Effects Of Finite Resolution Research Articles

MEASURING THE CLUMP MASS FUNCTION IN THE AGE OF SCUBA2,HERSCHEL, AND ALMA

We use simulated images of star-forming regions to explore the effects of various image acquisition techniques on the derived clump mass function. In particular, we focus on the effects of finite image angular resolution, the presence of noise, and spatial filtering. We find that, even when the image has been so heavily degraded with added noise and lowered angular resolution that the clumps it contains clearly no longer correspond to pre-stellar cores, still the clump mass function is typically consistent with the stellar initial mass function within their mutual uncertainties. We explain this result by suggesting that noise, source blending, and spatial filtering all randomly perturb the clump masses, biasing the mass function toward a lognormal form whose high-mass end mimics a Salpeter power law. We argue that this is a consequence of the central limit theorem and that it strongly limits our ability to accurately measure the true mass function of the clumps. We support this conclusion by showing that the characteristic mass scale of the clump mass function, represented by the ``break mass'', scales as a simple function of the angular resolution of the image from which the clump mass function is derived. This strongly constrains our ability to use the clump mass function to derive a star formation efficiency. We discuss the potential and limitations of the current and next generation of instruments for measuring the clump mass function.

Analogues of Cores and Stars in Simulated Molecular Clouds

AbstractWe use images derived from collapsing, turbulent molecular cloud simulations without sinks to explore the effects of finite image angular resolution and noise on the derived clump mass function. These effects randomly perturb the clump masses, producing a lognormal clump mass function with a Salpeter-like high mass end. We show that the characteristic break mass of the simulated clump mass functions changes with the angular resolution of the images in a way that is entirely consistent with the observations. We also present some cautionary tales regarding sink particles and highlight the need to ensure that sinks actually correspond to distinct collapsing objects. We test several popular numerical sink criteria in the literature and compare to converged, non-sink results.

Reconstruction of spatial qutrit states based on realistic measurement operators

Spatial qudit states can be realized by using multislits to discretize the transverse momentum of a photon. The merit of this kind of spatial qudit states is that the implementation of higher-dimensional qudits is relatively easy. As we have recently shown, the quantum states of these spatial qudits can be analyzed by scanning a single interference pattern. This method of single scan tomography can also be applied at higher dimensions, but the reconstruction becomes more sensitive to smaller details of the scanned patterns as the dimensions increase. In this paper, we investigate the effect of finite measurement resolution on the single scan tomography of spatial qutrits. Realistic measurement operators describing the spatial resolution of the measurement are introduced and the corresponding pattern functions for quantum state reconstruction are derived. We use the pattern functions to analyze experimental results for entangled pairs of spatial qutrits generated by spontaneous parametric downconversion. It is shown that a reliable reconstruction of the quantum state can be achieved with finite measurement resolution if this limitation of the measurement is included in the pattern functions of single scan tomography.

The probabilistic data association filter

The measurement selection for updating the state estimate of a target's track, known as data association, is essential for good performance in the presence of spurious measurements or clutter. A classification of tracking and data association approaches has been presented, as a pure MMSE approach, which amounts to a soft decision, and single best-hypothesis approach, which amounts to a hard decision. It has been shown that the optimal state estimator in the presence of data association uncertainty consists of the computation of the conditional pdf of the state x(k) given all information available at time k, namely, the prior information about the initial state, the intervening known inputs, and the sets of measurements through time k. It has also been pointed out that if the exact conditional pdf, which is a mixture, is available, then its recursion requires only the probabilities of the most recent association events. The conditions under which this result holds, namely whiteness of the noise, detection, and clutter processes, were presented. The PDAF and algorithms, which carry out data association and state estimation in clutter, have been described. A simple example was given to illustrate how the clutter and occasional missed detections can lead to track loss for a standard tracking filter, and how PDAF can keep the target in track under such circumstances. By using the Monte Carlo in a simulated based surveillance as an exampled shown. The numerous applications of the PDAF/JPDAF illustrated in Real-World Applications of PDAF and JPDAF show the potential pitfalls of using sophisticated algorithms for tracking in difficult environments as well as how to overcome them. The effect of finite sensor resolution can be a more severe problem than the data association and deserves special attention.

