Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

A model for probing large distance behaviour in high energy collisions

We apply to total cross-sections our model for soft gluon resummation in the infrared region. The model aims to probe large distance interactions in QCD. Our ansatz for an effective coupling for gluons and quarks in the infrared region follows an inverse power law which is singular but integrable. In the context of an eikonal formalism with QCD mini-jets, we study total hadronic cross-sections for protons, pions, photons. We estimate the total inelastic cross-section at LHC comparing with recent measurements and update previous results for survival probability.

Zero miss distance guidance using feedforward and periodic control

There have been attempts at obtaining robust guidance laws to ensure zero miss distance (ZMD) for interceptors with parametric uncertainties. All these laws require the plant to be of minimum phase type to enable the overall guidance loop transfer function to satisfy strict positive realness (SPR). The SPR property implies absolute stability of the closed loop system, and has been shown in the literature to lead to ZMD because it avoids saturation of lateral acceleration. In these works higher order interceptors are reduced to lower order equivalent models for which control laws are designed to ensure ZMD. However, it has also been shown that when the original system with right half plane (RHP) zeros is considered, the resulting miss distances, using such strategies, can be quite high. In this paper, an alternative approach using the circle criterion establishes the conditions for absolute stability of the guidance loop and relaxes the conservative nature of some earlier results arising from assumption of in�nite engagement time. Further, a feedforward scheme in conjunction with a lead-lag compensator is used as one control strategy while a generalized sampled hold function is used as a second strategy, to shift the RHP transmission zeros, thereby achieving ZMD. It is observed that merely shifting the RHP zero(s) to the left half plane reduces miss distances signi�cantly even when no additional controllers are used to ensure SPR conditions.

On the possible variation of the lightning striking distance as assumed in the IEC lightning protection standard as a function of structure height

The effect of structure height on the lightning striking distance is estimated using a lightning strike model that takes into account the effect of connecting leaders. According to the results, the lightning striking distance may differ significantly from the values assumed in the IEC standard for structure heights beyond 30m. However, for structure heights smaller than about 30m, the results show that the values assumed by IEC do not differ significantly from the predictions based on a lightning attachment model taking into account the effect of connecting leaders. However, since IEC assumes a smaller striking distance than the ones predicted by the adopted model one can conclude that the safety is not compromised in adhering to the IEC standard. Results obtained from the model are also compared with Collection Volume Method (CVM) and other commonly used lightning attachment models available in the literature. The results show that in the case of CVM the calculated attractive distances are much larger than the ones obtained using the physically based lightning attachment models. This indicates the possibility of compromising the lightning protection procedures when using CVM. (C) 2014 Elsevier B.V. All rights reserved.

Flocking at a distance in active granular matter

The self-organized motion of vast numbers of creatures in a single direction is a spectacular example of emergent order. Here, we recreate this phenomenon using actuated nonliving components. We report here that millimetre-sized tapered rods, rendered motile by contact with an underlying vibrated surface and interacting through a medium of spherical beads, undergo a phase transition to a state of spontaneous alignment of velocities and orientations above a threshold bead area fraction. Guided by a detailed simulation model, we construct an analytical theory of this flocking transition, with two ingredients: a moving rod drags beads; neighbouring rods reorient in the resulting flow like a weathercock in the wind. Theory and experiment agree on the structure of our phase diagram in the plane of rod and bead concentrations and power-law spatial correlations near the phase boundary. Our discovery suggests possible new mechanisms for the collective transport of particulate or cellular matter.

Males and females of the social wasp Ropalidia marginata do not differ in their cuticular hydrocarbon profiles and do not seem to use any long-distance volatile mate attraction cues

Sex pheromones are vital in communication between individuals belonging to opposite sexes and form an integral part of the reproductive biology of various species. Among insects, sexual dimorphism in CHCs has been reported from diverse taxa spanning seven different orders, and thereby CHCs have been implicated as sex pheromones. Because males and females of the primitively eusocial wasp Ropalidia marginata touch each other with their antennae during mating, before engaging in sperm transfer, a sex pheromone that is perceived via contact chemosensation through the antennae can possibly exist in this species. Since CHCs have been implied as sex pheromones in various insects (including hymenopterans), and since sexual dimorphism of CHCs should be an obligatory prerequisite for them to act as sex pheromones, we investigated whether males and females of R. marginata differ in their CHC profiles. We found only nonvolatile CHCs, and our results show absence of sexual dimorphism in CHCs, suggesting that CHCs do not function as sex pheromone in this species. A behavioral assay failed to show presence of mate attraction at a distance, thereby showing the absence of volatile long-distance mate attraction cues (that may originate from sources other than and in addition to CHCs).

Quantifying the Transmit Diversity Order of Euclidean Distance Based Antenna Selection in Spatial Modulation

In this letter, we quantify the transmit diversity order of the SM system operating in a closed-loop scenario. Specifically, the SM system relying on Euclidean distance based antenna subset selection (EDAS) is considered and the achievable diversity gain is evaluated. Furthermore, the resultant trade-off between the achievable diversity gain and switching gain is studied. Simulation results confirm our theoretical results. Specifically, at a symbol error rate of about 10(-4) the signal-to-noise ratio gain achieved by EDAS is about 7 dB in case of 16-QAM and about 5 dB in case of 64-QAM.

Effects of site stiffness and source to receiver distance on surface wave tests' results

By using six 4.5 Hz geophones, surface wave tests were performed on four different sites by dropping freely a 65 kg mass from a height of 5 m. The receivers were kept far away from the source to eliminate the arrival of body waves. Three different sources to nearest receiver distances (S), namely, 46 m, 56 m and 66 m, were chosen. Dispersion curves were drawn for all the sites. The maximum wavelength (lambda(max)), the maximum depth (d(max)) up to which exploration can be made and the frequency content of the signals depends on the site stiffness and the value of S. A stiffer site yields greater values of lambda(max) and d(max). For stiffer sites, an increase in S leads to an increase in lambda(max). The predominant time durations of the signals increase from stiffer to softer sites. An inverse analysis was also performed based on the stiffness matrix approach in conjunction with the maximum vertical flexibility coefficient of ground surface to establish the governing mode of excitation. For the Site 2, the results from the surface wave tests were found to compare reasonably well with that determined on the basis of cross boreholes seismic tests. (C) 2015 Elsevier Ltd. All rights reserved.

Global response sensitivity analysis using probability distance measures and generalization of Sobol's analysis

The study introduces two new alternatives for global response sensitivity analysis based on the application of the L-2-norm and Hellinger's metric for measuring distance between two probabilistic models. Both the procedures are shown to be capable of treating dependent non-Gaussian random variable models for the input variables. The sensitivity indices obtained based on the L2-norm involve second order moments of the response, and, when applied for the case of independent and identically distributed sequence of input random variables, it is shown to be related to the classical Sobol's response sensitivity indices. The analysis based on Hellinger's metric addresses variability across entire range or segments of the response probability density function. The measure is shown to be conceptually a more satisfying alternative to the Kullback-Leibler divergence based analysis which has been reported in the existing literature. Other issues addressed in the study cover Monte Carlo simulation based methods for computing the sensitivity indices and sensitivity analysis with respect to grouped variables. Illustrative examples consist of studies on global sensitivity analysis of natural frequencies of a random multi-degree of freedom system, response of a nonlinear frame, and safety margin associated with a nonlinear performance function. (C) 2015 Elsevier Ltd. All rights reserved.