Numerical mountain pass periodic solutions of a nonlinear spring equation

AbstractIn this paper, we show how the introduction of a nonlinear term in the classic spring model can produce dramatic results. We compute a large amplitude solution which is drastically different from the known linear, small amplitude solution. A dual variational formulation is given, recasting the problem as one in which saddle points correspond to solutions of the differential equation. Our computations are based on the numerical mountain pass algorithm developed by Choi and McKenna which was inspired by the theorems of Ambrosetti, Rabinowitz and Ekeland

High-mass-resolution MALDI mass spectrometry imaging reveals detailed spatial distribution of metabolites and lipids in roots of barley seedlings in response to salinity stress

Introduction Mass spectrometry imaging (MSI) is a technology that enables the visualization of the spatial distribution of hundreds to thousands of metabolites in the same tissue section simultaneously. Roots are below-ground plant organs that anchor plants to the soil, take up water and nutrients, and sense and respond to external stresses. Physiological responses to salinity are multifaceted and have predominantly been studied using whole plant tissues that cannot resolve plant salinity responses spatially. Objectives This study aimed to use a comprehensive approach to study the spatial distribution and profiles of metabolites, and to quantify the changes in the elemental content in young developing barley seminal roots before and after salinity stress. Methods Here, we used a combination of liquid chromatography–mass spectrometry (LC–MS), inductively coupled plasma mass spectrometry (ICP–MS), and matrix-assisted laser desorption/ionization (MALDI–MSI) platforms to profile and analyze the spatial distribution of ions, metabolites and lipids across three anatomically different barley root zones before and after a short-term salinity stress (150 mM NaCl). Results We localized, visualized and discriminated compounds in fine detail along longitudinal root sections and compared ion, metabolite, and lipid composition before and after salt stress. Large changes in the phosphatidylcholine (PC) profiles were observed as a response to salt stress with PC 34:n showing an overall reduction in salt treated roots. ICP–MS analysis quantified changes in the elemental content of roots with increases of Na+ and decreases of K+ content. Conclusion Our results established the suitability of combining three mass spectrometry platforms to analyze and map ionic and metabolic responses to salinity stress in plant roots and to elucidate tolerance mechanisms in response to abiotic stress, such as salinity stress

Safety of older people on stairs : behavioural factors

Falling on steps and stairs in the home is a serious problem for older people aged 65 and over, both in terms of the high frequency with which these accidents occur and their consequences. Although previous research has increased knowledge of personal and environmental factors involved in falls on stairs, behavioural aspects have received less attention. The aini of this investigation, therefore, was to improve understanding of how older people keep and use their stairs, and to assess the iniplications for stair safety. Interviews were conducted with 157 older people, aged between 65-96 years, in their own homes. Using a conibination of open and closed questions, participants were asked about their behaviour on and around thc stairs, awareness of safety factors and any history of falling on stairs. During each visit, information was collected about the stairs in the home including design and repair of stair coverings, number of handrails and thcir condition, objects on and around the stairs, lighting, and position of windows. Standard mthropometric dimensions of interviewees were recorded, along with other measurements including grip strength, ability to get up from a stool without using hands, and measures of visual acuity and depth perception

On slip pulses at a sheared frictional viscoelastic/ non deformable interface

We study the possibility for a semi-infinite block of linear viscoelastic material, in homogeneous frictional contact with a non-deformable one, to slide under shear via a periodic set of ``self-healing pulses'', i.e. a set of drifting slip regions separated by stick ones. We show that, contrary to existing experimental indications, such a mode of frictional sliding is impossible for an interface obeying a simple local Coulomb law of solid friction. We then discuss possible physical improvements of the friction model which might open the possibility of such dynamics, among which slip weakening of the friction coefficient, and stress the interest of developing systematic experimental investigations of this question.Comment: 23 pages, 3 figures. submitted to PR