Effect of Finite Spatial Resolution on the Turbulent Energy Spectrum Measured in the Coastal Ocean Bottom Boundary Layer

Abstract The effect of finite spatial resolution on the measured energy spectrum is examined via a parametric study using in situ particle image velocimetry (PIV) measurements performed in the bottom boundary layer on the Atlantic continental shelf. Two-dimensional (2D) box spatial filters of various scales are applied to the data, and these filtered distributions are used to compute 1D energy spectra in both frequency and wavenumber domains. It is found that energy levels are attenuated by more than 15% at all length scales that are smaller than 10 times the scale of the filter. Filtering both in the direction of the spectrum as well as perpendicular to it contributes to the extent of attenuation, the latter via implicit integration over all wavenumbers. At scales larger than that of the filter, Gaussian, nonlinear Butterworth, and median filters attenuate less energy than the box filter. When frequency spectra are converted using Taylor’s hypothesis, wave energy appears in wavenumber space at a location different than its true physical scale, which is much larger than the filter sizes. Consequently, wave energy is not attenuated and dominates over the turbulence through this spectral range. Because wave energy and turbulence respond differently to the filtering, modified spectral slopes at the transition between wave- and turbulence-dominated regions occur, resulting in inordinately steep spectral slopes. Finally, removal of the pressure-coherent part of the velocity signal is not sufficient to reveal the turbulence within the wave peak spectral range. Remaining energy in this range is still dominated by much larger scales.

Magnetic field intensification: comparison of 3D MHD simulations with Hinode/SP results

Recent spectro-polarimetric observations have provided detailed measurements of magnetic field, velocity and intensity during events of magnetic field intensification in the solar photosphere. We consider the temporal evolution of the relevant physical quantities for three cases of magnetic field intensification in a numerical simulation. We determine the evolution of the intensity, magnetic flux density and zero-crossing velocity derived from the synthetic Stokes parameters by taking into account the spectral and spatial resolution of the spectropolarimeter (SP) on board Hinode. The three events considered show a similar evolution: advection of magnetic flux to a granular vertex, development of a strong downflow, evacuation of the magnetic feature, increase of the field strength and the appearance of the bright point. We find that synthetic and real observations are qualitatively consistent and, for one of the cases considered, agree very well also quantitatively. The effect of finite resolution (spatial smearing) is most pronounced in the case of small features, for which the synthetic Hinode/SP observations miss the bright point formation and also the high-velocity downflows during the formation of the smaller magnetic features.

Resolution effects and scaling in numerical simulations of passive scalar mixing in turbulence

The effects of finite grid resolution on the statistics of small scales in direct numerical simulations of turbulent mixing of passive scalars are addressed in this paper. Simulations at up to 2048 3 grid points with grid spacing Δ x varied from about 2 to 1/2 Batchelor scales ( η B ) show that most conclusions on Schmidt number ( S c ) dependence from prior work at less stringent resolution remain qualitatively correct, although simulations at resolution Δ x ≈ η B are preferred and will give adequate results for many important quantities including the scalar dissipation intermittency exponent and structure functions at moderately high orders. For S c ≥ 1 , since η B = η S c − 1 / 2 (where η is the Kolmogorov scale), the requirement Δ x ≈ η B is more stringent than the corresponding criterion Δ x ≈ η for the velocity field, which is thus well resolved in simulations aimed at high Schmidt number mixing. A simple argument is given to help interpret the effects of Schmidt and Reynolds numbers on trends towards local isotropy and saturation of intermittency at high Schmidt number. The present results also provide evidence for a trend to isotropy at high Reynolds number with fixed S c = 1.0 . This is a new observation apparently not detected in less well resolved simulations in the past, and will require further investigation in the future.

