On the discrete spectrum of quantum layers

Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not totally geodesic. This geometric setting is known as a quantum layer. We consider the quantum particle to be governed by the Dirichlet Laplacian as Hamiltonian. Our work concerns the existence of bound states with energy beneath the essential spectrum, which implies the existence of discrete spectrum. We first prove that if the Gauss curvature is integrable, and the surface is weakly $\kappa$-parabolic, then the discrete spectrum is non-empty. This result implies that if the total Gauss curvature is non-positive, then the discrete spectrum is non-empty. We next prove that if the Gauss curvature is non-negative, then the discrete spectrum is non-empty. Finally, we prove that if the surface is parabolic, then the discrete spectrum is non-empty if the layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from previous version is proven here (Theorem 1.5), additional references include

Vesicle shape, molecular tilt, and the suppression of necks

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of $+2$ are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.Comment: 10 pages, 7 figures, submitted to Phy. Rew.

Dynamics of filaments and membranes in a viscous fluid

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for calculating internal stresses and forces, and we derive the full nonlinear equations of motion. In the case of membranes, we pay particular attention to the formulation of the equations of hydrodynamics on a curved, deforming surface. The formalism is illustrated by two simple case studies: (1) the twirling instability of straight elastic rod rotating in a viscous fluid, and (2) the pearling and buckling instabilities of a tubular liposome or polymersome.Comment: 26 pages, 12 figures, to be published in Reviews of Modern Physic

Grass-finished Beef Pilot Project: Cattle Performance

Consumer interest in the potential benefits of grass-finished beef is high, but adoption of this approach to cattle feeding has been limited in Iowa. Although some producers successfully meet this niche market demand, consistently producing a high-value carcass from forage-fed cattle is challenging. Intramuscular fat or marbling is a major factor in quality grading of beef. Marbling is heavily influenced by cattle genetics and energy concentration of the diet. Finishing cattle on grain is a proven approach to consistently produce a high-value carcass for the commodity beef market. Researchers at Iowa State University have pioneered the use of ultrasound measurements to select Angus cattle with high-marbling potential. Forage quality can be manipulated through pasture management, ultimately influencing cattle growth and performance. It is hypothesized that grass-finished cattle will consistently produce high value carcasses if excellent pasture management is combined with combining high-marbling genetics

Towards a sensitive search for variation of the fine structure constant using radio-frequency E1 transitions in atomic dysprosium

It has been proposed that the radio-frequency electric-dipole (E1) transition between two nearly degenerate opposite-parity states in atomic dysprosium should be highly sensitive to possible temporal variation of the fine structure constant ($\alpha$) [V. A. Dzuba, V. V. Flambaum, and J. K. Webb, Phys. Rev. A {\bf 59}, 230 (1999)]. We analyze here an experimental realization of the proposed search in progress in our laboratory, which involves monitoring the E1 transition frequency over a period of time using direct frequency counting techniques. We estimate that a statistical sensitivity of |\adota| \sim 10^{-18}/yr may be achieved and discuss possible systematic effects that may limit such a measurement.Comment: 8 pages, 7 figure

Pain Management in the Neonatal Piglet During Routine Management Procedures. Part 1: A Systematic Review of Randomized and Non-Randomized Intervention Studies

