Wave simulations in infinite spacetime
Chad McKell, Mohammad Sina Nabizadeh, Stephanie Wang, Albert Chern
Solving the wave equation on an infinite domain has been an ongoing challenge
in scientific computing. Conventional approaches to this problem only generate numerical solutions on a
small subset of the infinite domain. In this paper, we present a method for solving the wave equation on
the entire infinite domain using only finite computation time and memory. Our method is based on the
conformal invariance of the scalar wave equation under the Kelvin transformation in Minkowski spacetime. As
a result of the conformal invariance, any wave problem with compact initial data contained in a causality
cone is equivalent to a wave problem on a bounded set in Minkowski spacetime. We use this fact to perform
wave simulations in infinite spacetime using a finite discretization of the bounded spacetime with no
additional loss of accuracy introduced by the Kelvin transformation.

Acoustic Wave Simulation using the MinkowskiKelvin Transform
Chad McKell
In this work, I demonstrate that the conformal invariance of the wave equation under a Kelvin transform in
Minkowski spacetime allows for the efficient handling of complex geometric boundaries in
acoustic wave simulations. In particular, I use the transform to convert infinite domains into bounded
domains and curved boundaries into flat boundaries. I then solve the transformed wave problems using standard
numerical methods with no additional loss of accuracy introduced by the transform.

Optical corral using a standingwave Bessel beam
Chad McKell, Keith Bonin
Here we create a series of optical corrals and calculate their potential energy profile.
A standingwave Bessel beam is used to form traps in 1D (along the optical axis) and corrals in 2D, in planes
perpendicular to the optical axis at the antinodal regions of the standing waves. These optical corrals are formed
by an axicongenerated Bessel beam that is retroreflected back onto itself. We report on Mie calculations of the
2D optical corrals and then compare the resulting probability distributions to those observed for latex particles
of diameters 100, 200, and 300 nm. The experimental radial probability density function of tracked particles closely
mimics the theoretical optical structure of a Bessel standingwave corral. The Bessel standingwave corrals we have
characterized are being developed to measure rotational diffusion and torques on micro and nanorods to help
understand microfluidic behavior. The maximum forces on our small beads in the diffractionfree central zone of the
Bessel beam standing wave are 𝐹=0.5 pN and 𝐹⊥=0.1 pN.

RealTime Physical Modeling for Haptic Feedback Rendering
Chad McKell
Physical modeling is an effective signal processing method for enhancing realism in haptic feedback
rendering. In this study, realtime physicsbased simulations of linear elastic vibrations were developed for use in vibrotactile
displays. Applications to a variety of consumer use cases were explored. A discussion of future work on nonlinear modeling is
included. Advisor: Stefan Bilbao. (Edinburgh Seal: By Source, Fair use, wikipedia.org).
(Publication of thesis restricted by NDA). 
Sonification of opticallyordered Brownian motion
Chad McKell
In this paper, a method is outlined for the sonification of experimentallyobserved Brownian motion organized into optical
structures. Sounds were modeled after the tracked, threedimensional motion of Brownian microspheres confined in the
potential wells of a standingwave laser trap. Stochastic compositions based on freelydiffusing Brownian particles are
limited by the indeterminacy of the data range and by constraints on the data size and dimensions. In this study, these
limitations are overcome by using an optical trap to restrict the random motion to an ordered stack of twodimensional
regions of interest. It is argued that the confinement of the particles in the optical lattice provides an artistically
appealing geometric landscape for constructing digital audio effects and musical compositions based on experimental
Brownian motion. A discussion of future work on data mapping and computational modeling is included. The present study
finds relevance in the fields of stochastic music and sound design.

Confinement and Tracking of Brownian Particles in a Bessel Beam Standing Wave
Chad McKell
Optical trapping is a useful tool for manipulating microscopic particles and probing the physical
interactions of matter. However, previous optical trapping techniques introduced complications for analyzing Brownian particle
diffusion in viscous media because they either restricted the particles' motion or trapped the particles too close to a surface.
To our knowledge, this thesis presents the first realization of twodimensional, transverse tracking of Brownian microparticles
in multiple, surfaceisolated traps. To accomplish this, we used an axicongenerated, zerothorder Bessel beam standing wave whose
parameters were adjusted to allow tight axial confinement and loose transverse confinement of microscopicsized particles in the
central maximum of the Bessel beam. We chose a Bessel beam because its unique nondiffracting and selfhealing properties provided
distinct advantanges over a Gaussian beam. In particular, a Bessel beam standing wave was shown to produce optical potential wells
that are more abundant, uniform, and stable than those of a Gaussian standing wave. Advisor: Keith Bonin. (WFU Seal: By Source, Fair use, wikipedia.org).
