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In an earlier study on the Wiedemann–Franz Law and the thermoelectric figure of merit (FoM), we studied the electronic effects in detail. We briefly investigated the role of the lattice thermal conductivity in enhancing the FoM and derived the characteristic equations in the form of an offset-logarithmic function (a special case of the generalized Lambert W function) [1]. This work follows up with analytical and numerical solutions to the offset-log function and provides better insight into the materials parameter space. We find the extrema of the lattice thermal conductivity and comment on its role in optimizing the figure of merit.

[1] Yadav, A., Deshmukh, P. C., Roberts, K., Jisrawi, N. M., &amp; Valluri, S. R. (2019). “An analytic study of the Wiedemann–Franz law and the thermoelectric figure of merit”, Journal of Physics Communications, 3 (10), 105001.

CAP Virtual Congress 2021

An Analytical study of the role of lattice conductivity in the enhancement of the thermoelectric figure of merit

offset-log function

lambert w function

figure of merit

thermoelectric materials

thermal conductivity

Welcome to Delaware State University’s Annual Summer Research Symposium, and thank you for attending! Our symposium represents the culmination of students’ summer experiences in research at Delaware State University. This event showcases the work of college students working on faculty-led research projects, as well as middle and high school students experiencing research for the first time working in research groups. Whatever the case, this summer has been a unique experience for the students, and we hope a transformative one. Even for students who are not planning a career in scientific research, their summer experience has given them skills they will draw on for years to come. 
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 For the research participants, we hope that you will maintain contact with your research mentors and colleagues. Science is a relatively small community made up of disciplinary “neighborhoods”. If you continue to work in a discipline, the other folks in that discipline will be like your neighbors that you run into regularly. Staying in contact with them will help you keep up with the news of the neighborhood, and open doors to educational and career opportunities. Whether you continue in science or take a different career path, for this summer you have been part of the world of research, and you will benefit from that perspective for the rest of your life.

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DSU Summer Research Symposium 2021

Welcome to Delaware State University’s Annual Summer Research Symposium, and thank you for attending!

In an earlier study on the Wiedemann–Franz Law and the thermoelectric figure of merit (FoM), we studied the electronic effects in detail. We briefly investigated the role of the lattice thermal conductivity in enhancing the FoM and derived the characteristic equations in the form of an offset-logarithmic function (a special case of the generalized Lambert W function) [1]. This work follows up with analytical and numerical solutions to the offset-log function and provides better insight into the materials parameter space. We find the extrema of the lattice thermal conductivity and comment on its role in optimizing the figure of merit.

[1] Yadav, A., Deshmukh, P. C., Roberts, K., Jisrawi, N. M., & Valluri, S. R. (2019). “An analytic study of the Wiedemann–Franz law and the thermoelectric figure of merit”, Journal of Physics Communications, 3 (10), 105001.

technical paper

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Optical parametric amplifiers deliver intense ultrashort pulses with broadly tuneable frequencies, useful for strong field physics, high harmonic generation, and attosecond experiments. Currently, this nonlinear amplification scheme relies on the second order nonlinearity, $\chi^{(2)}$,which is made possible only by crystals without centro-symmetry. More recently, investigations into a non-collinear setup show an increase in the phase matching bandwidth, leading to the creation even shorter pulses [1]. In this presentation, we discuss our research involving non-collinear parametric amplification of ultrashort pulses using wide bandgap materials with centrosymmetry, previously reported as Kerr instability amplification (KIA) [2]. 

We find that by using these crystals that exploit the next order nonlinearity, $\chi^{(3)}$,we can choose our amplifying medium from a more general class of crystals and still can generate gain factors of g = 50 /mm, or amplification factors of > $10^{12}$ [3]. Without the constraint of centrosymmetry, we have a greater selection by varying the bandgap, thermal properties, and linear and nonlinear indices of refraction. We developed pulse propagation models to optimize the critical parameters for amplification, and we find that the amplified pulse duration is much shorter than the pump and can be independent of the seed. We test several high bandgap dielectrics to optimize our scheme. We experimentally demonstrate the octave spanning amplification, showing that KIA is closely linked to degenerate four-wave mixing. We also spectrally and temporally characterize the amplified pulses to show the agreement with theory.

