Boundedness and Stability of Impulsively Perturbed Systems in a Banach Space

Consider a linear impulsive equation in a Banach space $$\dot{x}(t)+A(t)x(t) = f(t), ~t \geq 0,$$ $$x(\tau_i +0)= B_i x(\tau_i -0) + \alpha_i,$$ with $\lim_{i \rightarrow \infty} \tau_i = \infty$. Suppose each solution of the corresponding semi-homogeneous equation $$\dot{x}(t)+A(t)x(t) = 0,$$ (2) is bounded for any bounded sequence $\{ \alpha_i \}$. The conditions are determined ensuring (a) the solution of the corresponding homogeneous equation has an exponential estimate; (b) each solution of (1),(2) is bounded on the half-line for any bounded $f$ and bounded sequence $\{ \alpha_i \}$ ; (c) $\lim_{t \rightarrow \infty}x(t)=0$ for any $f, \alpha_i$ tending to zero; (d) exponential estimate of $f$ implies a similar estimate for $x$.Comment: 19 pages, LaTex-fil

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

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

Effects of flow rate and gas mixture on the welfare of weaned and neonate pigs during gas euthanasia

The objectives of this study were to assess efficacy and welfare implications of gas euthanasia when applied to weaned and neonate pigs. Parameters associated with welfare, which were measured before loss of consciousness, included open-mouth breathing, ataxia, righting response, and escape attempts. Two age groups (weaned and neonate) were assessed in 9 gas treatments arranged in a 2 × 4 factorial design, with 2 gas types (CO2 = 100% CO2 and 50:50 = 50:50 CO2:argon) and 4 flow rates (box volume exchange/min: slow = 20%; medium = 35%; fast = 50%; prefill = prefilled followed by 20%) and a control treatment in which ambient air was passed through the box. Pig pairs (10/treatment) were placed in a modified Euthanex AgPro system (Euthanex Corp., Palmer, PA). Behavioral and physiological responses were observed directly and from video recordings for latency, duration, prevalence (percent of pigs affected), and frequency (number of occurrences/pig). Data were analyzed as linear mixed models or with a Cox proportional hazard model as appropriate. Piglet pair was the experimental unit. For the weaned pig, welfare was superior with CO2 relative to 50:50 within 1 or more flow rates on the basis of reduced duration of open-mouth breathing, duration of ataxia, frequency of escape attempts, and duration and frequency of righting response (P \u3c 0.05). No measured parameters indicated superior welfare with the use of 50:50, whereas latencies to loss of posture and last movement favored CO2 (P \u3c 0.05). Faster flow rates were associated with reduced (P \u3c 0.05) duration or frequency of open-mouth breathing, ataxia, and righting response, as well as superior (P\u3c 0.05) indicators of efficacy, including latencies to loss of posture, gasping, and last movement, relative to slower flow rates. Weaned pigs were more likely to defecate (P \u3c 0.01), display nasal discharge (P \u3c 0.05), and display longer (P \u3c 0.001) latencies to loss of posture and last movement than neonates. Duration of ataxia was the only parameter for which neonates were superior (P \u3c 0.01) to weaned pigs during euthanasia. As such, a 50:50 CO2:argon gas mixture and slower flow rates should be avoided when euthanizing weaned or neonate pigs with gas methods. Neonate pigs succumb to the effects of gas euthanasia quicker than weaned pigs and display fewer signs of distress

Nitrogen inputs and losses in response to chronic CO2 exposure in a subtropical oak woodland

Rising atmospheric CO2 concentrations may alter the nitrogen (N) content of ecosystems by changing N inputs and N losses, but responses vary in field experiments, possibly because multiple mechanisms are at play. We measured N fixation and N losses in a subtropical oak woodland exposed to 11 years of elevated atmospheric CO2 concentrations. We also explored the role of herbivory, carbon limitation, and competition for light or nutrients in shaping the response of N fixation to elevated CO2. Elevated CO2 did not significantly alter gaseous N losses, but lower recovery and deeper distribution in the soil of a long-term 15N tracer indicated that elevated CO2 increased leaching losses. Elevated CO2 had no effect on nonsymbiotic N fixation, and had a transient effect on symbiotic N fixation by the dominant legume. Elevated CO2 tended to reduce soil and plant concentrations of iron, molybdenum, phosphorus, and vanadium, nutrients essential for N fixation. Competition for nutrients and herbivory likely contributed to the declining response of N fixation to elevated CO2. These results indicate that positive responses of N fixation to elevated CO2 may be transient and that chronic exposure to elevated CO2 can increase N leaching. Models that assume increased fixation or reduced N losses with elevated CO2 may overestimate future N accumulation in the biosphere

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

Investigation into the cause of spontaneous emulsification of a free steel droplet : validation of the chemical exchange pathway

Small Fe-based droplets have been heated to a molten phase suspended within a slag medium to replicate a partial environment within the basic oxygen furnace (BOF). The confocal scanning laser microscope (CSLM) has been used as a heating platform to interrogate the effect of impurities and their transfer across the metal/slag interface, on the emulsification of the droplet into the slag medium. The samples were then examined through X-ray computer tomography (XCT) giving the mapping of emulsion dispersion in 3D space, calculating the changing of interfacial area between the two materials, and changes of material volume due to material transfer between metal and slag. Null experiments to rule out thermal gradients being the cause of emulsification have been conducted as well as replication of the previously reported study by Assis et al.[1] which has given insights into the mechanism of emulsification. Finally chemical analysis was conducted to discover the transfer of oxygen to be the cause of emulsification, leading to a new study of a system with undergoing oxygen equilibration

Novel sampling method for assessing human-pathogen interactions in the natural environment using boot socks and citizen scientists, with application to Campylobacter seasonality

This paper introduces a novel method for sampling pathogens in natural environments. It uses fabric boot socks worn over walkers' shoes to allow the collection of composite samples over large areas. Wide-area sampling is better suited to studies focusing on human exposure to pathogens (e.g., recreational walking). This sampling method is implemented using a citizen science approach: groups of three walkers wearing boot socks undertook one of six routes, 40 times over 16 months in the North West (NW) and East Anglian (EA) regions of England. To validate this methodology, we report the successful implementation of this citizen science approach, the observation that Campylobacter bacteria were detected on 47% of boot socks, and the observation that multiple boot socks from individual walks produced consistent results. The findings indicate higher Campylobacter levels in the livestock-dominated NW than in EA (55.8% versus 38.6%). Seasonal differences in the presence of Campylobacter bacteria were found between the regions, with indications of winter peaks in both regions but a spring peak in the NW. The presence of Campylobacter bacteria on boot socks was negatively associated with ambient temperature (P = 0.011) and positively associated with precipitation (P < 0.001), results consistent with our understanding of Campylobacter survival and the probability of material adhering to boot socks. Campylobacter jejuni was the predominant species found; Campylobacter coli was largely restricted to the livestock-dominated NW. Source attribution analysis indicated that the potential source of C. jejuni was predominantly sheep in the NW and wild birds in EA but did not differ between peak and nonpeak periods of human incidence