Postdoc Seminar, Institute for Mathematics and its Applications, University of Minnesota. Title: Numerical Analysis of Nonlocal Fracture Models. Date: April 4, 2017. See abstract and presentation pdf. Video of my talk can be found here.

• Visted IMA, University of Minnesota, from February 2 to June 2, 2017.

• Departmental Seminar, Department of Mechanical Engineering, Indian Institute of Science, Bangalore(India). Talked about my research as a graduate student. Date: August 19, 2016. Find the presentation pdf here.

• Departmental Seminar, Department of Mechanical Engineering, Indian Institute of Technology, Chennai (India). Talked about my research as a graduate student. Date: August 22, 2016. Find the presentation pdf here.

• ## Personal Interests and Hobbies

• I like building desktop computers and assembling all the parts. Currently I own Intel i7 5960X extreme processor. With liquid cooling loop, this processor can be clocked to speed as high as 4.5 GHz. See few pictures of my desktop with lquid cooling: 1,2,3,4,5. Pics of Asus 970 Pro Gaming Aura: 1,2,3,4.

• Recently, I updated the liquid cooling system of my desktop and installed couple of new sensors, new RGB fans and RGB lights. Desktop now has flow sensor which shows whether the coolant is flowing through the tubes and temperature sensor which measures the temperature of cooled liquid just before it flows into CPU. Here are couple of pictures: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.

• I have four parakeet pet birds. I like birds. Here are some pictures of my pet birds: 1, 2, 3, 4, 5, 6, 7. Here is video of birds taking bath: link.

• I like driving for long hours and covering long distances. So far I have completed three long distance journey. One was from Pittsburgh, PA, to Baton Rouge, LA. Second and third was from Baton Rouge, LA, to Minneapolis, MN.

• The following are examples of links to other interesting pages: The following links may be helpful in further editing of web pages: Search the web with Google!