Momentum dependence of the superconducting gap inBa1−xKxFe2As2

The precise momentum dependence of the superconducting gap in the iron-arsenide superconductor ${\text{Ba}}_{1\ensuremath{-}x}{\text{K}}_{x}{\text{Fe}}_{2}{\text{As}}_{2}$ (BKFA) with ${T}_{c}=32\text{ }\text{K}$ was determined from angle-resolved photoemission spectroscopy (ARPES) via fitting the distribution of the quasiparticle density to a model. The model incorporates finite lifetime and experimental resolution effects, as well as accounts for peculiarities of BKFA electronic structure. We have found that the value of the superconducting gap is practically the same for the inner $\ensuremath{\Gamma}$ barrel, $\mathrm{X}$ pocket, and ``blade'' pocket, and equals 9 meV, while the gap on the outer $\ensuremath{\Gamma}$ barrel is estimated to be less than 4 meV, resulting in $2\ensuremath{\Delta}/{k}_{B}{T}_{c}=6.8$ for the large gap and $2\ensuremath{\Delta}/{k}_{B}{T}_{c}l3$ for the small gap. A large $(77\ifmmode\pm\else\textpm\fi{}3\text{ }%)$ nonsuperconducting component in the photoemission signal is observed below ${T}_{c}$. Details of gap extraction from ARPES data are discussed in Appendixes A,B.

Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames

The effect of spatial averaging is important for scalar gradient measurements in turbulent nonpremixed flames, especially when the local dissipation length scale is small. Line imaging of Raman, Rayleigh and CO-LIF is used to investigate the effects of experimental resolution on the scalar variance and radial gradient in the near field of turbulent nonpremixed CH4/H2/N2 jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and B) and in piloted CH4/air jet flames at Reynolds numbers of 13,400, 22,400 and 33,600 (Sandia flames C/D/E). The finite spatial resolution effects are studied by applying the Box filter with varying filter widths. The resulting resolution curves for both scalar variance and mean squared-gradient follow nearly the same trends as theoretical curves calculated from the model turbulence kinetic energy spectrum of Pope. The observed collapse of resolution curves of mean squared-gradient for nearly all studied cases implies the shape of the dissipation spectrum is approximately universal. Fluid transport properties are shown to have no effect on the dissipation resolution curve, which implies that the dissipation length scale inferred from the square gradient is equivalent to the length scale for the scalar dissipation rate, which includes the diffusion coefficient. With the Box filter, the required spatial resolution to resolve 98% of the mean dissipation rate is about one−two times of the dissipation cutoff length scale (analogous to the Batchelor scale in turbulent isothermal flows). The effects of resolution on the variances of mixture fraction, temperature, and the inverted Rayleigh signal are also compared. The ratio of the filtered variance to the true variance is shown to depend nearly linearly on the probe resolution. The inverted Rayleigh scattering signal can be used to study the resolution effect on temperature variance even when the Rayleigh scattering cross section is not constant. The experimental results also indicate that these laboratory scale turbulent jet flames have small effective Reynolds numbers, such that there is some direct interaction of the large (energy containing) and small (dissipative) scalar length scales, especially for the near field case at x/d = 7.5 of the piloted Sandia flames C/D/E.

Corrections for underresolved scalar measurements in turbulent flows using a DNS database

We estimate the effect of finite spatial resolution of a probe for scalar measurements, using a database from direct numerical simulations (DNS). These are for homogeneous isotropic turbulence in temporal decay, Schmidt number unity, and low Taylor-microscale Reynolds number (≃27–42). The probe could be a cold wire for measuring temperature in a turbulent flow. Correction factors for the scalar variance, scalar dissipation rate, and mixed velocity-scalar derivative skewness are estimated, for a sensor length up to 15 times the Batchelor length scale. It is shown that the lack of resolution yields the largest attenuation on the dissipation rate, followed by the scalar variance. On the contrary, the mixed skewness, which is affected the least, is overestimated. Further, it is shown that if one estimates the mixed skewness via the scalar variance dynamical equation and neglects the term involving the time derivative of the scalar energy spectrum, large errors in the correction factor of the mixed skewness are introduced. Finally, it is found that correction factors obtained assuming Kraichnan scalar model spectrum and following Wyngaard (in Phys Fluids 14:2052–2054, 1971) approach are close to those from the DNS.

