Exact Solutions of Covariant Wave Equations with a Multipole Source Term on Curved Spacetimes

A formalism is presented for calculating exactsolutions of covariant inhomogeneous scalar and tensorwave equations whose source terms are arbitrary ordermultipoles on a curved background spacetime. The developed formalism is based on the theory ofthe higher-order fundamental solutions for wave equationwhich are the distributions that satisfy theinhomogeneous wave equation with the corresponding order covariant derivatives of the Dirac deltafunction on the right-hand side. Like the classicalGreen's function for a scalar wave equation, thehigher-order fundamental solutions contain a direct termwhich has support on the light cone as well as a tailterm which has support inside the light cone. Knowinghow to compute the fundamental solutions of arbitraryorder, one can find exact multipole solutions of wave equations on curved spacetimes. Wepresent complete recurrent algorithms for calculatingthe arbitrary-order fundamental solutions and the exactmultipole solutions in a form convenient for practical computations. As an example we apply thealgorithm to a massless scalar wave field on aparticular Robertson-Walker spacetime.     

Constructive influence of noise-flatness in correlation ratchets

The influence of noise-flatness on overdamped motion of Brownian particles in a 1D periodic system with a simple sawtooth potential subjected to both unbiased thermal noise and three-level telegraph noise is considered. The exact formula for the stationary probability flux (current) is presented. The phenomenon of multiple current reversals and some topological properties of the hypersurface of zero current in the parameter space of noises are investigated and illustrated by phase diagrams. The conditions for the existence of four current reversals versus the switching rate of nonequilibrium noise are given. An alternative interpretation of the results in terms of cross-correlation between two dichotomous noises is presented.     

Shielding against noise interfering with quantitation of insect infestations by acoustic detection systems in grain elevators

Acoustic devices used to detect hidden insect infestations must be shielded from noise in most practical applications. One device developed specifically for use in a noisy environment, the Acoustic Location ‘Fingerprinting’ Insect Detector (ALFID), counts the numbers of insects present in grain samples from shipments being graded for export at commercial grain elevators. This report considers the performance of ALFID's noise-shielding components, which include an enclosure for passive reduction of ambient noise, and an electronic system for active detection and masking of sounds originating outside the grain sample container. Sound pressure levels (SPLs) of ambient noise are reduced inside the enclosure by 60–90 dB at frequencies between 1 and 10 kHz, with a reduction of ~6.5 dB per octave (frequency doubling). The active noise-masking system protects ALFID from loud ambient sounds not sufficiently attenuated by the enclosure. If the output from one of four sensors mounted on the outside of the grain sample container rises above a preset amplitude threshold, a signal is triggered that inhibits acquisition of insect sound data from sensors inside the container. In tests of the complete ALFID system at a grain elevator with ambient noise of 73 ± W dB re 20 μPa SPL, the mean rate of noise-mask triggering was 5.5 s⁻¹, inhibiting acquisition of insect sounds for only 3.9% of the total testing period. This level of performance is sufficient to enable successful operation of ALFID under such noise conditions.     

Synthesis of diversely functionalized hexahydropyrrolo[2,3-b]indoles using domino reactions, olefination, isomerization and Claisen rearrangement followed by reductive cyclization

Hexahydropyrrolo[2,3-b]indoles 6 were synthesized in five steps from indolin-3-one 8 by a general and efficient method, in which elements of molecular diversity were readily added onto the 3a-position of the pyrrolo[2,3-b]indole ring system. Horner-Wadsworth-Emmons reaction of 2-allyloxyindolin-3-ones 7, derived from indolin-3-one 8 and a variety of allylic alcohols, smoothly proceeded with successive Claisen rearrangement to give the corresponding 3-allyl-3-cyanomethylindolin-2-ones 15. Indolin-2-ones 15 were converted into pyrrolo[2,3-b]indoles 6 using partial hydrolysis followed by reductive cyclization with LiAlH(4). Synthesis of N-methylated pyrrolo[2,3-b]indole derivatives 23 and 26 is also described.     

Topological investigations of binary and ternary mixtures: excess isentropic compressibilities

The speed of sound, U_ij 1,3-dioxolane (D) in binary mixtures (ij) with benzene, cyclohexane, n-hexane or n-heptane and U_ijk for 1,3-dioxolane in ternary mixtures (ijk) with the same hydrocarbons have been measured as a function of composition at 298.15 K. The observed data have been utilised to evaluate excess isentropic compressibility of binary, (κ_s^E)_ij and ternary (κ_s^E)_ijk mixtures using density and speed of sound values of the binary and ternary mixtures. The Moelyn-Huggins concept of interaction between the molecular surfaces of the components of a binary mixture [Polymer 12 (1971) 389] has been extended to evaluate excess isentropic compressibility of the studied binary and ternary mixtures. It has been observed that κ_s^E values predicted by a graph-theoretical approach using connectivities of third degree for binary mixtures compare reasonably well with their corresponding experimental values and κ_s^E for ternary mixtures are of the same sign and order of magnitude.     

Optimizing and assessing the performance of an algorithm that cross-correlates acquired acoustic emissions from internally feeding larvae to count infested wheat kernels in grain samples

An algorithm was developed with optimizable parameters to match sounds from individual insects in grain by cross-correlating signals from an acoustic sensor array. The algorithm was optimized in a series of trials conducted in the sample chamber of an Acoustic Location ‘Fingerprinting’ Insect Detector (ALFID). The sample chamber was filled with uninfested wheat, except for a single kernel, which was infested with an immature rice weevil. This kernel was placed at a known location in the sample chamber. With analysis parameters optimized, the algorithm successfully detected the single insect in 100% of the trials. The algorithm's capability to count multiple insects was assessed by combining signals in data files collected from single insects into a set that represented sounds from a pair of insects. In these analyses, the algorithm correctly detected the two insects in 100% of combinations three sensor spacings apart, 100% of combinations two sensor spacings apart, and 70% of combinations one sensor spacing apart. Based on these results and the dimensions of the ALFID sampling chamber, the algorithm has a 90% probability of identifying two randomly located insects producing sounds in a wheat sample.     

Quantifying larval infestation with an acoustical sensor array and cluster analysis of cross-correlation outputs

An automated, computer-based system was designed to quantify infestation of internally feeding larvae in a grain sample by obtaining data correlated with the location of sound sources. Information related to the relative arrival times of insect feeding sounds to an array of acoustic sensors is obtained despite the low signal to noise ratios and the differential distortion induced by sound propagation through the non-uniform grain medium to the different sensors. This is achieved by employing parallel acquisition of all sensor outputs and cross-correlation analyses of all adjacent sensor pairs in the vicinity of the sensor with the largest signal. The peak location times of the resulting cross-correlograms cluster together for multiple sounds produced by the same insect but otherwise are more broadly distributed. A cluster analysis algorithm was developed to group sounds with similar ‘fingerprints’ (i.e. patterns of peak locations across several cross-correlograms). Each sufficiently large group of matching sounds indicates the presence of an insect.