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Multiscale Materials Modeling
| Peridynamics |
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The peridynamics model is a nonlocal reformulation of solid mechanics. It describes the behavior of systems by integral equations, in contrast to
the classical continuum mechanics approach where differential equations are employed. Dependence upon differentiability of the displacement
field limits the applicability of classical mechanics models, whereas discontinuous displacements represent no mathematical or computational
difficulty for peridynamics. As a consequence, peridynamics has been applied to the study of material failure.
Peridynamics is a nonlocal model, and its computational structure is similar to molecular dynamics. I have investigated the connection between
peridynamics and molecular dynamics by studying the peridynamics model as an upscaling or continualization of molecular dynamics.
I found that PD recovers the same dispersion relation as does MD, when appropriate length scales are chosen.
This research was performed in collaboration with Michael L. Parks,
Max Gunzburger, and Richard B. Lehoucq.
Peridynamics was proposed in 2000 by Stewart Silling.
This research motivates peridynamics as a multiscale material model. In other words, peridynamics can be implemented to describe the appropriate dynamics
occurring at different scales.
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| Atomistic-to-Continuum Coupling |
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Atomistic models, such as molecular dynamics, are an accepted approach for describing material processes that occur at the microscopic level.
Unfortunately, practical systems involve too many particles to be feasibly treated using such methods.
As a result, approximations to atomistic models that are more efficient, yet have sufficient accuracy, are of interest.
Common approaches in the literature involve the coupling of two or more models, so that different models describe different regions of the system
using different approaches.
In atomistic-to-continuum (AtC) coupling techniques, an atomistic model is used in regions where microscale resolution is necessary but elsewhere,
a (discretized) continuum model is applied. A central question in AtC coupling methods is how to couple local continuum and nonlocal atomistic models.
I investigated an energy-based blending approach for AtC coupling and studied its convergence behavior. I derived analytical relations to connect
the atomistic and continuum models, which led to a consistent implementation of both models on the same system.
Furthermore, different approaches for the implementation of Dirichlet-type boundary conditions in the atomistic region were proposed,
which allowed for appropriate comparison between the performance of the discrete and continuum models.
In particular, I investigated the application of singular loads, and found that our AtC coupling approach performed better than
the corresponding continuum model, compared to a reference atomistic solution.
This research was performed in collaboration with Max Gunzburger.
This research motivates the implementation of AtC coupling models for cases where classical continuum models fail.
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Previous Research
| Application of Smolyak and Tensor Products to High Dimensional Integrations |
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During the first year of my Ph.D. program at Florida State University, I participated in a research project with Raúl Tempone.
The research involved the application of Smolyak and tensor product quadratures to high dimensional integrations, including the development of parallel
implementations using MPI.
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| Galaxy Formation |
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One dimensional hydrodynamical simulations reveal a critical mass scale for
combined gas and dark matter systems, above which we have an expanding stable shock and below which we observe cold infall of gas that builds a disc.
However, submillimeter observations reveal massive disc galaxies above the critical mass scale at high redshifts, which appear to be inconsistent with
the theoretical picture. In my Physics M.S. thesis, at the Hebrew University of Jerusalem, I investigated the filamentary structure appearing in N-body simulations of dark matter
and its relation to galaxy formation processes simulated using hydrodynamical simulations. In particular, I focused on the study of cold streams penetrating
through shocked gas.
Important differences in the filamentary structure of big and small halos at redshift z = 0 were found that explain the cold flows effect,
as well as its dependence on redshift. In addition, a strong correlation between the gas temperature and dark matter density profiles was found.
Furthermore, I calculated linear correlations between different parameters of dark matter halos
and found that dark matter properties are consistent with buildup by mergers.
This research was performed in collaboration with Avishai Dekel.
This research provided numerical support to the model postulated by Avishai Dekel and Yuval Birmboim, which explains the above observations.
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| Undergraduate Research |
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As part of my undergraduate studies, I have been involved in the following research projects:
- Ellipsometric measurements of thin layer structures in porous silicon
During the third year of my undergraduate physics program, I was involved in a research project in the group of
Amir Sa'ar at the Department of Applied Physics of the
Hebrew University of Jerusalem. During the project, I performed ellipsometric measurements of thin layer structures in porous silicon media,
in order to determine their width and dielectric coefficients. The project involved the use of the ellipsometer machine in the visual and near infrared ranges,
and the development of numerical algorithms to compute dielectric properties of materials.
- Shot noise measurements and development of techniques for the spectrum analyzer
During my undergraduate studies, I participated in a Summer Internship at the Weizmann Institute of Science in Rehovot, Israel.
I was involved in a research project in the group of Mordehai Heiblum,
at the Department of Condensed Matter Physics. The project involved measurements of shot noise,
which results were used to check Miliken's experimental results for the value of the electron's charge. In addition, we developed alternative techniques
for the spectrum analyzer.
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