Explicit convex and concave envelopes through polyhedral subdivisions with Unstable Equilibria

In this paper, we derive explicit characterizations of convex and concave envelopes of several nonlinear functions over various subsets of a hyper-rectangle. These envelopes are obtained by identifying polyhedral subdivisions of the hyper-rectangle over which the envelopes can be constructed easily. In particular, we use these techniques to derive, in closed-form, the concave envelopes of concave-extendable supermodular functions and the convex envelopes of disjunctive convex functions.

Particle-Hole Asymmetry in Doped Mott Insulators: Implications for Tunneling and Photoemission Spectroscopies

In a system with strong local repulsive interactions it should be more difficult to add an electron than to extract one. We make this idea precise by deriving various exact sum rules for the one-particle spectral function independent of the details of the Hamiltonian describing the system and of the nature of the ground state. We extend these results using a variational ansatz for the superconducting ground state and low lying excitations. Our results shed light on the striking asymmetry in the tunneling spectra of high Tc superconductors and should also be useful in estimating the local doping variations in inhomogeneous materials.Comment: 4 pages, no figure

Fermions in 3D Optical Lattices: Cooling Protocol to Obtain Antiferromagnetism

A major challenge in realizing antiferromagnetic (AF) and superfluid phases in optical lattices is the ability to cool fermions. We determine the equation of state for the 3D repulsive Fermi-Hubbard model as a function of the chemical potential, temperature and repulsion using unbiased determinantal quantum Monte Carlo methods, and we then use the local density approximation to model a harmonic trap. We show that increasing repulsion leads to cooling, but only in a trap, due to the redistribution of entropy from the center to the metallic wings. Thus, even when the average entropy per particle is larger than that required for antiferromagnetism in the homogeneous system, the trap enables the formation of an AF Mott phase.Comment: 4 pages; 5 figures; also see supplementary material in 2 pages with 1 figur

Understanding how porosity gradients can make a better filter using homogenization theory

Filters whose porosity decreases with depth are often more efficient at removing solute from a fluid than filters with a uniform porosity. We investigate this phenomenon via an extension of homogenization theory that accounts for a macroscale variation in microstructure. In the first stage of the paper, we homogenize the problems of flow through a filter with a near-periodic microstructure and of solute transport owing to advection, diffusion and filter adsorption. In the second stage, we use the computationally efficient homogenized equations to investigate and quantify why porosity gradients can improve filter efficiency. We find that a porosity gradient has a much larger effect on the uniformity of adsorption than it does on the total adsorption. This allows us to understand how a decreasing porosity can lead to a greater filter efficiency, by lowering the risk of localized blocking while maintaining the rate of total contaminant removal

Tibial tuberosity fracture in adult as an unusual pattern of injury

Tibial tuberosity avulsion is an uncommon fracture in adults, such lesions typically seen in adolescent male with well-developed quadriceps, ligaments when they are stronger than growth plate. We described a case of 51-year-old gentlemen had direct trauma to left knee, no risk factors were identified, not able to walk, difficulty in straight leg raise test, radiograph of left knee showed tibial tuberosity avulsion fracture. The fracture was treated with open reduction and internal fixation, f/u with successful rehabilitation which results in good range of motion and excellent function at knee joint. The aim of study is present unusual and rare case of tibial tuberosity Avulsion fracture in adult, early diagnosis, surgical mode of treatment, post-surgery rehabilitation and possible complications

Internet Versus Mailed Questionnaires: A Randomized Comparison (2)

BACKGROUND Low response rates among surgeons can threaten the validity of surveys. Internet technologies may reduce the time, effort, and financial resources needed to conduct surveys. OBJECTIVE We investigated whether using Web-based technology could increase the response rates to an international survey. METHODS We solicited opinions from the 442 surgeon–members of the Orthopaedic Trauma Association regarding the treatment of femoral neck fractures. We developed a self-administered questionnaire after conducting a literature review, focus groups, and key informant interviews, for which we used sampling to redundancy techniques. We administered an Internet version of the questionnaire on a Web site, as well as a paper version, which looked similar to the Internet version and which had identical content. Only those in our sample could access the Web site. We alternately assigned the participants to receive the survey by mail (n=221) or an email invitation to participate on the Internet (n=221). Non-respondents in the mail arm received up to three additional copies of the survey, while non-respondents in the Internet arm received up to three additional requests, including a final mailed copy. All participants in the Internet arm had an opportunity to request an emailed Portable Document Format (PDF) version. RESULTS The Internet arm demonstrated a lower response rate (99/221, 45%) than the mail questionnaire arm (129/221, 58%) (absolute difference 13%, 95% confidence interval 4%-22%, P<0.01). CONCLUSIONS. Our Internet-based survey to surgeons resulted in a significantly lower response rate than a traditional mailed survey. Researchers should not assume that the widespread availability and potential ease of Internet-based surveys will translate into higher response rates.Department of Surgery, McMaster University, Hamilton, Ontario, Canad

Upscaling diffusion through first-order volumetric sinks: a homogenization of bacterial nutrient uptake

In mathematical models that include nutrient delivery to bacteria, it is prohibitively expensive to include a pointwise nutrient uptake within small bacterial regions over bioreactor length-scales, and so such models often impose an effective uptake instead. In this paper, we systematically investigate how the effective uptake should scale with bacterial size and other microscale properties under first-order uptake kinetics. We homogenize the unsteady problem of nutrient diffusing through a locally periodic array of spherical bacteria, within which it is absorbed. We introduce a general model that could also be applied to other single-cell microorganisms, such as cyanobacteria, microalgae, protozoa, and yeast and we consider generalizations to arbitrary bacterial shapes, including some analytic results for ellipsoidal bacteria. We explore in detail the three distinguished limits of the system on the timescale of diffusion over the macroscale. When the bacterial size is of the same order as the distance between them, the effective uptake has two limiting behaviours, scaling with the bacterial volume for weak uptake and with the bacterial surface area for strong uptake. We derive the function that smoothly transitions between these two behaviours as the system parameters vary. Additionally, we explore the distinguished limit in which bacteria are much smaller than the distance between them and have a very strong uptake. In this limit, we find that the effective uptake is bounded above as the uptake rate grows without bound; we are able to quantify this and characterise the transition to the other limits we consider