Temporal Ordering in Quantum Mechanics

We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one particle (in higher dimensions). In quantum mechanics, we find that diffraction effects introduce a minimum inaccuracy to which the temporal order-of-arrival can be determined unambiguously. The minimum inaccuracy of the measurement is given by dt=1/E where E is the total kinetic energy of the two particles. Similar restrictions apply to the case of coincidence measurements. We show that these limitations are much weaker than limitations on measuring the time-of-arrival of a particle to a fixed location.Comment: New section added, arguing that order-of-arrival can be measured more accurately than time-of-arrival. To appear in Journal of Physics

Effects of electrojet turbulence on a magnetosphere-ionosphere simulation of a geomagnetic storm

Ionospheric conductance plays an important role in regulating the response of the magnetosphere‐ionosphere system to solar wind driving. Typically, models of magnetosphere‐ionosphere coupling include changes to ionospheric conductance driven by extreme ultraviolet ionization and electron precipitation. This paper shows that effects driven by the Farley‐Buneman instability can also create significant enhancements in the ionospheric conductance, with substantial impacts on geospace. We have implemented a method of including electrojet turbulence (ET) effects into the ionospheric conductance model utilized within geospace simulations. Our particular implementation is tested with simulations of the Lyon‐Fedder‐Mobarry global magnetosphere model coupled with the Rice Convection Model of the inner magnetosphere. We examine the impact of including ET‐modified conductances in a case study of the geomagnetic storm of 17 March 2013. Simulations with ET show a 13% reduction in the cross polar cap potential at the beginning of the storm and up to 20% increases in the Pedersen and Hall conductance. These simulation results show better agreement with Defense Meteorological Satellite Program observations, including capturing features of subauroral polarization streams. The field‐aligned current (FAC) patterns show little differences during the peak of storm and agree well with Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) reconstructions. Typically, the simulated FAC densities are stronger and at slightly higher latitudes than shown by AMPERE. The inner magnetospheric pressures derived from Tsyganenko‐Sitnov empirical magnetic field model show that the inclusion of the ET effects increases the peak pressure and brings the results into better agreement with the empirical model.This material is based upon work supported by NASA grants NNX14AI13G, NNX13AF92G, and NNX16AB80G. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This work used the XSEDE and TACC computational facilities, supported by National Science Foundation grant ACI-1053575. We would like to acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. We thank the AMPERE team and the AMPERE Science Center for providing the Iridium derived data products. All model output, simulation codes, and analysis routines are being preserved on the NCAR High-Performance Storage System and will be made available upon written request to the lead author of this publication. (NNX14AI13G - NASA; NNX13AF92G - NASA; NNX16AB80G - NASA; National Science Foundation; ACI-1053575 - National Science Foundation

Empowering and assisting natural human mobility: The simbiosis walker

This paper presents the complete development of the Simbiosis Smart Walker. The device is equipped with a set of sensor subsystems to acquire user-machine interaction forces and the temporal evolution of user's feet during gait. The authors present an adaptive filtering technique used for the identification and separation of different components found on the human-machine interaction forces. This technique allowed isolating the components related with the navigational commands and developing a Fuzzy logic controller to guide the device. The Smart Walker was clinically validated at the Spinal Cord Injury Hospital of Toledo - Spain, presenting great acceptability by spinal chord injury patients and clinical staf

Measurement of Time-of-Arrival in Quantum Mechanics

It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta t_A \sim 1/E_k$, where $E_k$ is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.Comment: References added. To appear in Phys. Rev.

