The influence of oscillations on energy estimates for damped wave models with time-dependent propagation speed and dissipation

The aim of this paper is to derive higher order energy estimates for solutions to the Cauchy problem for damped wave models with time-dependent propagation speed and dissipation. The model of interest is \begin{equation*} u_{tt}-\lambda^2(t)\omega^2(t)\Delta u +\rho(t)\omega(t)u_t=0, \quad u(0,x)=u_0(x), \,\, u_t(0,x)=u_1(x). \end{equation*} The coefficients $\lambda=\lambda(t)$ and $\rho=\rho(t)$ are shape functions and $\omega=\omega(t)$ is an oscillating function. If $\omega(t)\equiv1$ and $\rho(t)u_t$ is an "effective" dissipation term, then $L^2-L^2$ energy estimates are proved in [2]. In contrast, the main goal of the present paper is to generalize the previous results to coefficients including an oscillating function in the time-dependent coefficients. We will explain how the interplay between the shape functions and oscillating behavior of the coefficient will influence energy estimates.Comment: 37 pages, 2 figure

INFLUENCE OF APPLE CULTIVAR, TREE PHENOLOGY, AND LEAF QUALITY ON THE DEVELOPMENT AND MORTALITY OF CHORISTONEURA ROSACEANA (LEPIDOPTERA: TORTRICIDAE)

The obliquebanded leafroller, Choristoneura rosaceana (Harris), is a polyphagous insect that is occasionally a serious pest of apple trees. To determine how well adapted it is to this host plant, we studied its nutritional ecology by measuring the development and mortality of larvae and pupae reared on different sets of leaves. We investigated the influence of 3 apple cultivars, 2 time periods (June, July-August), and several leaf types, including those with different ages and different branch positions, on these processes. Larvae and pupae developed more rapidly with lower mortality on younger leaves than on older ones. When larvae were fed leaves collected from the same cultivar and branch position at different times during the season, developmental rates were faster and survival rates were higher earlier in the season. Development and survival were similar on leaves of all cultivar

Edge Effects in the Directionally Biased Distribution of Choristoneura rosaceana (Lepidoptera: Tortricidae) in Apple Orchards

Edge effect tests have been used in a number of studies on obliquebanded leafroller, Choristoneura rosaceana (Harris), to test for evidence of mated female immigration into pheromone-treated orchards. This type of test compares obliquebanded leafroller presence or activity around the perimeter of an orchard against presence or activity in the interior. Higher numbers detected around the edges of an orchard would indicate higher levels of flight activity at the edge, a pattern that could be generated by high levels of immigration. Recent work has shown that the spatial distribution of recaptured obliquebanded leafroller adults released from a single location can be directionally biased, which could obscure the ability to detect an edge effect. To test this theory, data from an orchard study conducted in 1991 that found no significant edge effect was reanalyzed. When we accounted for the directional bias in the distribution of first-generation mated female moths, we found an edge effect with significantly more mated females captured in the edge traps than in the center or mid-interior traps. No edge effect was found when the directional bias was ignored. In addition, second-generation males and mated females both showed a significant edge effect that had not been detected in the original analysis, which had combined both first- and second-generation dat

Development and Evaluation of a Control Decision Rule for First-Generation Spotted Tentiform Leafminer (Lepidoptera: Gracillariidae) in New York Apple Orchards

A pest control decision rule consisting of an action threshold and a sampling protocol was developed and evaluated for first-generation spotted tentiform leafminer, Phyllonorycter blancardella (F.). An action threshold of two eggs per leaf was chosen based on the criterion of preventing more than one first-generation mine per leaf. Two sequential classification sampling plans for first-generation eggs were developed, one based on variable intensity sampling and the other on the use of confidence intervals for stop limits. Both plans made use of the nested variance structure of leafminer egg counts and variance-mean models fit to estimated variance components. Performance of the two sequential procedures was studied using simulation and judged to be very similar. Use of either sampling plan required approximately 10-20 min. Over a 4-yr period, 87% of sampled orchards in western New York had leafminer populations that were below the threshold of two eggs per leaf. During this period, use of sample information to schedule insecticide treatments resulted in only one instance when a treatment may have been required and was not called for (n = 79). Widespread use of the decision rule would result in significant reductions in pesticide use with no attendant increase in risk to grower

