Spatial fluctuations in reaction-limited aggregation

A general method is used for describing reaction-diffusion systems, namely van Kampen's method of compounding moments, to study the spatial fluctuations in reaction-limited aggregation processes. The general formalism used here and in subsequent publications is developed. Then a particular model is considered that is of special interest, since it describes the occurrence of a phase transition (gelation). The corresponding rate constants for the reaction between two clusters of sizei and sizej areK _ij=ij (i, j=1, 2,). For thediffusion constants D _j of clusters of sizej the following class of models is considered:D _j=D if 1Js andD _j=0 ifj>s. The casess= ands< are studied separately. For the models= the equal-time and the two-time correlation functions are calculated; this modelbreaks down at the gel point. The breakdown is characterized by a divergence of the density fluctuations, and is caused by the large mobility of large clusters. For all models withs< the density fluctuations remain finite att _c, and the equal-time correlation functions in the pre- and in the post-gel stage are calculated. Many explicit and asymptotic results are given. From the exact solution the upper critical dimension in this gelling model isd _c=2.     

How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue     

THE SPATIAL DISTRIBUTION AND MOMENTS OF CIRCULAR FREELY JOINTED CHAIN

The spatial distribution function and second moments of circular freely jointed chain are derived based on an analytical method. The circular Gauss chain, which is simple for long chains, is compared with the circular freely jointed chain, which is exact for short chains. It is shown that the Gauss chain model predicts a more compact configurational distribution than the exact freely jointed chain. The two chain models, however, become closer to each other when the chain length increases. It is found that the difference of the mean square radius of gyration calculated with these two chain models is a constant, independent of the chain length.     

A comparison of measured room acoustics metrics using a spherical microphone array and conventional methods

The traditional microphone configuration used to measure room impulse responses (IRs) according to ISO 3382:2009 is an omnidirectional and figure-8 microphone pair. IRs measurements were taken in a 2500-seat auditorium to determine how the results from a spherical microphone array (an mh acoustics Eigenmike-em32) compare to those from the traditional microphone setup (a Brüel & Kjær Type-4192 omnidirectional microphone and a Sennheiser MKH30 figure-8 microphone). Measurements were obtained at six receiver locations, with three repetitions each in order to first evaluate repeatability. The metrics considered in this study were: reverberation time (T30), early decay time (EDT), clarity index (C80), strength (G), lateral energy fraction (J_LF) and late lateral energy level (L_J). Before calculating these quantities, the IRs were filtered to equalize the frequency response of the microphones and sound source. For the spherical array measurements, the omnidirectional (monopole) and figure-8 (dipole) patterns were extracted using beamforming. In terms of repeatability, the average standard deviation of the three measurements at each receiver location averaged across all metrics, receivers, and octave bands was found to be 0.01 just noticeable differences (JNDs). The analysis comparing the measurements from the two microphone configurations yielded differences which were less than 1 JND for the majority of metrics, with a few exceptions of EDT and C80 slightly above 1 JND. Based on this case study, these results indicate that spherical microphone arrays can be used to obtain valid room IR measurements, which will allow for the development of new metrics utilizing the higher spatial resolution made possible with spherical arrays.     

Evaluation of three interventions teaching area measurement as spatial structuring to young children

We evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process. Replicating microgenetic procedures we used in previous research with older children to ascertain whether we can build these competencies earlier, we also extended the previous focus on correctness to include analyses of children’s use of procedural and conceptual knowledge and examined individual differences in strategy shifts before and after transitions, enabling a more detailed examination of the hypothesized necessity of development through each level of a learning trajectory. The two experimental interventions focused on a dynamic conception of area measurement while also emphasizing unit concepts, such as unit identification, iteration, and composition. The findings confirm and extend earlier results that seeing a complete record of the structure of the 2D array—in the form of a drawing of organized rows and columns—supported children’s spatial structuring and performance.     

Finest image sharpening by use of the modified mask filter dealing with highest spatial frequencies

We demonstrate a new finding that the filtering-mask with merely four coefficients in the vertical and horizontal directions could be the best choice to achieve finest image sharpening. The mask's merit to better magnify highest spatial frequencies is unveiled by employing the nonlinear transfer function, which has been proved liable to reduce the overshooting effect. By use of this chosen mask, the enhanced image is capable of manifesting extreme sharpness.     

Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in ${\mathbb{R}}^d$ and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.     

Effect of variation in signal amplitude and transit time on reliability analysis of ultrasonic time of flight diffraction characterization of vertical and inclined cracks

The variation of amplitude and transit time of the diffracted signal from the crack-tip in complex geometry components and their resulting effect on the probability of detection (POD) and probability of sizing (POS) was studied. The diffracted signal amplitude has been evaluated from the standard expressions for diffraction coefficient, spatial attenuation and the transit time from the respective mathematical models for both vertical and inclined cracks. The same parameters namely the signal amplitude and the transit time have been measured through experiments conducted on simulated test specimens. It has been observed that the analytical and experimental results compare well with each other. Based on this result the trend and shape (width of the transition zone) of the POD/POS curves can be predicted.