References
[1] H. Fattahi et al, Third-generation femtosecond technology, Optica 1 45-63 (2014)
[2] G. Vampa, TJ Hammond et al, Kerr instability amplification, Science 359 673-675 (2018)
[3] M. Nesrallah et al, Theory of Kerr instability amplification, Optica 5 271-278 (2018)

Multi-octave Parametric Amplification for Ultrashort Laser Pulses

How diffusivity (e.g., of proteins in the plane of biomembranes) is impacted by obstruction has been explored using Lattice Monte Carlo methods for random and periodic obstacle configurations. However real systems are neither periodic nor totally random. We present a study of transient and steady-state molecular diffusion in two-dimensional ”Fuzzy” systems of immobile obstacles, \textit{i.e.,} systems which bridge the gap between the ideal periodic and random limits. In particular, we examine whether there are ”diffusion phase transitions”, i.e., abrupt quantitative and/or qualitative changes at some critical degree of disorder. For instance, while the crossover length $r^*$ (describing the transition from anomalous to normal diffusion) decreases when the concentration of obstacles, $\phi$, increases in a periodic system, it is the opposite for random systems. Interestingly, $r^*(\phi)$ can become a very weak function of $\phi$ in some fuzzy systems. We investigate several ways of creating tunable disorder leading to different behaviour, and we introduce a parameter describing how the disorder in fuzzy systems impacts diffusion. Furthermore we introduce a new relation between the crossover length $r^*$, and the properties of the (anomalous) transient regime, including the excess diffusivity that it generates. Finally we propose new connections between the properties of the transient and steady-state regimes, most notably the possibility of estimating the steady state diffusion coefficient using early time (transient) data.

Diffusion in a membrane in the presence of immobile obstacles: the role of disorder

SnIP is an exciting new quasi-1D van der Waals semiconductor with a unique double-helix structure at the atomic scale that shows promise as a new material for flexible electronics. However, due to the high resistivity of as-grown SnIP its true potential is not clear. In this work, we study SnIP-nanowire thin films using time-resolved THz spectroscopy (TRTS), a powerful ultrafast optical tool that enables picosecond-resolution measurement of the complex photoconductivity spectrum. Modeling the dispersion of the conductivity allows us to extract the carrier scattering rate, however, the choice of model can yield different values. We discuss our results in terms of the two most common models in the field, the Drude-Smith model and the plasmon model, and show how fluence-dependent spectroscopic studies can be used to differentiate the two experimentally. Moreover, with knowledge of the effective mass, the scattering rate enables us to calculate the carrier mobility. We performed an ab-initio study of the electronic structure in SnIP and extracted the effective mass tensor for several bands near the Fermi level. Along with the carrier scattering rate, we find a carrier mobility as high as 280 cm^2 V^-1s^-1, which is remarkably high for such a soft and flexible material and suggests that it is ideally suited for flexible electronics. Moreover, we find a large anisotropy in the electronic structure, which is due to the low symmetry and unique bond arrangement in SnIP. In the effective mass approximation, the preferred transport direction is band dependent, with preferential electron and hole transport parallel and perpendicular to the double-helix axis, respectively. Furthermore, we show that over a wide range of energies the conduction band dispersion shows quasi-2D behavior and discuss possible experimental evidence of this in our TRTS data.

High carrier mobility and anisotropic electronic structure in double-helix SnIP nanowires

The Electron Cyclotron Resonance Ion Source is a versatile and reliable source to charge-breed rare isotopes at the TRIUMF's Isotopes Separation and Acceleration (ISAC) facility. Significant research work has been done by different groups worldwide to improve the efficiency and performance of the ECRIS as a charge state booster. The most recent of these research works is the implementation of the two-frequency heating on the ECRIS. At the ISAC facility of TRIUMF, a 14.5 GHz PHOENIX booster which has been in operation since 2010 was recently upgraded to accommodate the two-frequency heating system using a single waveguide. The efficiency for charge breeding into a single charge state, which depends on the rare isotope that is being charge-bred, has been determined to be between 1 - 6 and will be improved by the activities started at TRIUMF. The CSB, and the corresponding beam transport lines are being investigated in terms of beam properties like beam emittance from the extraction system, and after the beam separation. A systematic investigation of the effect of the two-frequency heating technique on the intensity, emittance, and efficiency of the extracted beam is presently being conducted.

