The Relativistic Rotation

The classical rotation is not self-consistent in the framework of the special theory of relativity. the Relativistic rotation is obtained, which takes the relativistic effect into account. It is demonstrated that the angular frequency of classical rotation is only valid in local approximation. The properties of the relativistic rotation and the relativistic transverse Doppler shift are discussed in this work

Outlier detection using distributionally robust optimization under the Wasserstein metric

We present a Distributionally Robust Optimization (DRO) approach to outlier detection in a linear regression setting, where the closeness of probability distributions is measured using the Wasserstein metric. Training samples contaminated with outliers skew the regression plane computed by least squares and thus impede outlier detection. Classical approaches, such as robust regression, remedy this problem by downweighting the contribution of atypical data points. In contrast, our Wasserstein DRO approach hedges against a family of distributions that are close to the empirical distribution. We show that the resulting formulation encompasses a class of models, which include the regularized Least Absolute Deviation (LAD) as a special case. We provide new insights into the regularization term and give guidance on the selection of the regularization coefficient from the standpoint of a confidence region. We establish two types of performance guarantees for the solution to our formulation under mild conditions. One is related to its out-of-sample behavior, and the other concerns the discrepancy between the estimated and true regression planes. Extensive numerical results demonstrate the superiority of our approach to both robust regression and the regularized LAD in terms of estimation accuracy and outlier detection rates

Three-Body Elastic and Inelastic Scattering at Intermediate Energies

The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. For identical bosons this results in a three-dimensional integral equation in five variables, magnitudes of relative momenta and angles. The cross sections for both elastic and breakup processes in the intermediate energy range up to about 1 GeV are calculated based on a Malfliet-Tjon type potential, and the convergence of the multiple scattering series is investigated.Comment: Talk at the 18th International IUPAP Conference on Few-Body Problems in Physics, Aug. 21-26, 2006, Santos, Brazi

Enhanced binding revisited for a spinless particle in non-relativistic QED

We consider a spinless particle coupled to a quantized Bose field and show that such a system has a ground state for two classes of short-range potentials which are alone too weak to have a zero-energy resonance

Spurious detection of phase synchronization in coupled nonlinear oscillators

Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess data. We investigate to what extent the phase synchronization of two coupled R\"{o}ssler oscillators depends on (1) the broadness of their power spectrum, (2) the width of the band-pass filter, and (3) the level of added noise. We find that for identical coupling strengths, oscillators with broader power spectra exhibit weaker synchronization. Further, we find that within a broad band width range, band-pass filtering reduces the effect of noise but can lead to a spurious increase in the degree of synchronization with narrowing band width, even when the coupling between the two oscillators remains the same.Comment: 4 pages,6 figure

A metal–organic framework/α-alumina composite with a novel geometry for enhanced adsorptive separation

The development of a metal–organic framework/α-alumina composite leads to a novel concept: efficient adsorption occurs within a plurality of radial micro-channels with no loss of the active adsorbents during the process. This composite can effectively remediate arsenic contaminated water producing potable water recovery, whereas the conventional fixed bed requires eight times the amount of active adsorbents to achieve a similar performance

Effect of nonlinear filters on detrended fluctuation analysis

We investigate how various linear and nonlinear transformations affect the scaling properties of a signal, using the detrended fluctuation analysis (DFA). Specifically, we study the effect of three types of transforms: linear, nonlinear polynomial and logarithmic filters. We compare the scaling properties of signals before and after the transform. We find that linear filters do not change the correlation properties, while the effect of nonlinear polynomial and logarithmic filters strongly depends on (a) the strength of correlations in the original signal, (b) the power of the polynomial filter and (c) the offset in the logarithmic filter. We further investigate the correlation properties of three analytic functions: exponential, logarithmic, and power-law. While these three functions have in general different correlation properties, we find that there is a broad range of variable values, common for all three functions, where they exhibit identical scaling behavior. We further note that the scaling behavior of a class of other functions can be reduced to these three typical cases. We systematically test the performance of the DFA method in accurately estimating long-range power-law correlations in the output signals for different parameter values in the three types of filters, and the three analytic functions we consider.Comment: 12 pages, 7 figure

Optical Resonances in Reflectivity near Crystal Modes with Spatial Dispersion

We study the effect of spatial dispersion of crystal modes on optical properties such as the reflectivity $R$. As an example for isotropic media, we investigate the simplest model for phonons in ionic crystals and compare with previous results for highly anisotropic plasmons, which are now understood from a more general point of view. As a consequence of the wave vector dependence of the dielectric function small changes in the lineshape are predicted. Beyond that, if the frequency of minimal $R$ is near a pole of the dispersionless dielectric function, the relative amplitude of dips in $R$ with normal and anomalous dispersion differ significantly, if dissipation and disorder are low.Comment: 4 pages, 7 eps figures, minor change