Point configurations that are asymmetric yet balanced

A configuration of particles confined to a sphere is balanced if it is in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every sufficiently symmetrical configuration is balanced, but the converse is far from obvious. In 1957 Leech completely classified the balanced configurations in R^3, and his classification is equivalent to the converse for R^3. In this paper we disprove the converse in high dimensions. We construct several counterexamples, including one with trivial symmetry group.Comment: 10 page

The Power of Poincar\'e: Elucidating the Hidden Symmetries in Focal Conic Domains

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincar\'e symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures and tilt-grain boundaries.Comment: 4 pages, 3 included figure

Validity and Reliability of the Wahoo KICKR Cycle Ergometer

Cycle ergometers (CE) allow for the measurement of work and power during exercise. The Wahoo KICKR is an electronically-braked CE commonly used by coaches and athletes for exercise testing and training. PURPOSE: The purpose of this study was to determine the validity and reliability of the Wahoo KICKR CE for the measurement of power. METHODS: 12 recreationally active college students completed 3 separate workout sessions with 2 sessions on the Wahoo CE and 1 session on a mechanically-braked Monark CE. The order of sessions was randomized and counter-balanced. Seat height, handlebar height, and handlebar reach were also matched across trials. During the exercise sessions oxygen consumption (VO2) and heart rate (HR) were continuously measured. Following a 10-minute warmup, subjects completed an incremental exercise test consisting of 4, 5-minute stages starting at a work rate of 50 watts (W) and increasing by 50 W with each stage up to 200 W. Cadence was held at 71.5 revolutions per minute for all stages and trials. Validity was assessed by a dependent sample T-test comparing the first Wahoo session to the Monark trial. Reliability was assessed by a dependent sample T-test comparing the two Wahoo trials. RESULTS: HR and VO2 data across all trials and stages are displayed in the table. Both VO2 and HR were slightly lower when comparing the Wahoo to the Monark, but VO2 and HR were consistent when comparing the two Wahoo trials. CONCLUSION: This study showed that the Wahoo KICKR may slightly overestimate the work rate, particularly at higher workloads, but it is a consistent and reliable device. Based on these findings, coaches and athletes can have confidence incorporating the Wahoo CE into training programs and fitness testing. 50 W (n=12) 100 W (n=12) 150 W (n=12) 200 W (n=7) VO2 HR VO2 HR VO2 HR VO2 HR Wahoo 1 12.3 ± 1.4 101 ± 17 17.6 ± 2.3 118 ± 17 24.6 ± 3.5 145 ± 18 34.2 ± 5.2 160 ± 11 Monark 13.7 ± 1.6 102 ± 14 19.5 ± 2.0 122.8 ± 18 27.1 ± 3.4 152 ± 20 38.1 ± 6.9 167 ± 14 Wahoo 2 12.3 ± 1.5 98 ± 9 17.6 ± 2.6 118 ± 11 24.3 ± 3.4 144 ± 12 34.5 ± 4.6 161 ± 10 Validity P-value 0.004* 0.605 \u3c0.001* 0.009* \u3c0.001* 0.028* 0.011* 0.140 Reliability P-value 0.886 0.848 0.990 0.131 0.434 0.317 0.472 0.886 *p \u3c 0.05 All values represent mean ± S

Minimal resonances in annular non-Euclidean strips

Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of "conical" closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. Within this class of strips, we derive a condition under which a strip can have vanishing mean curvature along the center line.Comment: 14 pages, 13 figures. Published version. Updated references and added 2 figure

Response to pulmonary arterial hypertension drug therapies in patients with pulmonary arterial hypertension and cardiovascular risk factors.

