The Influences of the Musselman Family

For almost a century, the Musselman family has had huge influences on Adams County, PA. Many of those contributions are unknown by people today. So, based on the research of the Musselman Canning Company and the two Musselman Foundations, this paper is a study of the impacts the Musselman family has had on others and how it has achieved that influence. The main primary sources include the company’s publication, The Processor, the articles on local newspaper, and the collections in the Special Collection in Gettysburg College’s Musselman Library

On the existence of solutions to nonlinear systems of higher order Poisson type

In this paper, we study the existence of higher order Poisson type systems. In detail, we prove a Residue type phenomenon for the fundamental solution of Laplacian in \RR^n, n\ge 3. This is analogous to the Residue theorem for the Cauchy kernel in \CC. With the aid of the Residue type formula for the fundamental solution, we derive the higher order derivative formula for the Newtonian potential and obtain its appropriate \s C^{k, \alpha} estimates. The existence of solutions to higher order Poisson type nonlinear systems is concluded as an application of the fixed point theorem.Comment: 33 page

On Blow-up criterion for the Nonlinear Schr\"{o}dinger Equation

The blowup is studied for the nonlinear Schr\"{o}dinger equation $iu_{t}+\Delta u+ |u|^{p-1}u=0$ with $p$ is odd and $p\ge 1+\frac 4{N-2}$ (the energy-critical or energy-supercritical case). It is shown that the solution with negative energy $E(u_0)<0$ blows up in finite or infinite time. A new proof is also presented for the previous result in \cite{HoRo2}, in which a similar result but more general in a case of energy-subcritical was shown.Comment: In this version, we add a reference, and change some expressions in Englis

Flexible Multi-Group Single-Carrier Modulation: Optimal Subcarrier Grouping and Rate Maximization

Orthogonal frequency division multiplexing (OFDM) and single-carrier frequency domain equalization (SC-FDE) are two commonly adopted modulation schemes for frequency-selective channels. Compared to SC-FDE, OFDM generally achieves higher data rate, but at the cost of higher transmit signal peak-to-average power ratio (PAPR) that leads to lower power amplifier efficiency. This paper proposes a new modulation scheme, called flexible multi-group single-carrier (FMG-SC), which encapsulates both OFDM and SC-FDE as special cases, thus achieving more flexible rate-PAPR trade-offs between them. Specifically, a set of frequency subcarriers are flexibly divided into orthogonal groups based on their channel gains, and SC-FDE is applied over each of the groups to send different data streams in parallel. We aim to maximize the achievable sum-rate of all groups by optimizing the subcarrier-group mapping. We propose two low-complexity subcarrier grouping methods and show via simulation that they perform very close to the optimal grouping by exhaustive search. Simulation results also show the effectiveness of the proposed FMG-SC modulation scheme with optimized subcarrier grouping in improving the rate-PAPR trade-off over conventional OFDM and SC-FDE.Comment: Submitted for possible conference publicatio

Improving Thermoelectric Properties of Inorganic Clathrates by Atomic and Microscale Structure Engineering

As more countries are aiming for a carbon-neutral economy, technologies that utilize renewable energies are increasingly being considered. Thermoelectric materials enable the direct conversion between a thermal gradient and an electrical potential gradient, and are thus exploited for applications such as waste heat recovery. One of the prominent thermoelectric materials is the inorganic clathrate. Extensive research has been conducted over the past few decades to utilize its properties. However, several problems still remain ambiguous. In this thesis, we have studied the atomic and microscale structure of the clathrates and investigated its impact on the thermoelectric properties. Especially, with a combination of experiment and theoretical calculations, the existence of an order-disorder phase transition is confirmed. It further influences the electrical transport properties, since the band structure changes after the phase transition. The degree of chemical ordering can be controlled by the synthesis method, because materials reach different equilibrium states in either route. In addition, it is found that atomic vacancies can induce a peculiar transition effect in the electrical resistivity. In order to investigate its influence on the thermoelectric performance, a novel method is employed, where Ba8(AlxGa1–x)16Ge30 clathrates are synthesized by alloying Ba8Al16Ge30 with Ba8Ga16Ge30. This way a heterostructure is created, which contains the quaternary clathrate main phase and aggregates of Al particles. Consequently, the charge carrier mobility is largely improved to a value higher than that of the single crystal, while the lattice thermal conductivity is reduced due to the enhanced phonon scattering at different length scales. A greatly improved understanding of the process-structure-property relationship of clathrates is achieved in this thesis. The methodologies used, as well as the key findings, can be applicable for other material systems, and hence facilitate the future research in the thermoelectrics field