Chaos refers to dynamical systems that are exponentially sensitive to their initial conditions. While the sensitivity of the initial conditions of a chaotic system results in unpredictable long-term behavior, the global nature of a chaotic system often plays an important role for predicting its subsequent behavior. Using the logistic map (one of the simplest chaotic systems) and its Lyapunov exponents (a measure of the degree of chaos), I explore the pattern and stability of the high-order periods—one of the distinct global characteristic features of the logistic map—using Matlab. In this study, the simulations show a new pattern of repeating odd-cycle periods stemming from the 3-period cycle: a symmetric doubling cascade of odd-number periods in the chaotic phase of the map which are independent of their initial conditions. From further exploration of the even-cycle periods, a more complex ordered pattern of the whole number period cycles was found and it was found that the stability of higher periods in the chaotic region is highly dependent on their initial conditions. The closer the initial condition is to 0.5, which is the superstable fixed point of the logistic map, the more the stable high-periods are formed within the limited set of iterations. The discovery of the new ordered pattern and the stability of the whole-number periods in the chaotic phase of the logistic map can be used to predict the stable states of growth of a population model in its chaotic phase, and can be used for population studies in which the initial conditions are known only approximately. This has ramifications for mathematics, population biology, chemistry, physics, and the social sciences.

In classical electrodynamics, accelerated charges emit electromagnetic radiation. The associated energy loss of the particle can be modeled as a radiation reaction force, proportional to the change in acceleration. Including this force in the usual dynamical equation for a charged particle yields the Abraham-Lorentz-Dirac (ALD) equation. For point particles, solutions to the ALD equation are problematic. First, they require additional initial conditions beyond those needed in regular Newtonian dynamics, but more concerning are the presence of unphysical run-away solutions and acausal trajectories. These problems arise in the point-like limit of the theory, so it is possible that quantum mechanics is the more appropriate framework with which to address the problem. In order to explore the similarities and differences of the classical and quantum frameworks, we compute classical trajectories of charged particles in the presence of a Coulomb field, including radiation reaction. We compare the associated classical cross-section with the quantum field-theoretic cross-section for Coulombic scattering, including radiative corrections. With these calculations, we will be able to assess when the field theoretic formulation of single-photon emission can approximate the classical radiation reaction.

Barium and Ytterbium ions are the forerunner ion species for quantum computation and quantum information in trapped ion systems. Ion chains of ytterbium and barium have been proposed for a scalable quantum computer with computation done on ytterbium ions and photonic coupling between different ion traps with barium ions. Ytterbium 171+ has a nuclear spin of ½ meaning it has a splitting of the 6S ½ ground state into 2 hyperfine manifolds separated by around 12 GHz. This allows for an easily addressable 2 level quantum system with a long coherence time. Barium 138+ does not have any nuclear spin, but an applied magnetic field causes Zeeman splitting of the 6S ½ state due to the interaction of the magnetic field and the atom's magnetic dipole moment, of which can be used as a qubit. In this poster I will discuss sympathetic cooling of ytterbium ions by barium ions which is caused by mechanical coupling of the ions from a harmonic electric field from the ion trap and the coulomb repulsion between the ion species, and the results of a recent experiment involving sympathetic cooling of the mixed ion chains of ytterbium and barium. The experiment itself consists of a linear chain of ions consisting of two barium and two ytterbium ions trapped in a four-rod linear Paul trap. Temperature of the ions is determined by performing Rabi flops between the ground state of barium 138+ to a higher energy state. Using the results from the Rabi flops you can determine the average thermal occupation numbers of the ions. I will discuss my role in the optical setup on a narrow line-width laser at 1762nm that it used to perform the Rabi oscillations, and collecting data during the experiment.

Here we explore applications of multivariable calculus for studying three dimensional wave media in our environment. We employ regression based methods to derive analytic formulae for real wave. Using multivariable optimization methods, we derive the maxima, minima and saddle points of three dimensional functions. We use advanced data visualization methods to study the divergence and curl and illustrate how these can be used to study ocean waves- including their vorticity and circulation. The project provides hands on exploration of real world environmental science problems with advanced data visualization and shows how divergence and curl can be used to measure circulation and vorticity parameters of real wave media involving ocean waves. Real world manifestations of scalar and vector fields in our environment are also presented.

