Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

THE DESIGN AND SYNTHESIS OF SILOXANE PRECURSORS FOR CHIRAL PERIODIC MESOPOROUS ORGANOSILICA MATERIALS

The development of cost-effective and reliable methods for the synthesis and separation of asymmetric compounds is paramount in helping to meet society’s ever-growing demand for chiral small molecules. Of these methods, chiral heterogeneous supports are particularly appealing as they allow for the reuse of the chiral source. One such support, based on the synergy between chiral organic units and structurally stable inorganic silicon scaffolds are periodic mesoporous organosilicas (PMOs). In the work described herein, I examine some of the factors governing the transmission of chirality between chiral dopants and prochiral bulk phases in chiral PMO materials. In particular, the exploration of 1,1’-binaphthalene-bridged chiral dopants with a focus on the point of attachment into the materials. Moreover, the effects of ordering in the materials are examined and reveal that chirality transfer is more facile in materials with molecular-scale order then those containing amorphous walls. Secondly, the issues surrounding the synthesis and purification of aryl-triethoxysilanes as siloxane precursors are addressed. Both the introduction of a two-carbon linker and the direct attachment of allyl and mixed allyldiethoxysilane species are explored. This work demonstrates that allyldiethoxysilanes are ideal, in that they are stable enough to permit facile synthesis, while still being able to hydrolyze completely to produce well-ordered materials. Lastly, the production of new bulk phases for chiral PMO materials is examined by introducing new prochiral nitrogen-containing siloxane precursors. Biphenyldiamine and bipyridine-bridged siloxane precursors are readily synthesized on reasonable scales. Their use as the bulk siloxane precursor in the production of PMO materials however, is precluded by insufficient gelation and additional siloxane precursors are necessary for the production of ordered materials. In addition to the research detailed above that forms the body of this thesis, two short works are appended. The first details the production of polythiophene assemblies mediated through coordination nanospaces, while the second explores the production of N-heterocyclic carbene functionalized gold nanoparticles through ligand exchange.

Access Point Association Coordination in Densely Deployed 802.11 Wireless Networks

Dense deployment of wireless local area network (WLAN) access points (APs) is an important part of the next generation Wi-Fi and standardization (802.11ax) efforts are underway. Increasing demand for WLAN connectivity motivates such dense deployments, especially in geographical areas with large numbers of users, such as stadiums, large enterprises, multi-tenant buildings, and urban cities. Although densification of WLAN APs guarantees coverage, it is susceptible to increased interference and uncoordinated association of stations (STAs) to APs, which degrade network throughput. Therefore, to improve network throughput, algorithms are proposed in this thesis to optimally coordinate AP associations in the presence of interference. In essence, coordination of APs in dense WLANs (DWLANs) is achieved through coordination of STAs' associations with APs. While existing approaches suggest tuning of APs' beacon powers or using transmit power control (TPC) for association control, here, the signal-to-interference-plus-noise ratio (SINRs) of STAs and the clear channel assessment (CCA) threshold of the 802.11 MAC protocol are employed. The proposed algorithms in this thesis enhance throughput and minimize coverage holes inherent in cell breathing and TPC techniques by not altering the transmit powers of APs, which determine cell coverage. Besides uncoordinated AP associations, unnecessary frequent transmission deferment is envisaged as another problem in DWLANs due to the clear channel assessment aspect of the carrier sensing multiple access collision avoidance (CSMA/CA) scheme in 802.11 standards and the short spatial reuse distance between co-channel APs. To address this problem in addition to AP association coordination, an algorithm is proposed for CCA threshold adjustment in each AP cell, such that CCA threshold used in one cell mitigates transmission deferment in neighboring cells. Performance evaluation reveals that the proposed association optimization algorithms achieve significant gain in throughput when compared with the default strongest signal first (SSF) association scheme in the current 802.11 standard. Also, further gain in throughput is observed when the CCA threshold adjustment is combined with the optimized association. Results show that when STA-AP association is optimized and CCA threshold is adjusted in each cell, throughput improves. Finally, transmission delay and the number of packet re-transmissions due to collision and contention significantly decrease.