Lazy Abstraction-Based Controller Synthesis

We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster

Simulation-based reachability analysis for nonlinear systems using componentwise contraction properties

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of trajectories of the system and next establish bounds on the convergence or divergence between the samples and neighboring trajectories. We compute these bounds using contraction theory and reduce the conservatism by partitioning the state vector into several components and analyzing contraction properties separately in each direction. Among other benefits this allows us to analyze the effect of constant but uncertain parameters by treating them as state variables and partitioning them into a separate direction. We next present a numerical procedure to search for weighted norms that yield a prescribed contraction rate, which can be incorporated in the reachability algorithm to adjust the weights to minimize the growth of the reachable set

Interference with the Mate-Finding Communication System of the Obliquebanded Leafroller (Lepidoptera: Tortricidae) Using Synthetic Sex Pheromones

Effect of atmospheric permeation with synthetic sex pheromone on the behavior and control of obliquebanded leafroller, Choristoneura rosaceana (Harris), was studied in small and large plots in commercial apple orchards. Synthetic sex pheromone significantly reduced the ability of male moths to locate pheromone-baited traps and tethered females; however, no differences were found among 3 pheromone rates. Location of pheromone dispensers within the tree canopy did not alter the number of males locating pheromone-baited traps and mating tethered females. Obliquebanded leafroller activity was greatest in the upper positions of the tree canopy and no edge effect was observed around perimeters of large disrupted blocks. The presence of gravid feral females, mated tethered females, high larval densities, and fruit damage within large pheromone disrupted blocks indicate obliqubanded leafrollers mate in orchards treated with synthetic sex pheromone. However, fruit damage caused by obliquebanded leafroller larvae was similar in pheromone, pheromone plus insecticide, and insecticide treatment

Thermo-elasticity for anisotropic media in higher dimensions

In this note we develop tools to study the Cauchy problem for the system of thermo-elasticity in higher dimensions. The theory is developed for general homogeneous anisotropic media under non-degeneracy conditions. For degenerate cases a method of treatment is sketched and for the cases of cubic media and hexagonal media detailed studies are provided.Comment: 33 pages, 5 figure

Global generalized solutions for Maxwell-alpha and Euler-alpha equations

We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. We also discuss the idea of dissipative solution in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit

Energy drink use, problem drinking and drinking motives in a diverse sample of Alaskan college students

Background. Recent research has identified the use of caffeinated energy drinks as a common, potentially risky behaviour among college students that is linked to alcohol misuse and consequences. Research also suggests that energy drink consumption is related to other risky behaviours such as tobacco use, marijuana use and risky sexual activity. Objective. This research sought to examine the associations between frequency of energy drink consumption and problematic alcohol use, alcohol-related consequences, symptoms of alcohol dependence and drinking motives in an ethnically diverse sample of college students in Alaska. We also sought to examine whether ethnic group moderated these associations in the present sample of White, Alaska Native/American Indian and other ethnic minority college students. Design. A paper-and-pencil self-report questionnaire was completed by a sample of 298 college students. Analysis of covariance (ANCOVA) was used to examine the effects of energy drink use, ethnic group and energy drink by ethnic group interactions on alcohol outcomes after controlling for variance attributed to gender, age and frequency of binge drinking. Results. Greater energy drink consumption was significantly associated with greater hazardous drinking, alcohol consequences, alcohol dependence symptoms, drinking for enhancement motives and drinking to cope. There were no main effects of ethnic group, and there were no significant energy drink by ethnic group interactions. Conclusion. These findings replicate those of other studies examining the associations between energy drink use and alcohol problems, but contrary to previous research we did not find ethnic minority status to be protective. It is possible that energy drink consumption may serve as a marker for other health risk behaviours among students of various ethnic groups