Predictive flow-field estimation

We are considering the problem of real-time prediction of 3D turbulent velocity fields based on a small number of scalar measurements. The method of proper orthogonal decomposition (POD) allows for the decomposition of an ensemble of velocity fields into a set of spatial basis functions and a set of temporal coefficients. The computation of the temporal coefficients is by no means a trivial matter, especially when one is faced with a large number of modes. In this paper we discuss the use of radial basis function (RBF) models to capture the discrete time evolution and nonlinear dynamics of the POD coefficients. Further, we propose the use of regularized regression techniques to generate models that provide mappings between the POD coefficients and scalar measurements. As a final step towards real-time prediction, the state-space RBF models and regression measurement models are combined using unscented Kalman filters to produce optimal solutions such that a balance between the state models and measurement models is achieved.The proposed methods are tested for two specific cases. The classical Lorenz model is chosen to demonstrate the use and effectiveness of RBF models as a potential candidate for state models. Flow around a wall-mounted cube in a channel at Re=20,000 is considered as the second case. The aim for the second case is to be able to accurately predict the POD coefficients outside the ensemble. It is shown that a large number of POD coefficients is required to approximate the velocity fields with sufficient accuracy. The RBF models are created based on only the temporal information available from the initial ensemble, and it is shown that the RBF model is able to correctly approximate the high-dimensional phase space. Combined with the unscented Kalman filter it is indeed possible to track the evolution of the POD coefficients for a long time. The robustness of the filter is demonstrated by considering the presence of noise in measurements and using measurement information at time steps greater than the evolution time step.     

Room evacuation in the presence of an obstacle

The investigation of human behaviour while trying to escape from a room under panic is an important issue in complex systems research. Several authors have called attention to the fact that placing an obstacle near the exit improves the evacuation time of the room (Helbing et al. (2000, 2005) [2] and [8], Hughes (2003) [6], Johansson and Helbing (2005) [16], Piccoli and Tosin (2009) [5]). We studied this effect in the context of the “social force model” (Helbing et al. (2000) [2]). We show that placing an obstacle does not guarantee, by itself, better chances of survival for all pedestrians. The way they choose to avoid the obstacle is critical for their own performance. We found not only that the faster they try to escape, the slower they get out (“faster is slower” effect), but also, the short cut they might take in order to get to the exit will probably do no better (“clever is not always better” effect).     

Income distribution: Boltzmann analysis and its extension

The paper aims at describing income distribution in moderate income regions. Starting with dividing income behaviors into the two parts: random and deterministic, and by introducing “instantaneous model” for theoretical derivations and “cumulative model” for positive tests, this paper applies the equilibrium approach of statistical mechanics in the study of nonconserved individual income course. The random income follows a stationary distribution similar to the Maxwell–Boltzmann distribution in the instantaneous model. Combining this result with marginal analysis, the probability distribution of individual income process that is composed of the random and deterministic income courses approximately obeys a distribution law mixing exponential function with a logarithmic prefactor. Using the census or income survey data of USA, UK, Japan, and New Zealand, the distribution law has been tested. The results show that it agrees very well with most of the empirical data. The discussion suggests that there might be essentially different income processes to happen in moderate and high income regions.     

Anomalous is ubiquitous

Brownian motion is widely considered the quintessential model of diffusion processes—the most elemental random transport processes in Science and Engineering. Yet so, examples of diffusion processes displaying highly non-Brownian statistics–commonly termed “Anomalous Diffusion” processes–are omnipresent both in the natural sciences and in engineered systems. The scientific interest in Anomalous Diffusion and its applications is growing exponentially in the recent years. In this Paper we review the key statistics of Anomalous Diffusion processes: sub-diffusion and super-diffusion, long-range dependence and the Joseph effect, Lévy statistics and the Noah effect, and 1/f noise. We further present a theoretical model–generalizing the Einstein–Smoluchowski diffusion model–which provides a unified explanation for the prevalence of Anomalous Diffusion statistics. Our model shows that what is commonly perceived as “anomalous” is in effect ubiquitous.     

Erratum to “Scaling properties of the Baxter–Wu model” [Physica A 390 (2011) 3369–3384]

We detail numerical corrections for the paper “Scaling properties of the Baxter–Wu model”, Velonakis, I.N., Martinos, S.S., Physica A, 390 (2011) 3369–3384.     

Three-lane changing behaviour simulation using a modified optimal velocity model

In real urban traffic, roadways are usually multilane and are divided into fast, medium and slow lanes according to different velocity restrictions. Microscopic modelling of single lane has been studied widely using discrete cellular automata and continuous optimal velocity models. In this paper, we extend the continuous single-lane models (OV model and FVD model) to simulate the lane-changing behaviour on an urban roadway that consists of three lanes. Considering headway difference, velocity difference, safety distance, and the probability of lane-changing intention, a comprehensive lane-changing rule set is constructed. We analyse the fundamental diagram and reveal the “faster-is-slower” effect in urban traffic induced by lane-changing behaviour. We also investigate the effect of lane-changing behaviour on the distribution of vehicles, velocity, flow and headway. Asymmetrical phenomenon with symmetrical rules on urban roadway and density inversion on the slow lane were also found. The simulation results indicate that lane-changing behaviour is not advisable on crowded urban roadway. It is hoped that information from this study may be useful for traffic control and individual moving strategy on urban roadway.     