Vortex Rings in two Component Bose-Einstein Condensates

We study the structure of the vortex core in two-component Bose-Einstein condensates. We demonstrate that the order parameter may not vanish and the symmetry may not be restored in the core of the vortex. In this case such vortices can form vortex rings known as vortons in particle physics literature. In contrast with well-studied superfluid $^4He$, where similar vortex rings can be stable due to Magnus force only if they move, the vortex rings in two-component BECs can be stable even if they are at rest. This beautiful effect was first discussed by Witten in the cosmic string context, where it was shown that the stabilization occurs due to condensation of the second component of the field in the vortex core. This second condensate trapped in the core may carry a current along the vortex ring counteracting the effect of string tension that causes the loop to shrink. We speculate that such vortons may have been already observed in the laboratory. We also speculate that the experimental study of topological structures in BECs can provide a unique opportunity to study cosmology and astrophysics by doing laboratory experiments.Comment: 21 pages, 2 figure

Monitoring the Indigenous heritage within the Reef 2050 Integrated Monitoring and Reporting Program: final report of the Indigenous Heritage Expert Group

An accessible copy of this report is not yet available from this repository, please contact [email protected] for more information

Designing a suite of measurements to understand the critical zone

Many scientists have begun to refer to the earth surface environment from the upper canopy to the depths of bedrock as the critical zone (CZ). Identification of the CZ as an integral object worthy of study implicitly posits that the study of the whole earth surface will provide benefits that do not arise when studying the individual parts. To study the CZ, however, requires prioritizing among the measurements that can be made – and we do not generally agree on the priorities. Currently, the Susquehanna Shale Hills Critical Zone Observatory (SSHCZO) is expanding from a small original focus area (0.08 km2 , Shale Hills catchment), to a larger watershed (164 km2 , Shavers Creek watershed) and is grappling with the prioritization. This effort is an expansion from a monolithologic first-order forested catchment to a watershed that encompasses several lithologies (shale, sandstone, limestone) and land use types (forest, agriculture). The goal of the project remains the same: to understand water, energy, gas, solute, and sediment (WEGSS) fluxes that are occurring today in the context of the record of those fluxes over geologic time as recorded in soil profiles, the sedimentary record, and landscape morphology. Given the small size of the Shale Hills catchment, the original design incorporated measurement of as many parameters as possible at high temporal and spatial density. In the larger Shavers Creek watershed, however, we must focus the measurements. We describe a strategy of data collection and modeling based on a geomorphological and land use framework that builds on the hillslope as the basic unit. Interpolation and extrapolation beyond specific sites relies on geophysical surveying, remote sensing, geomorphic analysis, the study of natural integrators such as streams, groundwaters or air, and application of a suite of CZ models. We hypothesize that measurements of a few important variables at strategic locations within a geomorphological framework will allow development of predictive models of CZ behavior. In turn, the measurements and models will reveal how the larger watershed will respond to perturbations both now and into the future

Two-body Z′Z' decays in the minimal 331 model

The two-body decays of the extra neutral boson Z_2 predicted by the minimal 331 model are analyzed. At the three-level it can decay into standard model particles as well as exotic quarks and the new gauge bosons predicted by the model. The decays into a lepton pair are strongly suppressed, with $Br(Z_2 --> l^+l^-) ~ 10^{-2}$ and $Br(Z_2 --> \bar{\nu}_l \nu) ~ 10^{-3}$. In the bosonic sector, Z_2 would decay mainly into a pair of bilepton gauge bosons, with a branching ratio below the 0.1 level. The Z_2 boson has thus a leptophobic and bileptophobic nature and it would decay dominantly into quark pairs. The anomaly-induced decays $Z_2 --> Z_1\gamma$ and $Z_2 --> Z_1Z_1$, which occurs at the one-loop level are studied. It is found that $Br(Z_2 --> Z_1\gamma) ~ 10^{-9}$ and $Br(Z_2 --> Z_1Z_1) ~ 10^{-6}$ at most. As for the $Z_2 --> W^+W^-$ and $Z_2 --> Z_1H$ decays, with H a relatively light Higgs boson, they are induced via Z'-Z mixing. It is obtained that $Br(Z_2 --> W^+W^-) ~ 10^{-2}$ and $Br (Z_2 --> Z_1H) ~ 10^{-5}$. We also examine the flavor changing neutral current decays $Z_2 --> tc$ and $Z_2 --> tu$, which may have branching fractions as large as $10^{-3}$ and $10^{-5}$, respectively, and thus may be of phenomenological interest.Comment: 14 pages, 3 figures, submitted to Physical Review