A system model for assessing scalar dissipation measurement accuracy in turbulent flows

A system model is developed to investigate independent and coupled effects of resolution, noise and data processing algorithms on the accuracy of the scalar gradient and dissipation measurements in turbulent flows. Finite resolution effects are simulated by spectral filtering, noise is modelled as an additive source in the model spectrum and differencing stencils are analysed as digital filters. In the current study, the effective resolution is proposed to be a proper criterion for quantifying the resolution requirement for scalar gradient and dissipation measurement. Both effective resolution and noise-induced apparent dissipation are mainly determined by the system transfer function. The finite resolution results, based upon a model scalar energy spectrum, are shown to agree with non-reacting experimental data. The coupled resolution-noise results show three regions in the mean scalar dissipation rate measurement: noise-dominated region, noise-resolution correlated region and resolution-dominated region. Different noise levels lead to different resolution error curves for the measured mean scalar dissipation rate. Experimental procedures and guidelines to improve the scalar gradient and dissipation experiments are proposed, based on these model study results. The proposed system approach can also be applied to other derived quantities involving complex transfer functions.

On the uncertainty of the mean of digitized measurements

Two equations relating to the effect of finite resolution on the uncertainty of a sample mean give the impression of being contradictory. One suggests that knowing the data to be digitized increases uncertainty while the other might be thought to imply the opposite. This issue is clarified and relevant concepts are discussed. This discussion leads to the development of a new approximation relating to the uncertainty of an estimate obtained by taking the mean of a set of digital measurement results. This result is consistent with others published recently in implying that resolution error can usually be ignored in such a situation. The solution to this problem obtained in a Bayesian analysis with the usual non-informative prior distribution is shown to give an inappropriate result when all the observations are equal and to exhibit anomalous behaviour in certain other circumstances. One of the appendices describes an estimator that has smaller mean-square error than the sample mean when averaging over the set of measurement problems of this type.

Spatial variations in the velocity field and real solar granulation

In this paper, the physical conditions within the inhomogeneous solar atmosphere have been reconstructed by means of solving the inverse problem of non-local thermodynamic equilibrium (NLTE) radiative transfer. The profiles of the λ= 523.42 nm Fe i spectral line of high spatial and time resolution were used as observational data. The velocity field has been studied for the real solar granulation in the superadiabatic layer and overshooting convection region. Also, we investigate the vertical structure of the inhomogeneous solar photosphere and consider the penetration of granules from the convective region into the upper layers of the stable atmosphere. The microturbulent velocity appears to be minimal at the bottom of the overshooting convection region and increases sharply through the superadiabatic layer and upper photosphere. High-turbulence layers emerge either in the central part of a flow or at the boundary of an incipient flow with subsequent drift towards the centre of the flow. Wide descending flows tend to disintegrate into structures having turbulence augmented and these structures correspond to the flows of matter. High microturbulence of the intensive flows provokes steep temperature depression in the upper photosphere leading to the second inversion of temperature for the intergranules. The inversion of vertical velocities is observed to be frequent in the solar granulation. Some of the convective flows reach the minimum temperature region. Vertical convective velocities of the matter flows are found to be smaller in the middle and upper photosphere. Also, the effect of finite resolution on spatial variations of the velocities in the solar photosphere has been estimated.

Spatial resolution and noise considerations in determining scalar dissipation rate from passive scalar image data

The effects of photonic shot noise and finite spatial resolution on the scalar dissipation rate were investigated for the analytical profile of a passive scalar layer subjected to a compressive strain, and the results were applied to interpret measured data from spray mixing data from an internal combustion engine. A Monte Carlo approach was employed. The measured scalar dissipation rate is underestimated, and the layer width measured at 20% of the peak height is overestimated by the finite resolution. The ratio of the local scalar spread value to the noise level, the spread-noise ratio, was found to describe the noise effects, which principally results in an overestimation of the scalar dissipation rate, especially at high resolution levels. The Nyquist resolution provides a good compromise between the sampling bias at low resolution and the noise bias at high resolution. Top hat filtering the raw data prior to calculation of the scalar dissipation rate was found to, effectively, reduce spatial resolution, whereas median filtering preserved the resolution. Both filters had a comparable effect on noise reduction. The evaluation of experimental data showed that a significant fraction of data reside at low spread-noise ratio and are biased by noise. The peak scalar dissipation rate is, however, not biased by noise and a method of estimating spatial resolution based on the peak scalar dissipation rate is described.