The age at diagnosis of pulmonary arterial hypertension (PAH) and the prevalence of cardiovascular (CV) risk factors are increasing. We sought to determine whether the response to drug therapy was influenced by CV risk factors in PAH patients. We studied consecutive incident PAH patients (n = 146) between January 1, 2008, and July 15, 2011. Patients were divided into two groups: the PAH-No CV group included patients with no CV risk factors (obesity, systemic hypertension, type 2 diabetes mellitus, permanent atrial fibrillation, mitral and/or aortic valve disease, and coronary artery disease), and the PAH-CV group included patients with at least one. The response to PAH treatment was analyzed in all the patients who received PAH drug therapy. The PAH-No CV group included 43 patients, and the PAH-CV group included 69 patients. Patients in the PAH-No CV group were younger than those in the PAH-CV group (P < 0.0001). In the PAH-No CV group, 16 patients (37%) improved on treatment and 27 (63%) did not improve, compared with 11 (16%) and 58 (84%) in the PAH-CV group, respectively (P = 0.027 after adjustment for age). There was no difference in survival at 30 months (P = 0.218). In conclusion, in addition to older age, CV risk factors may predict a reduced response to PAH drug therapy in patients with PAH

Intermediate Wakimoto modules for Affine sl(n+1)

We construct certain boson type realizations of affine sl(n+1) that depend on a parameter r. When r=0 we get a Fock space realization of Imaginary Verma modules appearing in the work of the first author and when r=n they are the Wakimoto modules described in the work of Feigin and Frenkel

Colloquium : disclination loops, point defects, and all that in nematic liquid crystals

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet

Toxicity and Environmental Health Hazards of Petroleum Products in Wells Used for Drinking Water in the Intermountain West

Introduction: Groundwater is aprimary source of drinking water for about 50 percent of the population in the U.S. This source of drinking water has been generally regarded as safe from contamination. Several papers indicate that numerous underground storage tanks containing petroleum products may be leaking and contaminating public water supply wells across the U.S. (Matis, 1971; Ferguson, 1979; Woodhull, 1981; Burmaster and Harris, 1982; Lehman, 1984; Dowd, 1984; OTA, 1984). A study conducted by the Utah Cureau of Solid and Hazardous Wastes in 1985 concluded that there are at least 2,314 underground steel tanks, most of which are used to store gasoline and diesel fuel, in Utah which are more than 20 years old and may be leaking. Contamination of well water by petrolium products from leaking underground storage tanks (LUST) is a matter of increasing concern. LUST pose a serious threat to the groundwater and public health. Leaks of petroleum products from LUST at industrial plants, commercial establishments (e.g., automobile service stations), and other operations could be expected to increase the types and concentrations of petroleum products in groundwater used for drinking and exposure of humans to the toxic effects of these chemical compounds. Petroleum products are persistent and highly mobile contaminatns which are difficult to remove from groundwater. In addition, many of these chemicals are known or suspected carcinogens or mutagens which can pose undesireable human health risks (e.g., cancer, birth defects, and other chronic conditions) at 10 ppb and below (Council on Environmental Quality, 1980). There is a need for more research on the types and concentrations of petroleum products (e.g., benzene, toluene, ethylbenzene) found in public water supply wells used for drinking water and the immunotoxic and neurotoxic effects of these organic compounds. The objectives of this research project were: 1. To characterize petroleum products in raw water from wells used for drinking water in selected areas (industrial, commercial, and other) of Utah. 2. To evaluate the toxicity of selected petroleum products in experimental animals, with emphasis on the following: a. Immunotoxic and hypersensitivity effects. b. Neurotoxic and behavioral effects

Impact of an Irreversibly Adsorbed Layer on Local Viscosity of Nanoconfined Polymer Melts

We report the origin of the effect of nanoscale confinement on the local viscosity of entangled polystyrene (PS) films at temperatures far above the glass transition temperature. By using marker x-ray photon correlation spectroscopy with gold nanoparticles embedded in the PS films prepared on solid substrates, we have determined the local viscosity as a function of the distance from the polymer-substrate interface. The results show the impact of a very thin adsorbed layer ( 7 nm in thickness) even without specific interactions of the polymer with the substrate, overcoming the effect of a surface mobile layer at the air-polymer interface and thereby resulting in a significant increase in the local viscosity as approaching the substrate interface.T. K. acknowledges the financial support from NSF Grant No. CMMI-084626. Uses of the Advanced Photon Source and the National Synchrotron Light Source were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contracts No. DE-AC02- 06CH11357 and No. DE-AC02-98CH10886, respectively