# Graduate School Research

in Grad

## Fatigue Fracture

Filler for fatigue fracture

(a)Total charge density according to the renormalized solution through the notion of a polarizable vacuum. (b) The new effective potential \(\Phi_{VP}/\Phi_0 = 1-exp(-a/2r)\) is compared to the electrostatic Coloumb potential \(\Phi_C = q/4\pi\varepsilon_0 r\).

Unfortunately our project wasn’t funded so I moved into the next project

## Metamaterials – massive light

Metamaterials are most known for invisibility. Here is some science

When I first started working with Professor Dentcho Genov, he was finishing work cite on invisibility to mass. Through some discussions on the topic, we arrive at the question ** can we build a metamaterial that makes light massive?** Put another way, could we hold like like we hold a baseball?

## A Classical Rendition of the Polarizable Vacuum

The electron self-energy paradox states that the energy required to build an electron is infinite. A resolution to the self-energy paradox can be achieved by re-deriving the electron’s electric potential while assuming the vacuum of space to be filled with an unknown, polarizable, dielectric material. In the standard model, this effective medium can be viewed as being comprised of particle-antiparticle pairs (dipoles) that are emergent from the vacuum. Here, we demonstrate how the vacuum polarizability can be used to derive a “quantum” correction to the classical Coulomb potential. Our result asymptotically reduces to the Coulomb potential for distances larger than the classical electron radius.

(a)Total charge density according to the renormalized solution through the notion of a polarizable vacuum. (b) The new effective potential \(\Phi_{VP}/\Phi_0 = 1-exp(-a/2r)\) is compared to the electrostatic Coloumb potential \(\Phi_C = q/4\pi\varepsilon_0 r\).

Applying this general solution to the electron yields

(a)Total charge density according to the renormalized solution through the notion of a polarizable vacuum. (b) The new effective potential \(\Phi_{VP}/\Phi_0 = 1-exp(-a/2r)\) is compared to the electrostatic Coloumb potential \(\Phi_C = q/4\pi\varepsilon_0 r\).

## Classical Renormalization of the Point Charge

We extend the classical rendition of the polarizable vacuum to positronium. Our model of positronium shows that first order corrections are related to the so-called Darwin term in relativistic quantum mechanics. This is the first classical theorem that can successfully account for pair annihilation, as is commonly encountered with PET imaging.

Plotted is the interaction potential $V_int$. At large distances the interaction potential converges to the Coulomb potential. (b) The total energy is plotted as a function of separation distance. As the two particles approach (\(R/a \rightarrow 0\)) each other and the separation goes to zero, the total energy goes to zero at the origin. This is synonymous with annihilation. For the first time, we have a self-consistent description of fundamental particle interactions without infinities and including pair annihilation.