Modelling photo-detectors in quantum optics

Photo-detection plays a fundamental role in experimental quantum optics and is of particular importance in the emerging field of linear optics quantum computing. Present theoretical treatment of photo-detectors is highly idealized and fails to consider many important physical effects. We present a physically motivated model for photo-detectors which accommodates for the effects of finite resolution, bandwidth and efficiency, as well as dark counts and dead-time. We apply our model to two simple well-known applications, which illustrates the significance of these characteristics.

Apparent Fractal Dimensions in the HMF Model

We show that recent observations of fractal dimensions in the μ‐space of N‐body Hamiltonian systems with long‐range interactions are due to finite N and finite resolution effects. We provide strong numerical evidence that, in the continuum (Vlasov) limit, a set which initially is not a fractal (e.g., a line in 2D) remains such for all finite times. We perform this analysis for the Hamiltonian mean field (HMF) model, which describes the motion of a system of N fully coupled rotors. The analysis can be indirectly confirmed by studying the evolution of a large set of initial points for the Chirikov standard map.

Application of expectation maximization algorithms for image resolution improvement in a small animal PET system

Modern positron emission tomography (PET) systems, offering high counting rate capabilities, high sensitivity, and near-submillimeter coordinate resolution, require fast image reconstruction software that can operate on list-mode data and take into account most of finite resolution effects such as photon scattering, positron range in tissue, and detector features. It has already been demonstrated that the expectation maximization (EM) method with extended system matrix modeling looks very attractive for image resolution recovery in PET imaging studies. In this paper, the performance of EM-based algorithms (in particular, their ability to improve the image resolution) is evaluated for a small animal PET imager with several phantoms. The achievement of a substantial decrease in processing time using an EM deblurring procedure is shown, as is an approach to successfully treat what are essentially nonspace-invariant resolution effects within a shift-invariant model.

A Novel Single Base Station Location Technique for Microcellular Wireless Networks: Description and Validation by a Deterministic Propagation Model

Positioning algorithms in cellular networks has become increasingly important as a means of supporting emerging services that require a sufficiently precise estimation of the position of the mobile terminal (MT) associated with a given base station (BS). Currently, even the most sophisticated positioning algorithms require at least three BSs to achieve satisfactory precision. This paper presents a novel algorithm that makes use of a single-BS antenna array to locate MTs in cellular networks. A triangulation technique is utilized and supported by some minimal information about the environment in the BS neighborhood. This algorithm is shown to perform well when operating in a microcellular environment with perfect channel-parameter estimation. The effect of finite resolution of the input parameters is also investigated. The performance is analyzed for a universal mobile telecommunications system microcellular scenario through a three-dimensional deterministic channel model. Finally, the performance of the proposed positioning technique is compared to the well-known location method based on the time-of-arrival measurements at three different BSs.

Limits in wavelength measurement of optical signals

We determine the maximum accuracy in the wavelength measurement of finite-bandwidth optical signals. The limit is dependent on the spectral and coherence properties of the optical signal and on the available optical power. We also investigate the effect of finite measurement resolution in the wavelength measurement.

Assessing coherent feature kinematics in ocean models

We propose a method for comparing ocean models based on their ability to reproduce the kinematics associated with coherent features such as mesoscale eddies. Of particular focus is the reproduction of transport and mixing processes around the feature in question. The feature boundaries are represented by material curves, known as effective invariant manifolds, and the error in the location of the manifolds as manifest in different models is measured here in terms of separation area and distance between them. As part of the case for such a Lagrangian discriminant of ocean models, we show that, in reference to a Rossby wave, critical-layer kinematic model, an Eulerian error metric based on energy is insufficient to determine the proximity of vortex boundaries in different perturbations. The manifold comparison technique developed here is applied to a model double-gyre flow to analyze the effects of finite resolution and uncertainty in wind forcing. The results of the Lagrangian evaluation showed that, in the resolution experiments, the manifold accuracy correlates with the average Eulerian error ( L 2 norm of the velocity error field). However, for the models with modulated wind forcing, the Eulerian error was found to be an inadequate indicator of the quality of transport predictions.