Improvement of the Efficiency of the TRIUMF Charge State Booster

Social distancing measures have been the main non-pharmaceutical intervention (NPI) against the COVID-19 pandemic. Numerous large-scale analyses have studied how these measures have affected human movement, finding sizeable drops in average mobility. Yet comparatively little attention has been paid to higher-order effects such as “superspreading events” which are known to be outsized drivers of pandemics. Networks with heterogeneous (high variance) distributions of contacts can dramatically accelerate spreading processes, even if the average number of contacts is low. This stresses the need to quantify higher-order effects, and the (in)ability of existing NPI to reduce them.

Here we assess this by applying tools of statistical physics to approximately 12 billion anonymized mobile phone traces from 2.33 million devices in the Chicago metropolitan area, from Jan.1 to Jun.30, 2020, covering the first wave of state- and city-level social distancing measures in the pandemic. To identify potential super-spreading events, we grid these data at a fine spatial and temporal resolution, revealing large, transient co-localizations of people which we term hotspot events. We then ask about the spatiotemporal distribution of these events and the mobility statistics of the people participating in them--both before and after the implementation of social distancing measures. 
Encouragingly, we find that distancing policies heralded a dramatic rarefaction of people, reflected in an increase in the entropy of their spatial distribution. As a result, we observe a concomitant drop in hotspot event frequency, with the largest reduction occurring in the urban core. This, however, belies a more worrisome trend: though we observe a large average reduction in the amount people travel (as measured by individual radius of gyration), this fails to be true for the subset of users participating in hotspot events. These users display higher-than-average baseline mobility, which persists (and even increases) during the post-lockdown period.

Our findings indicate that though social distancing policies may succeed in reducing average mobility, their effectiveness in reducing the key driver of spreading processes on networks (the second moment of the degree distribution) may be more limited. This in turn suggests the need for additional NPI specifically targeted at “super-spreading events”.

Quantifying Density Hotspots and Potential Superspreading Events During COVID-19

Liquid Argon (LAr) is used as a target material by many WIMP dark matter search experiments for its high light-yield and excellent background rejection capability. LAr produces scintillation light at 128nm, which conventionally requires a wavelength shifting (WLS) material to be detected by photomultiplier tubes. Tetraphenyl-butadiene (TPB) is the WLS material of choice for most LAr detectors, including DEAP-3600 at SNOLAB, and is used to shift the primary scintillation light. Our work aims to characterize candidate thin films containing pyrene developed at Carleton University. Their long fluorescence time constant can be used for efficient rejection of pathological detector backgrounds. Fluorescence yield and mechanical stability in cryogenic conditions are also investigated. We describe the Queen's University cryogenic test facility which boasts good optical efficiency and a base temperature of 4K. We present results from pyrene thin films with various concentrations and purity as well as TPB as a reference.

Characterization of wavelength shifters for background rejection in liquid argon dark matter experiments

We discuss interaction of gravitational waves with matter including plasma and its implications for cosmology.

Gravitational Waves interacting with matter in cosmology

Trapped-ion quantum states are well-known to be good candidates for qubits in quantum computing. I will study the application of an adiabatic method known as STIRAP to achieve qubit switching. Stimulated Raman Adiabatic Passage (STIRAP) is a method of quantum control that utilizes a specific atomic structure known as a 3-Level Lambda System (3LLS). The system consists of two ground states that are coupled to an intermediate excited state via two counter-intuitively ordered pulses known as the Stokes and pump pulses. STIRAP is a notable method of population transfer because not only is it robust against small experimental variations, but it also has the unique property to allow the complete transfer of population between the two ground states without ever suffering population loss due to spontaneous emission from the excited state. STIRAP can be extended to other chain-wise connected multi-level systems such as those that are present in the trapped-ion. In this study, I will numerically determine the optimal pump and Stokes pulses that will maximize qubit switching in 3, 5, and 7-quantum states of the trapped-ion, and discuss the potential applicability of this method in quantum computing.

