• Villumsen Erichsen posted an update 6 months, 3 weeks ago

    In this work, we provide experimental evidence of nonlinear wave propagation in a triangular lattice of repulsive magnets supported by an elastic foundation of thin pillars, and we interpret all the individual features of the nonlinear wave field through the lens of a phonon band calculation that precisely accounts for the interparticle repulsive forces. We confirm the coexistence of two spectrally distinct components (homogeneous and forced) in the wave response that is induced via second harmonic generation (SHG) as a result of the quadratic nonlinearity embedded in the magnetic interaction. The detection of the forced component, specifically, allows us to attribute unequivocally the generation of harmonics to the nonlinear mechanisms germane to the lattice. We show that the spatial characteristics of the second harmonic components are markedly different from those exhibited by the fundamental harmonic. This endows the lattice with a functionality enrichment capability, whereby additional modal characteristics and directivity patterns can be triggered and tuned by merely increasing the amplitude of excitation.We study trapping of particles diffusing in a two-dimensional rectangular chamber by a binding site located at the end of a rectangular sleeve. To reach the site a particle first has to enter the sleeve. After that it has two options to come back to the chamber or to diffuse to the site where it is trapped. The main result of the present work is a simple expression for the mean particle lifetime as a function of its starting position and geometric parameters of the system. This expression is obtained by an approximate reduction of the initial two-dimensional problem to the effective one-dimensional one which can be solved with relative ease. Our analytical predictions are tested against the results obtained from Brownian dynamics simulations. The test shows excellent agreement between the two for a wide range of the geometric parameters of the system.In this study, we investigate the percolation threshold of curved linear objects, describing them as quadratic Bézier curves. Using Monte Carlo simulations, we calculate the critical number densities of the curves with different curviness. We also obtain the excluded area of the curves. https://www.selleckchem.com/products/chlorin-e6.html When an excluded area is given, we can find the critical number density of the curves with arbitrary curviness. Apparent conductivity exponents are computed for the curves, and these values are found to be analogous to that of sticks in the percolative region for a junction resistance dominant system. These results can be used to analyze the optoelectrical performance of metal nanowire films because the high-aspect-ratio metal nanowires can be easily curved during coating.We study the collective response of small random tree networks of diffusively coupled excitable elements to stimuli applied to leaf nodes. Such networks model the morphology of certain sensory neurons that possess branched myelinated dendrites with excitable nodes of Ranvier at every branch point and at leaf nodes. Leaf nodes receive random inputs along with a stimulus and initiate action potentials that propagate through the tree. We quantify the collective response registered at the central node using mutual information. We show that in the strong-coupling limit, the statistics of the number of nodes and leaves determines the mutual information. At the same time, the collective response is insensitive to particular node connectivity and distribution of stimulus over leaf nodes. However, for intermediate coupling, the mutual information may strongly depend on the stimulus distribution among leaf nodes. We identify a mechanism behind the competition of leaf nodes that leads to nonmonotonous dependence of mutual information on coupling strength. We show that a localized stimulus given to a tree branch can be occluded by the background firing of unstimulated branches, thus suppressing mutual information. Nonetheless, the mutual information can be enhanced by a proper stimulus localization and tuning of coupling strength.By controlling synaptic and neural correlations, deep learning has achieved empirical successes in improving classification performances. How synaptic correlations affect neural correlations to produce disentangled hidden representations remains elusive. Here we propose a simplified model of dimension reduction, taking into account pairwise correlations among synapses, to reveal the mechanism underlying how the synaptic correlations affect dimension reduction. Our theory determines the scaling of synaptic correlations requiring only mathematical self-consistency for both binary and continuous synapses. The theory also predicts that weakly correlated synapses encourage dimension reduction compared to their orthogonal counterparts. In addition, these synapses attenuate the decorrelation process along the network depth. These two computational roles are explained by a proposed mean-field equation. The theoretical predictions are in excellent agreement with numerical simulations, and the key features are also captured by deep learning with Hebbian rules.Understanding the motion of particles on an air-liquid interface can impact a wide range of scientific fields and applications. Diamagnetic particles floating on an air-paramagnetic-liquid interface are previously known to have a repulsive motion from a magnet. Here, we show a motion mechanism where the diamagnetic particles floating on the air-paramagnetic-liquid interface are attracted and eventually trapped at an off-center distance from the magnet. The behavior of magnetic particles has been also studied and the motion mechanisms are theorized in a unified framework, revealing that the motion of particles on an air-paramagnetic-liquid interface is governed not only by magnetic energy, but as an interplay of the curvature of the interface deformation created by the nonuniform magnetic field, the gravitational potential, and the magnetic energy from the particle and the liquid. The attractive motion mechanism has been applied in directed self-assembly and robotic particle guiding.

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