Structure functions and intermittency in ionospheric plasma turbulence

Low frequency electrostatic turbulence in the ionospheric E-region is studied by means of numerical and experimental methods. We use the structure functions of the electrostatic potential as a diagnostics of the fluctuations. We demonstrate the inherently intermittent nature of the low level turbulence in the collisional ionospheric plasma by using results for the space-time varying electrostatic potential from two dimensional numerical simulations. An instrumented rocket can not directly detect the one-point potential variation, and most measurements rely on records of potential differences between two probes. With reference to the space observations we demonstrate that the results obtained by potential difference measurements can differ significantly from the one-point results. It was found, in particular, that the intermittency signatures become much weaker, when the proper rocket-probe configuration is implemented. We analyze also signals from an actual ionospheric rocket experiment, and find a reasonably good agreement with the appropriate simulation results, demonstrating again that rocket data, obtained as those analyzed here, are unlikely to give an adequate representation of intermittent features of the low frequency ionospheric plasma turbulence for the given conditions

Notes on the integration of numerical relativity waveforms

A primary goal of numerical relativity is to provide estimates of the wave strain, $h$, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, $\psi_4$. Assuming Bondi gauge, transforming to the strain $h$ reduces to integration of $\psi_4$ twice in time. Integrations performed in either the time or frequency domain, however, lead to secular non-linear drifts in the resulting strain $h$. These non-linear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular non-linear drifts in the resulting strain.Comment: 23 pages, 10 figures, matches final published versio

Low-frequency electrostatic waves in the ionospheric E-region: a comparison of rocket observations and numerical simulations

International audienceLow frequency electrostatic waves in the lower parts of the ionosphere are studied by a comparison of observations by instrumented rockets and of results from numerical simulations. Particular attention is given to the spectral properties of the waves. On the basis of a good agreement between the observations and the simulations, it can be argued that the most important nonlinear dynamics can be accounted for in a 2-D numerical model, referring to a plane perpendicular to a locally homogeneous magnetic field. It does not seem necessary to take into account turbulent fluctuations or motions in the neutral gas component. The numerical simulations explain the observed strongly intermittent nature of the fluctuations: secondary instabilities develop on the large scale gradients of the largest amplitude waves, and the small scale dynamics is strongly influenced by these secondary instabilities. We compare potential variations obtained at a single position in the numerical simulations with two point potential-difference signals, where the latter is the adequate representation for the data obtained by instrumented rockets. We can demonstrate a significant reduction in the amount of information concerning the plasma turbulence when the latter signal is used for analysis. In particular we show that the bicoherence estimate is strongly affected. The conclusions have implications for studies of low frequency ionospheric fluctuations in the E and F regions by instrumented rockets, and also for other methods relying on difference measurements, using two probes with large separation. The analysis also resolves a long standing controversy concerning the supersonic phase velocities of these cross-field instabilities being observed in laboratory experiments

The Importance of Audit Firm Characteristics and the Drivers of Auditor Change in UK Listed Companies

This paper explores the importance of audit firm characteristics and the factors motivating auditor change based on questionnaire responses from 210 listed UK companies (a response rate of 70%). Twenty-nine potentially desirable auditor characteristics are identified from the extant literature and their importance elicited. Exploratory factor analysis reduces these variables to eight uncorrelated underlying dimensions: reputation/quality; acceptability to third parties; value for money; ability to provide non-audit services; small audit firm; specialist industry knowledge; non-Big Six large audit firm; and geographical proximity. Insights into the nature of 'the Big Six factor' emerge. Two thirds of companies had recently considered changing auditors; the main reasons cited being audit fee level, dissatisfaction with audit quality and changes in top management. Of those companies that considered change, 73% did not actually do so, the main reasons cited being fee reduction by the incumbent and avoidance of disruption. Thus audit fee levels are both a key precipitator of change and a key factor in retaining the status quo

Time-of-Arrival States

Although one can show formally that a time-of-arrival operator cannot exist, one can modify the low momentum behaviour of the operator slightly so that it is self-adjoint. We show that such a modification results in the difficulty that the eigenstates are drastically altered. In an eigenstate of the modified time-of-arrival operator, the particle, at the predicted time-of-arrival, is found far away from the point of arrival with probability 1/2.Comment: 15 pages, 2 figure