Noninteracting Fermions in infinite dimensions

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at least pedagogically. Which implies all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. In this paper, this fact is discussed and explained. I hope, this article will be helpful for graduate students to study the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010

Counter Rotating Open Rotor Animation using Particle Image Velocimetry

This article describes the two accompanying fluid dynamics videos for the "Counter rotating open rotor flow field investigation using stereoscopic Particle Image Velocimetry" presented at the 64th Annual Meeting of the APS Division of Fluid Dynamics in Baltimore, Maryland, November 20-22, 2011.Comment: Videos are include

The Use of Bone Morphogenetic Protein in the Intervertebral Disk Space in Minimally Invasive Transforaminal Lumbar Interbody Fusion

Study Design: Retrospective Cohort. Objective: The objective of this study was to characterize one surgeon’s experience over a 10-year period using rhBMP-2 in the disk space for minimally invasive transforaminal lumbar interbody fusion (MIS TLIF). Summary of Background Data: MIS TLIF has been utilized as a technique for decreasing patients’ immediate postoperative pain, decreasing blood loss, and shortened hospital stays. Effectiveness and complications of rhBMP-2’s use in the disk space is limited because of its off-label status. Methods: Retrospective analysis of consecutive MIS TLIFs performed by senior author between 2004 and 2014. rhBMP-2 was used in the disk space in all cases. Patients were stratified based on the dose of rhBMP-2 utilized. Patients had 9 to 12 month computerized tomography scan to evaluate for bony fusion and continued follow-up for 18 months. Results: A total of 688 patients underwent a MIS TLIF. A medium kit of rhBMP-2 was utilized in 97 patients, and small kit was used in 591 patients. Fusion rate was 97.9% and this was not different between the 2 groups with 96/97 patients fusing in the medium kit group and 577/591 patients fusing in the small kit group. Five patients taken back to the operating room for symptomatic pseudoarthrosis, 4 reoperated for bony hyperostosis, and 10 radiographic pseudoarthroses that did not require reoperation. A statistically significant difference in the rate of foraminal hyperostosis was found when using a medium sized kit of rhBMP-2 was 4.12% (4/97 patients), compared with a small kit (0/591 patients, P=0.0004). Conclusions: Utilization of rhBMP-2 in an MIS TLIF leads to high fusion rate (97.9%), with an acceptable complication profile. The development of foraminal hyperostosis is a rare complication that only affected 0.6% of patients, and seems to be a dose related complication, as this complication was eliminated when a lower dose of rhBMP-2 was utilized

Making Sense of the Legendre Transform

The Legendre transform is an important tool in theoretical physics, playing a critical role in classical mechanics, statistical mechanics, and thermodynamics. Yet, in typical undergraduate or graduate courses, the power of motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We review and modify the presentation of Legendre transforms in a way that explicates the formal mathematics, resulting in manifestly symmetric equations, thereby clarifying the structure of the transform algebraically and geometrically. Then we bring in the physics to motivate the transform as a way of choosing independent variables that are more easily controlled. We demonstrate how the Legendre transform arises naturally from statistical mechanics and show how the use of dimensionless thermodynamic potentials leads to more natural and symmetric relations.Comment: 11 pages, 3 figure

Correlation of Early Outcomes and Intradiscal Interleukin-6 Expression in Lumbar Fusion Patients.

OBJECTIVE: To determine if there is correlation between intradiscal levels of interleukin-6 (IL-6) and early outcome measures in patients undergoing lumbar fusion for painful disc degeneration. METHODS: Intervertebral disc tissue was separated into annulus fibrosus/nucleus pulposus and cultured separately in vitro in serum-free medium (Opti-MEM). Conditioned media was collected after 48 hours. The concentration of IL-6 was quantified using enzyme-linked immunosorbent assay. Pearson correlation coefficients quantified relationships between IL-6 levels and pre- and postoperative visual analogue scale (VAS) back pain and Oswestry Disability Index (ODI), as well as change in VAS/ODI. RESULTS: Sixteen discs were harvested from 9 patients undergoing anterior lumbar interbody fusion (mean age, 47.4 years; range, 21-70 years). Mean preoperative and 6-month postoperative VAS were 8.1 and 3.7, respectively. Mean preoperative and postoperative ODI were 56.2 and 25.6, respectively. There were significant positive correlations between IL-6 expression and postoperative VAS (ρ = 0.38, p = 0.048) and ODI (ρ = 0.44, p = 0.02). No significant correlations were found between intradiscal IL-6 expression and preoperative VAS (ρ = -0.12, p = 0.54). Trends were seen associating IL-6 expression and change in VAS/ODI (ρ = -0.35 p = 0.067; ρ = -0.34, p = 0.08, respectively). A trend associated IL-6 and preoperative ODI (ρ = 0.36, p = 0.063). CONCLUSION: The direct association between IL-6 expression and VAS/ODI suggests patients with elevated intradiscal cytokine expression may have worse early outcomes than those with lower expression of IL-6 after surgery for symptomatic disc degeneration

The QCD equation of state and the effects of the charm

We present an update on the QCD equation of state of the Wuppertal-Budapest Collaboration, extending our previous studies [JHEP 0601 (2006) 089, JHEP 1011 (2010) 077]. A Symanzik improved gauge and a stout-link improved staggered fermion action is utilized. We discuss partial quenching and present preliminary results for the fully dynamical charmed equation of state.Comment: Talk presented at the XXIX International Symposium on Lattice Field Theory, July 10-16, 2011, Lake Tahoe, Californi

SEASAT: A satellite scatterometer illumination times of selected in situ sites

A list of times that the SEASAT A Satellite Scatterometer (SASS) illuminated from directly above or directly abeam, selected surface sites where in situ winds were measured is provided. The list is ordered by the Greenwich Mean Time (GMT) of the midpoint of the illumination period (hit time) for a given surface site. The site identification, the orbit number and the direction from the subtrack in which the truth lies are provided. The accuracy of these times depends in part upon the ascending node times, which are estimated to be within +.1 sec, and on the illumination time relative to the ascending node, which is estimated to be within +6 seconds. The uncertainties in the times provided were judged to be sufficiently small to allow efficient and accurate extraction of SASS and in situ data at the selected surface sites. The list contains approximately six thousand hit times from 61 geographically dispersed sites

Metal-Ferroelectric-Metal heterostructures with Schottky contacts I. Influence of the ferroelectric properties

A model for Metal-Ferroelectric-Metal structures with Schottky contacts is proposed. The model adapts the general theories of metal-semiconductor rectifying contacts for the particular case of metal-ferroelectric contact by introducing: the ferroelectric polarization as a sheet of surface charge located at a finite distance from the electrode interface; a deep trapping level of high concentration; the static and dynamic values of the dielectric constant. Consequences of the proposed model on relevant quantities of the Schottky contact such as built-in voltage, charge density and depletion width, as well as on the interpretation of the current-voltage and capacitance-voltage characteristics are discussed in detail.Comment: 14 pages with 4 figures, manuscript under revision at Journal of Applied Physics for more than 1 year (submitted May 2004, first revision September 2004, second revision May 2005