Morphological and dynamical aspects of the room evacuation process

We study the evacuation of a set of 200 pedestrians from a room under a state of panic. The dynamics of the pedestrians is given by the Social Force Model. The degree of panic is controlled by a parameter v_d which represents the velocity at which pedestrians wish to move. We show that the “faster is slower effect” can be understood in terms of the works performed by the different forces present in the system and the role played by dissipative terms in the model. Beyond the maximum flow rate the “granular cluster” mass distribution displays a transition from exponentially decaying to “U-shaped” as this value of v_d evacuation efficiency begins to decrease rapidly.     

Heavy particle modes and signature of the I-Regime

The recently discovered properties of the I-confinement Regime are explained as resulting from the excitation of a heavy particle mode. The theoretically predicted mode phase velocity in the direction of the electron diamagnetic velocity and the induced confinement of impurities at the edge of the plasma column have been confirmed by the experiments. The direction of the mode phase velocity is consistent with that (opposite) of the spontaneous rotation in the plasma core. The mode is of the “ion-mixing” type, in that it does not produce any electron transport across the fields and it involves significant poloidal magnetic field fluctuations.     

Symplectic random vibration analysis of a vehicle moving on an infinitely long periodic track

Based on the pseudo-excitation method (PEM), symplectic mathematical scheme and Schur decomposition, the random responses of coupled vehicle-track systems are analyzed. The vehicle is modeled as a spring-mass-damper system and the track is regarded as an infinitely long substructural chain consisting of three layers, i.e. the rails, sleepers and ballast. The vehicle and track are coupled via linear springs and the “moving-vehicle model” is adopted. The latter assumes that the vehicle moves along a static track for which the rail irregularity is further assumed to be a zero-mean valued stationary Gaussian random process. The problem is then solved efficiently as follows. Initially, PEM is used to transform the rail random excitations into deterministic harmonic excitations. The symplectic mathematical scheme is then applied to establish a low degree of freedom equation of motion with periodic coefficients. In turn these are transformed into a linear equation set whose upper triangular coefficient matrix is established using the Schur decomposition scheme. Finally, the frequency-dependent terms are separated from the load vector to avoid repeated computations for different frequencies associated with the pseudo-excitations. The proposed method is subsequently justified by comparison with a Monte-Carlo simulation; the fixed-vehicle model and the moving-vehicle model are compared and the influences of vehicle velocity and class of track on system responses are also discussed.     

A unified model for price return distributions used in econophysics

For a decade, a new theoretical movement called “econophysics” has been initiated by some physicists who began to publish articles devoted to the study of economic and financial phenomena. Since then, econophysicists have written a very prolific literature about the way of characterizing the evolution of financial prices. Today, there is an “extreme diversity” of models recently developed by econophysicists whose research is sometimes presented as an ill-defined field. The objective of this paper is precisely to provide a unified framework in order to contribute to unify econophysics and to base this new field on shared scientific standards.     

POD analysis on the sphere wake at a subcritical Reynolds number

Abstract  

Flow characteristics of turbulent wake behind a sphere at a subcritical flow regime were experimentally investigated. The particle image velocimetry measurements and proper orthogonal decomposition (POD) modal analysis were employed to get detailed flow information such as the wavy structure, swirling motion and coherent structures of the sphere wake. The variation of turbulent intensities of the radial and circumferential velocity components showed the swirling motion of sphere wake in the cross-sectional planes. The relative contribution of the POD mode 1, 2 and 3 in eigenvalues was 26, 11, and 8%, respectively. The general pattern of velocity fields for the POD mode 1 in the near-wake region of x/d = 0.7–1.4 is similar with that of time-averaged mean velocity fields. In addition, the sweeping flow in the region from x/d = 1.5 to x/d = 2.0 possesses wavy structure of the sphere wake. The experimental results of the present study would contribute to the fundamental understanding of the turbulent near-wake behind a sphere.     

Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities are shown to demonstrate nonuniversal correlations due to localization. Varying energy E and mean free path l enable us to experimentally tune from localized to delocalized states. Large level-to-level inverse participation ratio ( I2) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about . The spatial density autocorrelations of eigenfunctions are shown to spatially decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma models.     

