Exactly Conservative Integrators

Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.Comment: 30 pages, postscript (1.3MB). Submitted to SIAM J. Sci. Comput

Featured Piece

This year the General Editors continued the tradition started last year by creating a feature piece to show our appreciation for the History Department. We selected four professors from the faculty to answer a question about history: what figure/event/idea inspires your interest in history? Reading their responses helped give us insight into the thoughts of these brilliant minds and further help us understand their passion for the subject we all share a common love and interest in. We hope that you enjoy reading their responses as much as we did. The four members of the faculty we spoke with are Dr. Abou Bamba, Dr. William Bowman, Dr. David Hadley, and Magdalena Sánchez

Modelling the quark propagator

The quark propagator is at the core of lattice hadron spectrum calculations as well as studies in other nonperturbative schemes. We investigate the quark propagator with an improved staggered action (Asqtad) and an improved gluon action, which provides good quality data down to small quark masses. This is used to construct ans\"{a}tze suitable for model hadron calculations as well as adding to our intuitive understanding of QCD.Comment: Lattice2002(spectrum

Scaling Behavior of the Landau Gauge Overlap Quark Propagator

The properties of the momentum space quark propagator in Landau gauge are examined for the overlap quark action in quenched lattice QCD. Numerical calculations are done on three lattices with different lattice spacings and similar physical volumes to explore the approach of the quark propagator towards the continuum limit. We have calculated the nonperturbative momentum-dependent wavefunction renormalization function $Z(p^2)$ and the nonperturbative mass function $M(p^2)$ for a variety of bare quark masses and extrapolate to the chiral limit. We find the behavior of $Z(p^2)$ and $M(p^2)$ are in good agreement for the two finer lattices in the chiral limit. The quark condensate is also calculated.Comment: 3 pages, Lattice2003(Chiral fermions

Novel inferences of ionisation & recombination for particle/power balance during detached discharges using deuterium Balmer line spectroscopy

The physics of divertor detachment is determined by divertor power, particle and momentum balance. This work provides a novel analysis technique of the Balmer line series to obtain a full particle/power balance measurement of the divertor. This supplies new information to understand what controls the divertor target ion flux during detachment. Atomic deuterium excitation emission is separated from recombination quantitatively using Balmer series line ratios. This enables analysing those two components individually, providing ionisation/recombination source/sinks and hydrogenic power loss measurements. Probabilistic Monte Carlo techniques were employed to obtain full error propagation - eventually resulting in probability density functions for each output variable. Both local and overall particle and power balance in the divertor are then obtained. These techniques and their assumptions have been verified by comparing the analysed synthetic diagnostic 'measurements' obtained from SOLPS simulation results for the same discharge. Power/particle balance measurements have been obtained during attached and detached conditions on the TCV tokamak.Comment: The analysis results of this paper were formerly in arXiv:1810.0496

Scaling behavior of quark propagator in full QCD

We study the scaling behavior of the quark propagator on two lattices with similar physical volume in Landau gauge with 2+1 flavors of dynamical quarks in order to test whether we are close to the continuum limit for these lattices. We use configurations generated with an improved staggered (``Asqtad'') action by the MILC collaboration. The calculations are performed on $28^3\times 96$ lattices with lattice spacing $a = 0.09$ fm and on $20^3\times 64$ lattices with lattice spacing $a = 0.12$ fm. We calculate the quark mass function, $M(q^2)$, and the wave-function renormalization function, $Z(q^2)$, for a variety of bare quark masses. Comparing the behavior of these functions on the two sets of lattices we find that both $Z(q^2)$ and $M(q^2)$ show little sensitivity to the ultraviolet cutoff.Comment: 6 pages, 5 figure

Operative management of partial-thickness tears of the proximal hamstring muscles in athletes.

BACKGROUND: Partial tears of the hamstring muscle origin represent a challenging clinical problem to the patient and orthopaedic surgeon. Although nonoperative treatment is frequently met with limited success, there is a paucity of data on the efficacy of surgical management for partial proximal hamstring tears in the active and athletic population. PURPOSE: To evaluate the results of an anatomic repair for partial tears of the hamstring muscle origin in athletes. STUDY DESIGN: Case series; Level of evidence, 4. METHODS: The records of 17 patients with partial tears of the proximal hamstring origin were reviewed after institutional review board approval was obtained. All patients were treated with open debridement and primary tendon repair after failure of at least 6 months of nonoperative therapy. Clinical and operative records, radiographs, and magnetic resonance images were reviewed for all patients. A patient-reported outcomes survey was completed by 14 patients that included the Lower Extremity Functional Score (LEFS), Marx activity rating scale, custom LEFS and Marx scales, and subjective patient satisfaction scores. Early and late postoperative complications were recorded. RESULTS: There were 3 male and 14 female patients; their average age was 43 years (range, 19-64 years) and average follow-up was 32 months (range, 12-51 months). There were 2 collegiate athletes (field hockey, track), 14 amateur athletes (distance running, waterskiing, tennis), and a professional bodybuilder. Postoperative LEFS was 73.3 ± 9.9 (range, 50-80) and custom LEFS was 66.7 ± 17.0 (range, 37-80) of a maximum 80 points. The most commonly reported difficulty was with prolonged sitting and explosive direction change while running. The average Marx score was 6.5 ± 5.3 (range, 0-16) of a maximum 16, correlating with a greater return to recreational running activities in this patient cohort than regular participation in pivoting or cutting sports. Marx custom scores were 20 of a maximum 20 in all patients, demonstrating no disability in the operative extremity with activities of daily living. No patient underwent a subsequent surgery. One patient was not satisfied with the result and reported persistent symptoms during competitive distance running. All patients were able to return to their preoperative level of activity after surgery. CONCLUSION: Anatomic surgical treatment of partial proximal hamstring avulsions can lead to satisfactory functional outcomes, a high rate of return to athletic activity, and low complication rate. This procedure should be reserved for patients who have failed an extended course of nonoperative treatment, and the proximity of the sciatic nerve mandates a careful assessment of the risk-benefit ratio before surgery is undertaken