Summersjordan4921

The counterintuitive fact that wave chaos appears in the bending spectrum of free rectangular thin plates is presented. After extensive numerical simulations, varying the ratio between the length of its sides, it is shown that (i) frequency levels belonging to different symmetry classes cross each other and (ii) for levels within the same symmetry sector, only avoided crossings appear. The consequence of anticrossings is studied by calculating the distribution of the ratio of consecutive level spacings for each symmetry class. The resulting ratio distributions disagree with the expected Poissonian result. They are then compared with some well-known transition distributions between Poisson and the Gaussian orthogonal random matrix ensemble. It is found that the distribution of the ratio of consecutive level spacings agrees with the prediction of the Rosenzweig-Porter model. Also, the normal-mode vibration amplitudes are found experimentally on aluminum plates, before and after an avoided crossing for symmetrical-symmetrical, symmetrical-antisymmetrical, and antisymmetrical-symmetrical classes. The measured modes show an excellent agreement with our numerical predictions. selleckchem The expected Poissonian distribution is recovered for the simply supported rectangular plate.We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected subpopulations. In this setup, oscillators belonging to the same group interact via symmetric couplings while the interaction between subpopulations occurs in an asymmetric fashion. By employing the dimensional reduction scheme of the Ott-Antonsen (OA) theory, we verify the existence of traveling wave and π-states, in addition to the classical fully synchronized and incoherent states. Bistability between all collective states is reported. Analytical results are generally in excellent agreement with simulations; for some parameters and initial conditions, however, we numerically detect chimera-like states which are not captured by the OA theory.The brain demands a significant fraction of the energy budget in an organism; in humans, it accounts for 2% of the body mass, but utilizes 20% of the total energy metabolized. This is due to the large load required for information processing; spiking demands from neurons are high but are a key component to understanding brain functioning. Astrocytic brain cells contribute to the healthy functioning of brain circuits by mediating neuronal network energy and facilitating the formation and stabilization of synaptic connectivity. During development, spontaneous activity influences synaptic formation, shaping brain circuit construction, and adverse astrocyte mutations can lead to pathological processes impacting cognitive impairment due to inefficiencies in network spiking activity. We have developed a measure that quantifies information stability within in vitro networks consisting of mixed neural-astrocyte cells. Brain cells were harvested from mice with mutations to a gene associated with the strongest known genetic risk factor for Alzheimer's disease, APOE. We calculate energy states of the networks and using these states, we present an entropy-based measure to assess changes in information stability over time. We show that during development, stability profiles of spontaneous network activity are modified by exogenous astrocytes and that network stability, in terms of the rate of change of entropy, is allele dependent.We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of noninteracting line segments and disks in two spatial dimensions. These examples serve as models for electrical percolation of elongated and flat nanofillers in thin film composites. While the standard contact volume argument and extensions thereof in connectedness percolation theory yield accurate predictions for slender nanofillers in three dimensions, they fail to do so in two dimensions, making our test a stringent one. In fact, neither a systematic order-by-order correction to the standard argument nor invoking the connectedness version of the Percus-Yevick approximation yield significant improvements for either type of particle. Making use of simple geometric considerations, our new method predicts a percolation threshold of ρ_cl^2≈5.83 for segments of length l, which is close to the ρ_cl^2≈5.64 found in Monte Carlo simulations. For disks of area a we find ρ_ca≈1.00, close to the Monte Carlo result of ρ_ca≈1.13. We discuss the shortcomings of the conventional approaches and explain how usage of the nearest-neighbor distribution in our method bypasses those complications.We revisit the indentation of a thin solid sheet of size R_sheet suspended on a circular hole of radius R≪R_sheet in a smooth rigid substrate, addressing the effects of boundary conditions at the hole's edge. Introducing a basic theoretical model for the van der Waals (vdW) sheet-substrate attraction, we demonstrate the dramatic effect of replacing the clamping condition (Schwerin model) with a sliding condition, whereby the supported part of the sheet is allowed to slide towards the indenter and relax the induced hoop compression through angstrom-scale deflections from the thermodynamic equilibrium (determined by the vdW potential). We highlight the possibility that the indentation force F may not exhibit the commonly anticipated cubic dependence on the indentation depth (F∝δ^3), in which the proportionality constant is governed by the sheet's stretching modulus and the hole's radius R, but rather a pseduolinear response F∝δ, whereby the proportionality constant is governed by the bending modulus, the vdW attraction, and the sheet's size R_sheet≫R.We discuss large deviation properties of continuous-time random walks (CTRWs) and present a general expression for the large deviation rate in CTRWs in terms of the corresponding rates for the distributions of steps' lengths and waiting times. In the case of Gaussian distribution of steps' lengths the general expression reduces to a sequence of two Legendre transformations applied to the cumulant generating function of waiting times. The discussion of several examples (Bernoulli and Gaussian random walks with exponentially distributed waiting times, Gaussian random walks with one-sided Lévy and Pareto-distributed waiting times) reveals interesting general properties of such large deviations.