EFFECTS OF END CAP AND ASPECT RATIO ON TRANSMISSION OF SOUND ACROSS A TRUSS-LIKE PERIODIC DOUBLE PANEL

Transmission of sound across 2-D truss-like periodic double panels separated by an air gap and in contact with an acoustic fluid on the external faces is analyzed. Each panel is made of repeated cells. Combining the transfer matrices of the unit cell forms a set of equations for the overall elastic frequency response. The acoustic pressure in the fluids is expressed using a source boundary element method. Adding rigid reflecting end caps confines the air in the gap between panels which influences sound transmission. Measured values of transmission loss differ from the 2-D model by the wide low-frequency dip of the mass-spring-mass or “msm” resonance also termed the “air gap resonance”. In this case, the panels act as rigid masses and the air gap acts as an adiabatic air spring. Results from the idealized 3-D and 2-D models, incorporating rigid cavities and elastic plates, reveal that the “msm” dip is absent in 2-D models radiating into a semi-infinite medium. The dip strengthens as aspect ratio approaches unity. Even when the dip disappears in 2-D, TL rises more steeply for frequencies above the “msm” frequency.     

An interferometer based on the Talbot effect

The moiré effect is very sensitive in detecting small differences between two similar gratings. These differences might be caused by an object with phase gradient placed between the two gratings. The performance of such an instrument can be understood in terms of the “Talbot effect” (also called “Fourier imaging” or “self-imaging”). Slight modifications provide shearing interferences and the second derivative of the object.     

Many polarized radiative transfer models

This note is an introduction to the reprint of the 1991 JQSRT article “A new polarized atmospheric radiative transfer model” by K.F. Evans and G.L. Stephens. We discuss the significance of the article, how our two plane-parallel polarized radiative transfer codes came about, how our codes have been used, and more recent developments in polarized radiative transfer modeling.     

Bianchi cosmologies with anisotropic matter: Locally rotationally symmetric models

The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following. (i) There exist matter models, compatible with the standard energy conditions, such that solutions of Bianchi type IX (closed cosmologies) need not necessarily recollapse; there is an open set of forever expanding solutions. (ii) Generic type IX solutions associated with a matter model like Vlasov matter exhibit oscillatory behavior toward the initial singularity. This behavior differs significantly from that of vacuum/perfect fluid cosmologies; hence “matter matters”. Finally, we indicate that our methods can probably be extended to treat a number of open problems—in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.     

Elastic modes frequencies in the mirrors with “ears” for parametric oscillatory instability in advanced LIGO interferometer

We discuss the importance of accurate numerical calculation of elastic modes in the mirrors with suspension “ears” in advanced LIGO interferometer to enable precise predictions of parametric oscillatory instability problem. We show that “ears” of test masses produce additional shift of elastic modes frequencies which is larger than relaxation rate of optical modes. These shifts may increase the possibility of parametric oscillatory instability.     

A Timoshenko-beam-on-Pasternak-foundation analogy for cylindrical shells

A Timoshenko-beam-on-Pasternak-foundation model is developed for the analysis of thin elastic cylindrical shells. This model aims to bridge the gap between the Love-Kirchhoff theory and the approximate beam-on-elastic-foundation model of Vlasov (“long-wave” model), which accounts for only longitudinal stretching and circumferential bending. The new model improves on the assumptions of the “long-wave” model by accounting for the effects of two additional actions, namely, in-plane shearing and twist. The model is used to derive “explicit” design formulae for (1) the fundamental natural frequencies for vibration of a uniform cylindrical shell having six sets of end restraints, and (2) the circumferential modenumbers associated with the fundamental mode. A comprehensive comparative study of the predictions of both models against available results in the literature and results obtained by the finite-element method has shown that the proposed model significantly extends the limits of the validity of the “long-wave” model.     

Effective metrics in the non-minimal Einstein-Yang-Mills-Higgs theory

We formulate a self-consistent non-minimal five-parameter Einstein-Yang-Mills-Higgs (EYMH) model and analyse it in terms of effective (associated, color and color-acoustic) metrics. We use a formalism of constitutive tensors in order to reformulate master equations for the gauge, scalar and gravitational fields and reconstruct in the algebraic manner the so-called associated metrics for the Yang-Mills field. Using WKB-approximation we find color metrics for the Yang-Mills field and color-acoustic metric for the Higgs field in the framework of five-parameter EYMH model. Based on explicit representation of these effective metrics for the EYMH system with uniaxial symmetry, we consider cosmological applications for Bianchi-I, FLRW and de Sitter models. We focus on the analysis of the obtained expressions for velocities of propagation of longitudinal and transversal color and color-acoustic waves in a (quasi)vacuum interacting with curvature; we show that curvature coupling results in time variations of these velocities. We show, that the effective metrics can be regular or can possess singularities depending on the choice of the parameters of non-minimal coupling in the cosmological models under discussion. We consider a physical interpretation of such singularities in terms of phase velocities of color and color-acoustic waves, using the terms “wave stopping” and “trapped surface”.