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

Blow-up of the energy at infinity for 2 by 2 systems

AbstractThe goal of this paper is to study the long time behavior of the energy of solutions to 2 by 2 linear hyperbolic systems. Some blow-up results at t=∞ are given for a large class of initial data of the Cauchy problem. We shall prove the optimality of these results for a special class of systems. We present also an example of generalized energy conservation under a Cm stabilization condition

Rate-determining process in MISIM photocells for optoelectronic conversion using photo-induced pure polarization current without carrier transfer across interfaces

Recently, we proposed a [metal|insulator|semiconductor|insulator|metal] (MISIM) photocell, as a novel architecture for high-speed organic photodetectors. The electric polarization in the S layer, induced by modulated light illumination, propagates into the outside circuit as a polarization current through the I layers, without any carrier transfer across the interfaces. In the present work, we examined the MISIM photocells consisting of zinc-phthalocyanine(ZnPc)-C60 bilayers for the S layer and Parylene C for the two I layers, to understand the fundamental aspects of the MISIM photocells, such as current polarity and modulation-frequency dependence. It was found that, in such devices, the current polarity was primarily determined by the polarization in the S layer, which was induced by the donor–acceptor charge-transfer upon illumination. Furthermore, the ON and OFF current, which appeared in the periods of illumination-on and -off, respectively, exhibited significantly different dependence on the modulation frequency. This was well-explained by an imbalance between a quick polarization in the S layer during illumination and its slow relaxation in the dark

Numerical analysis of the light modulation by the frustule of Gomphonema parvulum : the role of integrated optical components

Siliceous diatom frustules present a huge variety of shapes and nanometric pore patterns. A better understanding of the light modulation by these frustules is required to determine whether or not they might have photobiological roles besides their possible utilization as building blocks in photonic applications. In this study, we propose a novel approach for analyzing the near-field light modulation by small pennate diatom frustules, utilizing the frustule of Gomphonema parvulum as a model. Numerical analysis was carried out for the wave propagation across selected 2D cross-sections in a statistically representative 3D model for the valve based on the finite element frequency domain method. The influences of light wavelength (vacuum wavelengths from 300 to 800 nm) and refractive index changes, as well as structural parameters, on the light modulation were investigated and compared to theoretical predictions when possible. The results showed complex interference patterns resulting from the overlay of different optical phenomena, which can be explained by the presence of a few integrated optical components in the valve. Moreover, studies on the complete frustule in an aqueous medium allow the discussion of its possible photobiological relevance. Furthermore, our results may enable the simple screening of unstudied pennate frustules for photonic applications

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

Perturbation theorems for Hele-Shaw flows and their applications

In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions with initial functions close to but are not polynomial. Applications of this theorem are given in the suction or injection case. In the former case, we show that if the initial domain is close to a disk, most of fluid will be sucked before the strong solution blows up. In the later case, we obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows in terms of invariant Richardson complex moments. This rescaling behavior result generalizes a recent result regarding large-time rescaling behavior for small data in terms of moments. As a byproduct of a theorem in this paper, a short proof of existence and uniqueness of strong solutions to the Polubarinova-Galin equation is given.Comment: 25 page

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

Hele-Shaw flows with nonlinear kinetic undercooling regularization

The Hele-Shaw flows with nonlinear kinetic undercooling regularization were discussed. The velocity vector field v ≡ (vx, vy)of a two-dimensional flow driven by a single sink at the origin with continuous intensity q0 = q0(t) was found. The nonlinear system of equations for the coefficients h̃n was reported

Trap Response and Fruit Damage by Obliquebanded Leafroller (Lepidoptera: Tortricidae) in Pheromone-Treated Apple Orchards in New York

Pheromone disruptants were tested from 1989 to 1992 in western New York to determine effect on trap catch and potential use in the control of obliquebanded leafroller. Choristoneura rosaceana (Harris), using polyethylene tube tie and controlled-release membrane dispensers in plots of 0.2-2.4 ha. Effectiveness of pheromone at different application rates and canopy locations was evaluated using synthetic pheromone-baited traps, molassesbaited traps, and by inspecting foliar terminals and fruit for leafroller damage. All pheromone treatments significantly reduced (by 56-97%) pheromone trap catches of male moths compared with catches in nontreated blocks. One application of a natural-blend formulation at 988 dispensers per hectare was better than 494/ha at disrupting trap catch of both Rights that occur during the year. However, mated female moths were present in the orchard center as frequently as anywhere else in a pheromone-treated block, indicating either immigration from outside sources or resident females that were not prevented from mating by the pheromone. The membrane dispenser emitted the 3-component natural blend at proportions similar to those in wild female moths. Pheromone traps placed in the tops of trees in a pheromone-treated orchard always caught higher numbers of male moths than those in lower- or middle-canopy positions. Pheromone treatment resulted in fruit damage similar to that of a pheromone + insecticide treatment under low to moderate leafroller population pressure (i.e., 3-5% fruit damage in untreated orchards); however, no control method was able to reduce damage to acceptable levels in all case