Monte Carlo simulations employ random probability distribution statistics to estimate areas and volumes. Here, we employ Monte Carlo simulations to estimate the numerical value of π. We inscribe a circle in a square board and throw N darts using random values for both x and y. The probability that the dart lies within the circle = area of circle/area of square. This relationship allows us to estimate π. We wrote EXCEL/JAVA code for this research. The accuracy of estimated π is improved as the number of darts N --> ∞. This research allows us to combine mathematics, computer programming and data visualization to estimate π. Important applications of Monte Carlo simulations to find areas and volumes of complex objects including rivers, landscapes and organisms which cannot be represented by analytic functions will be discussed.

RNA Polymerase (RNAP) is found in all cellular organisms and synthesizes RNA from DNA through a process known as transcription. Using a single-molecule tool, Single-molecule Picometer Resolution Nanopore Tweezers (SPRNT), developed by Gundlach’s Nanopore Lab at the UW, we can track the motion of individual RNAP molecules along DNA at unprecedented spatial and temporal resolution. In this technique, a single nanopore, a biological transmembrane protein, is isolated in a phospholipid bilayer separating two wells both filled with salt solutions. An applied electric field drives ions through the pore, and the ion current is measured. Negatively charged DNA is also driven through the nanopore, partially blocking the ion current. The DNA is sequenced based on the changing ion current as each of the four DNA nucleotides sequentially pass through the pore and block the flow of ions. In SPRNT, the motion of a known sequence of DNA through the nanopore is controlled by a molecular motor (like RNAP), in order to understand how an enzyme moves along DNA. Using this technique, we can detect single base pair steps of RNAP along DNA as brief as 1 ms. In this work, we expand upon initial SPRNT experiments tracking RNAP and analyze the kinetics of RNAP during transcription in biological relevant conditions (1 mM NTPs, 37C) on a long DNA template (up to 6 kbp). We calculate the rate of NTP incorporation and stepping behavior (probabilities of different step types) at many different DNA template sequences using this technique. The results demonstrate how DNA sequences as well as applied force can affect the stepping behavior (probabilities of different step types) and stepping rate of RNAP. A complete understanding of RNAP and its transcriptional regulatory behaviors will enable scientific and medical communities to better understand a variety of genetic diseases associated with transcription.

X-ray spectroscopic techniques utilize selective x-ray absorption or fluorescence to interrogate the element-specific properties of atoms in a sample of interest, such as oxidation state, ligand identities, and bond lengths. Until recently, x-ray spectroscopic techniques have been primarily limited to large-scale synchrotron facilities employing expensive commercial crystal analyzers. This leads to high barriers to access because of high competition for synchrotron beamtime and the large cost of acquiring optics not presently possessed by the facility. Over the past several years, the Seidler lab has pioneered solutions to both these problems. First, the development of lab-scale x-ray absorption and emission spectroscopy apparatus has enabled a wide range of studies without need for the synchrotron, and second, by designing an inexpensive method for manufacturing the necessary crystal analyzers. I focus here on the second issue, improving the availability and decreasing the cost of the crystal analyzers. Crystal analyzers are at the heart of high energy resolution x-ray spectrometers. They serve the same role as a prism or grating in visible-light spectrometers, that is, they disperse x-rays into their component energies. Our work using temporary vacuum forming of silicon wafers reduces the cost of such optics from $5000 - $10,000 to only a few hundred dollars. Furthermore, the use of vacuum together with modern computer-assisted machining gives the freedom to use either the traditional spherical shape or a superior customized toroidal form, specific to each study. These advances in instrumentation will dramatically speed up analysis of materials and permit feedback on synthesis procedures, battery performance, detection of hazardous chemicals, and catalyst activity.

Astrophysical measurements indicate that the universe has three main constituents: the ordinary matter, dark matter, and dark energy. Ordinary matter is the matter that we see in our daily lives and only contributes a small percentage of the total matter of the universe, while the dark matter takes up 84.5% of the total mass of the universe. There are several candidates for what dark matter could possibly be, one of which is a particle called the axion. The axion may be detected using a device called "axion haloscope", in which axion dark matter resonantly converts to a microwave photon when interacting with the magnetic field. These resulting photons can be detected with low noise electronics. The Electric Tiger is an "axion haloscope", an experiment made up of a waveguide. The waveguide is a rectangular box which contains dielectrics positioned at equal distances within the cavity, with the distance between the dielectrics retracting or extending. Changing the distances between the dielectrics makes the device sensitive to the detection of the axion signal in the magnetic field for a range of possible axion signals. The preliminary results of this experiment will detect or exclude axion dark matter in the previously unexplored range of masses for the axion particle.