Routine procedures carried out on piglets (i.e. castration, tail docking, teeth clipping, and ear notching) are considered painful. Unfortunately the efficacy of current pain mitigation modalities is poorly understood. The aim of this systematic review was to synthesize the existing primary scientific literature regarding the effectiveness of pain management interventions used for routine procedures on piglets. The review question was, \u27In piglets under twenty-eight days old, undergoing castration, tail docking, teeth clipping, and/or methods of identification that involve cutting of the ear tissue, what is the effect of pain mitigation compared with no pain mitigation on behavioral and non-behavioral outcomes that indicate procedural pain and post-procedural pain?\u27 A review protocol was designed a priori. Data sources used were Agricola (EBSCO), CAB Abstracts (Thomson Reuters), PubMed, Web of Science (Thomson Reuters), BIOSIS Previews (Thomson Reuters), and ProQuest Dissertations & Theses Full Text. No restrictions on year of publication or language were placed on the search. Eligible studies assessed an intervention designed to mitigate the pain of the procedures of interest and included a comparison group that did not receive an intervention. Eligible non-English studies were translated using a translation service. Two reviewers independently screened titles and abstracts for relevance using pre-defined questions. Data were extracted from relevant articles onto pre-defined forms. From the 2203 retrieved citations forty publications, containing 52 studies met the eligibility criteria. In 40 studies, piglets underwent castration only. In seven studies, piglets underwent tail docking only. In one study, piglets underwent teeth clipping only, and in one study piglets underwent ear notching only. Three studies used multiple procedures. Thirty-two trial arms assessed general anesthesia protocols, 30 trial arms assessed local anesthetic protocols, and 28 trial arms assessed non-steroidal anti-inflammatory drugs (NSAIDs) protocols. Forty-one trial arms were controls where piglets received either placebo or no treatment. Forty-five outcomes were extracted from the studies, however only the results from studies that assessed cortisol (six studies), β-endorphins (one study), vocalisations (nine studies), and pain-related behaviors (nine studies) are reported. Other outcomes were reported in only one or two studies. Confident decision making will likely be difficult based on this body of work because lack of comprehensive reporting precludes calculation of the magnitude of pain mitigation for most outcomes

Pain management in the neonatal piglet during routine management procedures. Part 2:Grading the quality of evidence and the strength of recommendations

Piglets reared in swine production in the USA undergo painful procedures that include castration, tail docking, teeth clipping, and identification with ear notching or tagging. These procedures are usually performed without pain mitigation. The objective of this project was to develop recommendations for pain mitigation in 1- to 28-day-old piglets undergoing these procedures. The National Pork Board funded project to develop recommendations for pain mitigation in piglets. Recommendation development followed a defined multi-step process that included an evidence summary and estimates of the efficacies of interventions. The results of a systematic review of the interventions were reported in a companion paper. This manuscript describes the recommendation development process and the final recommendations. Recommendations were developed for three interventions (CO2/O2 general anesthesia, non-steroidal anti-inflammatory drugs (NSAIDs), and lidocaine) for use during castration. The ability to make strong recommendations was limited by low-quality evidence and strong certainty about variation in stakeholder values and preferences. The panel strongly recommended against the use of a CO2/O2 general anesthesia mixture, weakly recommended for the use of NSAIDs and weakly recommended against the use of lidocaine for pain mitigation during castration of 1- to 28-day-old piglets

The compensation of Gaussian curvature in developable cones is local

In this paper we use the angular deficit scheme [V. Borrelli, F. Cazals, and J.-M. Morvan, {\sl Computer Aided Geometric Design} {\bf 20}, 319 (2003)] to determine the distribution of Gaussian curvature in developable cones (d-cones) [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, {\sl Nature} {\bf 401}, 46 (1999)] numerically. These d-cones are formed by pushing a thin elastic sheet into a circular container. Negative Gaussian curvatures are identified at the rim where the sheet touches the container. Around the rim there are two narrow bands with positive Gaussian curvatures. The integral of the (negative) Gaussian curvature near the rim is almost completely compensated by that of the two adjacent bands. This suggests that the Gauss-Bonnet theorem which constrains the integral of Gaussian curvature globally does not explain the spontaneous curvature cancellation phenomenon [T. Liang and T. A. Witten, {\sl Phys. Rev. E} {\bf 73}, 046604 (2006)]. The locality of the compensation seems to increase for decreasing d-cone thickness. The angular deficit scheme also provides a new way to confirm the curvature cancellation phenomenon.Comment: 12 pages; 5 figure