Quantum Control of Trapped Ions using Stimulated Raman Adiabatic Passage

**Introduction:** MRI’s low sensitivity, caused by the use of nuclei with low-gyromagnetic ratios or low magnetic field strength, can presently be improved with expensive high-field MRI-hardware and/or expensive enriched-isotopes. We propose a new method that does not require any extra signal-averaging or hardware to improve the quality of MRI images. We will use a significant k-space under-sampling acquisition method where only a certain percentage of the k-space points will be acquired per image, corresponding to the acceleration-factor (AF); it follows that one can acquire ten under-sampled images in the same time as one fully-sampled image. Averaging each possible combination of images of the under-sampled set, a density decay curve can then be fitted and reconstructed using the Stretched-Exponential-Model (SEM) combined with Compressed Sensing (CS).1
**Method:** 1H MR was performed on a resolution-phantom at the low-field (0.074T) MRI scanner using a home-built RF coil. Nine 2D fully-sampled k-spaces were acquired. Combinations of 2, 3, and 4 averages were carried out for each possible permutation, resulting in 14 k-spaces total (2 combinations for 4 averages, etc.); these were retroactively under-sampled for three AF’s (7, 10, 14). 3 Cartesian sampling schemes (FGRE, x-Centric2, & 8-sector FE Sectoral3) were used. The SNR attenuation is assumed to represent a decrease of the resonant isotope density in phantom after diluting it with the non-resonant isotope. The resulting signal decay (density) curve was fitted using the Abascal method.1
**Results:** The SNR of the 9 k-space averaged image and the original image was 16 and 5, respectively. The SNR of the three sampling schemes is 15 for FGRE, 19 for x-Centric, and 17 for FE Sectoral.
**Conclusion:** The improved SNR of the generated images for all sampling schemes demonstrate that the SEM equation can be adapted for fitting the SNR decay dependence of the MR signal. Since this technique does not require extra hardware, the proposed method could be implemented in current MRI-systems and yield improved images. Due to the CS-based reconstruction, the higher AF leads to more visible artefacting; this could be reduced by a Deep Learning-based correction after the fact.4
**References:**
**1** Abascal et al. IEEE Trans Med Imaging (2018); **2** Ouriadov et al. MRM (2017); **3** Khrapitchev et al. JMR (2006); **4** Duan et al. MRM (2019)

The Use of a Novel Sampling/Reconstruction Method for Non-Proton and Low Field MRI

**Introduction:** A non-invasive imaging method: inhaled hyperpolarized (HP) 129Xe magnetic resonance imaging (MRI) is currently used to measure lung structure and function.***1*** Simultaneous ventilation/perfusion (V/P) lung measurements of functional gas exchange within the lungs can be obtained using this MRI approach because of the high solubility of xenon in lung tissue as compared to other imaging gases. This measurement is possible due to the distinct and large range of chemical shifts (~200ppm) of 129Xe when residing within barrier and RBC (e.g., barrier and RBC phase xenon) compared to the gas phase. Therefore, 129Xe is a unique probe for exploring xenon within and beyond the lung, such as lung parenchyma (barrier), RBC, and even other organs such as the **brain**, heart and kidney.
[15O]water positron emission tomography (PET) is the gold standard imaging method for determining cerebral perfusion.***2,3*** In this study, simultaneous 129Xe-based MRI and [15O]water PET images were collected and compared. 

**Methods:** A 60mL plastic syringe was used in which 30mL of the hyperpolarized 129Xe gas was dissolved in [15O]-water solution (30mL) After dissolving, all leftover xenon gas was removed from the syringe. A turn-key, spin-exchange polarizer system (Polarean 9820 129Xe polarizer) was used for obtaining Hyperpolarized 129Xe gas. 129Xe dissolved phase images were acquired in a 3T PET/MRI (Siemens Biograph mMR) scanner. [15O]water PET data were acquired simultaneously with 129Xe MRI using the integrated PET system in the 3T PET/MRI. 

**Results:** Two consecutive 2D axial 129Xe MRI images and two (2D and 3D) [15O]water PET images were acquired simultaneously. 129Xe/PET images indicate that the diameter of the phantom from both PET and MRI images are similar. Both 129Xe images demonstrate a sufficient SNR level (80 and 10 respectively) suggesting that 3D 129Xe imaging is possible. 

**Conclusions:** The results of this proof-of-concept study clearly indicate the feasibility of the simultaneous hyperpolarized 129Xe MRI and [15O]water PET measurements. This demonstration enables the next step, namely, in-vivo double tracer brain perfusion imaging which we plan to perform using a small animal model.

***References:***
***1***.Kaushik, S. S. et al. MRM (2016); ***2***. Fan, A., et. al. JCBFM (2016); ***3.*** Ssali. T., et. al. JNM (2018).

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