Polymer based fullerenes are used as photovoltaics in solar panels. Fullerene C60 molecules have icosahedral based structures resembling geodesic domes. Fullerenes have convex polyhedral shapes which obey Euler’s topological rules. Their novel structures involve Golden ratios. Here we use vector calculus methods to calculate bond lengths and bond angles and provide estimates for the volume and surface area of the molecule. The calculated average bond length (1.4320 Å), edge length (2.4252 Å), bond angle (116o) are in good agreement with reported experiments. The estimated fullerene molecularvolume is 788 Å3 and surface area is 426 Å2. To understand the critical effect of dimensionality on volume, we have studied the volume of a hypersphere in n-dimensions. The project provides hands on exploration of real world problems and data visualization.

The nitrogen vacancy (NV) center is a defect in diamond that forms a quantum mechanical system that can be controlled via optical and radio frequency (RF) manipulations. When excited on resonance, the photoluminescence intensity emitted by an NV center decreases as it changes spin state. With an ensemble of NV centers, we can use this feature to create a demonstration that enables this strictly quantum mechanical phenomenon to be observed by the human eye. I created a setup for measuring the change in photoluminescence in order to measure changes in the optical contrast between on and off resonance photoluminescence from varied optical and RF powers. From this data I was able to optimize the contrast in photoluminescence from my sample. Then, I simplified the setup down to the necessary components for visual observation and made the setup portable. This demonstration provides a visual mechanism to understand and observe fundamental quantum mechanical properties while also learning about the NV center and its use in magnetic field sensing.

As the student population in universities and colleges becomes increasingly diverse, the learning environment in science classes needs to improve to accommodate students with different backgrounds. The goal of this research is to investigate how current 4-year science professors use teaching methods to make their instruction more inclusive and accessible for all students. We interviewed several professors across the United States who have attended to issues of diversity, equity, and inclusion in their teaching and transcribed those interviews. We then identified themes and/or unique perspectives in the transcriptions that highlight these instructors’ ideas and instructional practices. In this presentation, we share the results of that qualitative analysis, aiming to provide insight into how some science professors are working to improve student experiences. We also share potential ways in which other instructors might apply these ideas and practices in their own classrooms.

 Studying the ground-strike force and acceleration of male and female runners can provide information about gait and foot strike patterns and can contribute to improved running efficiency in individual runners. Researchers at Southern Methodist University have showed that the motion of two anatomically discrete components of the body’s mass sufficiently explained the vertical ground reaction force-time waveform pattern observed during human running. The anatomical differences of male and female runners lower extremities were compared biomechanically by using force and acceleration data combined with video analysis to assess gait patterns. This experiment further examines the acceleration and force created by runners, while moving through their respective biomechanical patterns, by assessing the impact force and acceleration patterns of the lower limb joints. Acceleration data was collected at the ankle, knee, and hip of the runners to better understand the overall force distribution throughout the lower limbs. Preliminary data shows force differences between sprinters and distance runners, seen at each joint in the lower limb with the largest difference occurring at the hip. When comparing males versus females the preliminary data also shows differing force patterns through the observed reference points. This data will contribute to a better understanding of the biomechanical differences in male and female gait patterns when sprinting versus running for distance, which could lead to better injury recovery. Therapeutic evaluations of injured limb could be made by looking at the forces experienced throughout each limb during injury recovery to better personalize and appraise individual rehabilitation progress.

A neutrino is a neutral massless particle in the Standard Model of particle physics. However, this conflicts with observations of neutrino oscillations that require neutrinos to have nonzero masses. This conflict motivates a direct measurement of neutrino mass. The Project 8 Research Collaboration’s approach to direct neutrino mass measurement utilizes a developed technique called Cyclotron Radiation Emission Spectroscopy (CRES). In CRES, the energy of a single electron in a uniform magnetic field determines the frequency of the electromagnetic radiation emitted by the gyrating electron. For a precise measurement of electron energy, knowledge of the field’s value and stability is essential. Project 8 uses electron spin resonance (ESR) probes to monitor the magnetic field’s stability. This work aims at quantifying the contribution from the magnetic field fluctuations to the error budget on a neutrino mass measurement. I will present my analysis of the Project 8 ESR data to measure fluctuations within the magnetic field, such as drift, with a least-squares analysis method, providing an in-depth look in the stability of the field.