Vulnerability Analysis of Modern Electric Grids: A Mathematical Optimization Approach

Electrical power must be transmitted through a vast and complicated network of interconnected grids to arrive at one’s fingertips. The US electric grid network and its components are rapidly advancing and adapting to the advent of smart technologies. Production of electricity is transitioning to sustainable processes derived from renewable energy sources like wind and solar power to decrease dependence on nonrenewable fossil fuels. These newly pervasive natures of smart technology and the variable power supply of renewable energy introduce previously unexamined vulnerabilities into the modern electric grid. Disruption of grid operations is not uncommon, and the effects can be economically and societally severe. Thus, a vulnerability analysis can provide decision makers with the ability to characterize points of improvement in the networks they supervise. This thesis performs a vulnerability analysis of electric grid operations including storage. This vulnerability analysis is achieved through a set of numerical experiments on a multi-period optimal power flow model including storage and variable demand. This model resulted in an analysis indicating storage is helpful in increasing resilience in networks with excess generation, no matter how severe the disruption. Networks with constrained generation benefit little, if at all, from storage. This analysis allows us to conclude careful implementation is the best way to improve electric grid security in the face of widespread use of renewable energy and smart technology

The Generalized Green's function Cluster Expansion: A Python package for simulating polarons

We present an efficient implementation of the Generalized Green's function Cluster Expansion (GGCE), which is a new method for computing the ground-state properties and dynamics of polarons (single electrons coupled to lattice vibrations) in model electron-phonon systems. The GGCE works at arbitrary temperature and is well suited for a variety of electron-phonon couplings, including, but not limited to, site and bond Holstein and Peierls (Su-Schrieffer-Heeger) couplings, and couplings to multiple phonon modes with different energy scales and coupling strengths. Quick calculations can be performed efficiently on a laptop using solvers from NumPy and SciPy, or in parallel at scale using the PETSc sparse linear solver engine.Comment: 3 pages, software can be found open source under the BSD-3-clause license at github.com/x94carbone/GGC

Detecting fractions of electrons in the high-TcT_c cuprates

We propose several tests of the idea that the electron is fractionalized in the underdoped and undoped cuprates. These include the ac Josephson effect, and tunneling into small superconducting grains in the Coulomb blockade regime. In both cases, we argue that the results are qualitatively modified from the conventional ones if the insulating tunnel barrier is fractionalized. These experiments directly detect the possible existence of the chargon - a charge $e$ spinless boson - in the insulator. The effects described in this paper provide a means to probing whether the undoped cuprate (despite it's magnetism) is fractionalized. Thus, the experiments discussed here are complementary to the flux-trapping experiment we proposed in our earlier work(cond-mat/0006481).Comment: 7 pages, 5 figure

The alpha angle as a predictor of contralateral slipped capital femoral epiphysis

Purpose Contralateral hip involvement in slipped capital femoral epiphysis (SCFE) is common. Femoral head−neck asphericity, as measured by an elevated alpha angle, has not previously been assessed with respect to SCFE risk. Our aim was to assess the utility of the alpha angle in predicting contralateral SCFE. Methods: We retrospectively reviewed 168 patients (94 males) managed surgically for unilateral SCFE between 2001 and 2013 who had a minimum of 18 months follow-up. The alpha angle, the posterior sloping angle (PSA), and the modified Oxford score were recorded for every patient at the time of initial SCFE presentation. Follow-up clinical records and radiographs were assessed to determine the presence of absence of contralateral SCFE. Results: Forty-five patients (27 %) developed a contralateral SCFE. Patients who developed a contralateral SCFE had a significantly higher alpha angle (51° vs 45°, p 0.10) between patients who developed a contralateral SCFE and those who did not. Using a proposed alpha angle of 50.5° as a threshold for prophylactic fixation, 26 (58 %) of the 45 cases of contralateral SCFE in our study would have been prevented and 18 (15 %) of 123 patients would have undergone fixation unnecessarily. Conclusions: We found the alpha angle to positively correlate with contralateral SCFE risk. Patients with significantly elevated alpha angles may be at greater risk of contralateral SCFE and benefit from further investigation or prophylactic hip fixation

Stereocilia-staircase spacing is influenced by myosin III motors and their cargos espin-1 and espin-like

Hair cells tightly control the dimensions of their stereocilia, which are actin-rich protrusions with graded heights that mediate mechanotransduction in the inner ear. Two members of the myosin-III family, MYO3A and MYO3B, are thought to regulate stereocilia length by transporting cargos that control actin polymerization at stereocilia tips. We show that eliminating espin-1 (ESPN-1), an isoform of ESPN and a myosin-III cargo, dramatically alters the slope of the stereocilia staircase in a subset of hair cells. Furthermore, we show that espin-like (ESPNL), primarily present in developing stereocilia, is also a myosin-III cargo and is essential for normal hearing. ESPN-1 and ESPNL each bind MYO3A and MYO3B, but differentially influence how the two motors function. Consequently, functional properties of different motor-cargo combinations differentially affect molecular transport and the length of actin protrusions. This mechanism is used by hair cells to establish the required range of stereocilia lengths within a single cell