A cure for the sonic point glitch

Among the various numerical schemes developed since the '80s for the computation of the compressible Euler equations, the vast majority produce in certain cases spurious pressure glitches at sonic points. This flaw is particularly visible in the computation of transonic expansions and leads to unphysical "expansion shocks" when the flow undergoes rapid change of direction. The analysis of this flaw is presented, based on a series of numerical experiments. For Flux-Vector Splitting methods, it is suggested that it is not the order of differentiability of the numerical flux which is crucial but the way the pressure at an interface is calculated. A new way of evaluating the pressure at the interface is proposed, based upon kinetic theory, and is applied to most current available algorithms including Flux Vector Splitting and Flux-Difference Splitting methods as well as recent hybrid schemes (AUSM, HUS)

3D UAV Trajectory and Communication Design for Simultaneous Uplink and Downlink Transmission

In this paper, we investigate the unmanned aerial vehicle (UAV)-Aided simultaneous uplink and downlink transmission networks, where one UAV acting as a disseminator is connected to multiple access points (AP), and the other UAV acting as a base station (BS) collects data from numerous sensor nodes (SNs). The goal of this paper is to maximize the system throughput by jointly optimizing the 3D UAV trajectory, communication scheduling, and UAV-AP/SN transmit power. We first consider a special case where the UAV-BS and UAV-AP trajectories are pre-determined. Although the resulting problem is an integer and non-convex optimization problem, a globally optimal solution is obtained by applying the polyblock outer approximation (POA) method based on the problem's hidden monotonic structure. Subsequently, for the general case considering the 3D UAV trajectory optimization, an efficient iterative algorithm is proposed to alternately optimize the divided sub-problems based on the successive convex approximation (SCA) technique. Numerical results demonstrate that the proposed design is able to achieve significant system throughput gain over the benchmarks. In addition, the SCA-based method can achieve nearly the same performance as the POA-based method with much lower computational complexity

Factor Analysis for Spectral Estimation

Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy.Comment: 5 pages, 3 figures; 12th International Conference Sampling Theory and Applications, July 3-7, 2017, Tallinn, Estoni

Multitaper estimation on arbitrary domains

Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian tapers is only tractable for certain symmetric domains, such as rectangles or disks. In addition, no performance bounds are currently available for the mean squared error of the spectral density estimate. This situation is inadequate for applications such as cryo-electron microscopy, where noise models must be estimated from irregular domains with small sample sizes. We show that the multitaper estimator only depends on the linear space spanned by the tapers. As a result, Slepian tapers may be replaced by proxy tapers spanning the same subspace (validating the common practice of using partially converged solutions to the Slepian eigenproblem as tapers). These proxies may consequently be calculated using standard numerical algorithms for block diagonalization. We also prove a set of performance bounds for multitaper estimators on arbitrary domains. The method is demonstrated on synthetic and experimental datasets from cryo-electron microscopy, where it reduces mean squared error by a factor of two or more compared to traditional methods.Comment: 28 pages, 11 figure

Prediction of smoke filling in large volumes by means of data assimilation-based numerical simulations

The concept of numerical simulations for real-time Numerical Fire Forecasting is illustrated for the case of natural smoke filling of a large-scale atrium in case of fire. The numerical simulations are performed within the Inverse Zone Modelling framework. The technique consists of assimilating collected data for a certain parameter, in casu the smoke layer height, into the zone model in order to estimate an unknown of the problem ('model invariant'), mainly the fire heat release rate. A forecast in terms of evolution of smoke level and temperature can then be produced. Because zone model calculations are very fast, positive lead times of several minutes are obtained. The developed model produces reliable forecasts for the cases considered. Equally important, the robustness of the technique is illustrated: the sensitivity of the results to the 'initial guess' of the model invariants is small (i.e. the method converges easily); one model invariant is sufficient to obtain reliable predictions for smoke layer height evolution; the data assimilation window length does not affect the results significantly. The method automatically provides a different value for the plume entrainment constant, depending on the position of the fire (in the middle of the atrium or in a corner)

Power Law Tails in the Italian Personal Income Distribution

We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977--2002. We find that the upper tail of the distribution is consistent with a Pareto-power law type distribution, while the rest follows a two-parameter lognormal distribution. The results of our analysis show a shift of the distribution and a change of the indexes specifying it over time. As regards the first issue, we test the hypothesis that the evolution of both gross domestic product and personal income is governed by similar mechanisms, pointing to the existence of correlation between these quantities. The fluctuations of the shape of income distribution are instead quantified by establishing some links with the business cycle phases experienced by the Italian economy over the years covered by our dataset.Comment: Latex2e v1.6; 14 pages with 10 figures; preprint submitted to Physica

ESTIMATION OF INCOME DISTRIBUTION AND DETECTION OF SUBPOPULATIONS: AN EXPLANATORY MODEL

Inequality and polarization analyses are complementary but conceptually different. They are usually implemented independently in practic e, with different a priori assumptions and different tools. In this paper, we develop a unique method to study simultaneously these different and complementary concerns. Based on mixture models, the method we develop includes at the same time : an estimation of income distribution with no a priori assumptions - a decomposition in several homogeneous subpopulations - an explanatory model to study the structure of the income distribution.

One Dimensional Chain with Long Range Hopping

The one-dimensional (1D) tight binding model with random nearest neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effects of random long range (power-law) hopping with an ensemble averaged magnitude \expectation{|t_{ij}|} \propto |i-j|^{-\sigma} in the 1D chain, while maintaining the particle-hole symmetry present in the nearest neighbor model. We find, in agreement with results of position space renormalization group techniques applied to the random XY spin chain with power-law interactions, that there is a change of behavior when the power-law exponent $\sigma$ becomes smaller than 2

Versatile Markovian models for networks with asymmetric TCP sources

In this paper we use Stochastic Petri Nets (SPNs) to study the interaction of multiple TCP sources that share one or two buffers, thereby considerably extending earlier work. We first consider two sources sharing a buffer and investigate the consequences of two popular assumptions for the loss process in terms of fairness and link utilization. The results obtained by our model are in agreement with existing analytic models or are closer to results obtained by ns-2 simulations. We then study a network consisting of three sources and two buffers and provide evidence that link sharing is approximately minimum-potential-delay-fair in case of equal round-trip times. \u