Some investigations into the numerical solution of initial value problems in ordinary differential equations

PhD ThesisIn this thesis several topics in the numerical solution of the initial value problem in first-order ordinary diff'erentlal equations are investigated, Consideration is given initially to stiff differential equations and their solution by stiffly-stable linear multistep methods which incorporate second derivative terms. Attempts are made to increase the size of the stability regions for these methods both by particular choices for the third characteristic polynomial and by the use of optimization techniques while investigations are carried out regarding the capabilities of a high order method. Subsequent work is concerned with the development of Runge-Kutta methods which include second-derivative terms and are implicit with respect to y rather than k. Methods of order three and four are proposed which are L-stable. The major part of the thesis is devoted to the establishment of recurrence relations for operators associated with linear multistep methods which are based on a non-polynomial representation of the theoretical solution. A complete set of recurrence relations is developed for both implicit and explicit multistep methods which are based on a representation involving a polynomial part and any number of arbitrary functions. The amount of work involved in obtaining mulc iste, :ne::l'lJds by this technique is considered and criteria are proposed to Jecide when this particular method of derivation should be em~loyed. The thesis is conclud~d by using Prony's method to develop one-step methods and multistep methods which are exponentially adaptive and as such can be useful in obtaining solutions to problems which are exponential in nature

Features in the ion emission of Cu, Al, and C plasmas produced by ultrafast laser ablation

© 2015 AIP Publishing LLC. The bi-modal nature of charge integrated ion kinetic energy distributions, which result from ultrafast laser produced plasmas, is discussed in this paper. A negatively biased Faraday cup was used as a charge collector to measure ion distributions from three different solid targets that had been irradiated with an ultrafast laser in the fluence range 0.1-1 J/cm2. A bi-modal time of flight distribution is found for all three targets (C, Al, and Cu). In the case of the metallic targets (Al and Cu), high- and low-kinetic energy peaks exhibit quite different dependencies on laser fluence, whereas for the semi-metallic target (C), both peaks scale similarly with ultrafast laser fluence. The results are discussed within the framework of a one dimensional capacitor model resulting in ion acceleration

Plan of the Southerly and Westerly Part of the Town of Edmunds

Plan of the south-westerly part of the town of Edmunds, particularly the land in dispute between Aaron and Benjamin Hobart. The Hobart dispute encompassed a total of 134 1/4 acres along the length of the 6th Range. The disputed lines are labeled J-E and G-F. The map scale is 1:15,840 or 80 rods per inch.https://digitalcommons.library.umaine.edu/mainebicentennial/1042/thumbnail.jp

Structure and Composition of Pollen Grains of Vernal Plants

Among the first morphological studies of pollen were those of Malpighi (1686) and of Grew (1675). While numerous articles on their structure and composition of pollen have been contributed, the amount of data available in application to several problems involved in such study is yet somewhat fragmentar

Body Composition and Perceived Stress through a Calendar Year in NCAA I Female Volleyball Players

International Journal of Exercise Science 12(5): 433-443, 2019. The aim of the study was to track changes of perceived stress and body composition across an entire calendar year in National Collegiate Athletic Association (NCAA) division I female volleyball players. We hypothesized that perceived stress and body composition would vary between the competitive season and off-season, with the largest changes occurring during time points prior to the onset and after the end of the competitive season. Eight female volleyball players participated in a longitudinal study. Body mass, body mass index (BMI), percent body fat, fat mass, and fat free mass were obtained during the early, mid, late, and off season and during the pre, early, mid, and late competitive season. The perceived stress scale-10 was used to appraise stress levels. BMI and body mass were significantly higher in pre-season compared to early-offseason. Changes in BMI between these points were due to increase in fat mass. Fat mass and percent body fat were significantly higher in pre-season compared to late off-season, mid-season, and late season. Perceived stress was significantly higher at the mid-season compared to early offseason. A significant positive correlation existed between BMI and body fat (p\u3c0.05, r=0.69), while a significant negative correlation existed between percent body fat and perceived stress (p\u3c0.05, r=0.34). Tracking body composition and perceived stress in collegiate female volleyball players can provide informative feedback on the training status and well-being of female collegiate athletes. Interestingly, it appears stress in these athletes may be more dependent upon the school session rather than participation in competitive sports

Information Flow in Entangled Quantum Systems

All information in quantum systems is, notwithstanding Bell's theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is transmitted through 'classical' (i.e. decoherent) information channels.Comment: PostScript version now available: http://www.qubit.org/people/patrickh/Papers/InformationFlow.p

No Evidence for Orbital Loop Currents in Charge Ordered YBa2_2Cu3_3O6+x_{6+x} from Polarized Neutron Diffraction

It has been proposed that the pseudogap state of underdoped cuprate superconductors may be due to a transition to a phase which has circulating currents within each unit cell. Here, we use polarized neutron diffraction to search for the corresponding orbital moments in two samples of underdoped YBa$_2$Cu$_3$O$_{6+x}$ with doping levels $p=0.104$ and 0.123. In contrast to some other reports using polarized neutrons, but in agreement with nuclear magnetic resonance and muon spin rotation measurements, we find no evidence for the appearance of magnetic order below 300 K. Thus, our experiment suggests that such order is not an intrinsic property of high-quality cuprate superconductor single crystals. Our results provide an upper bound for a possible orbital loop moment which depends on the pattern of currents within the unit cell. For example, for the CC-$\theta_{II}$ pattern proposed by Varma, we find that the ordered moment per current loop is less than 0.013 $\mu_B$ for $p=0.104$.Comment: Comments in arXiv:1710.08173v1 fully addresse