Three-dimensional Density Field Research Articles

Recovering the topology of the intergalactic medium at z∼ 2

We investigate how well the three-dimensional density field of neutral hydrogen in the intergalactic medium (IGM) can be reconstructed using the Lyman α absorptions observed along lines-of-sight to quasars separated by arcmin distances in projection on the sky. We use cosmological hydrodynamical simulations to compare the topologies of different fields: dark matter, gas and neutral hydrogen optical depth and to investigate how well the topology of the IGM can be recovered from the Wiener interpolation method implemented by Pichon et al. The global statistical and topological properties of the recovered field are analysed quantitatively through the power spectrum, the probability distribution function (PDF), the Euler characteristics, its associated critical point counts and the filling factor of underdense regions. The local geometrical properties of the field are analysed using the local skeleton by defining the concept of interskeleton distance. As a consequence of the nearly lognormal nature of the density distribution at the scales under consideration, the tomography is best carried out on the logarithm of the density rather than the density itself. At scales larger than ∼1.4 〈dLOS〉, where 〈dLOS〉 is the mean separation between lines-of-sight, the reconstruction accurately recovers the topological features of the large-scale density distribution of the gas, in particular the filamentary structures: the interskeleton distance between the reconstruction and the exact solution is smaller than 〈dLOS〉. At scales larger than the intrinsic smoothing length of the inversion procedure, the power spectrum of the recovered H i density field matches well that of the original one and the low-order moments of the PDF are well recovered as well as the shape of the Euler characteristic. The integral errors on the PDF and the critical point counts are indeed small, less than 20 per cent for a mean line-of-sight separation smaller than ∼2.5 arcmin. The small deviations between the reconstruction and the exact solution mainly reflect departures from the lognormal behaviour that are ascribed to highly non-linear objects in overdense regions.

Three-dimensional analysis of collective relativistic electron motion and coherent harmonic generation driven by an intense pulsed Gaussian beam

Collective electron motion driven by intense laser pulses can become highly nonlinear as results of the $\mathbf{v}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ term in the Lorentz force and the relativistic mass increase effect. These nonlinear effects are the bases of many nonlinear phenomena in high-field physics. Using paraxial expansion we analyzed the three-dimensional collective relativistic motion of electrons driven by an intense pulsed Gaussian beam. We solved the three-dimensional velocity field and density field of the electrons, as well as the scalar potential field resulting from the electron density modulation, in terms of the vector potential of the laser pulse in the highly relativistic regime. From the solutions we derived an analytical expression for the nonlinear oscillation of the electric current density. The results are applied to a systematical analysis of coherent relativistic harmonic generation as a demonstration of the applications. Extensive comparison with published experimental data is made, and the remarkable agreement provides a strong support to the analysis presented in this paper.

Dark energy and curvature from a future baryonic acoustic oscillation survey using the Lyman-αforest

We explore the requirements for a Lyman-$\ensuremath{\alpha}$ forest survey designed to measure the angular diameter distance and Hubble parameter at $2\ensuremath{\lesssim}z\ensuremath{\lesssim}4$ using the standard ruler provided by baryonic acoustic oscillations (BAO). The goal would be to obtain a high enough density of sources to probe the three-dimensional density field on the scale of the BAO feature. A percent-level measurement in this redshift range can almost double the Dark Energy Task Force figure of merit, relative to the case with only a similar precision measurement at $z\ensuremath{\sim}1$, if the Universe is not assumed to be flat. This improvement is greater than the one obtained by doubling the size of the $z\ensuremath{\sim}1$ survey, with Planck and a weak Sloan Digital Sky Survey-like $z=0.3$ BAO measurement assumed in each case. Galaxy BAO surveys at $z\ensuremath{\sim}1$ may be able to make an effective $\mathrm{Ly}\ensuremath{\alpha}$ forest measurement simultaneously at minimal added cost, because the required number density of quasars is relatively small. We discuss the constraining power as a function of area, magnitude limit (density of quasars), resolution, and signal-to-noise of the spectra. For example, a survey covering 2000 sq. deg. and achieving $S/N=1.8$ per \AA{} at $g=23$ ($\ensuremath{\sim}40\text{ }\text{ }\mathrm{quasars}$ per sq. deg.) with an $R\ensuremath{\gtrsim}250$ spectrograph is sufficient to measure both the radial and transverse oscillation scales to 1.4% from the $\mathrm{Ly}\ensuremath{\alpha}$ forest (or better, if fainter magnitudes and possibly Lyman-break galaxies can be used). At fixed integration time and in the sky-noise-dominated limit, a wider, noisier survey is generally more efficient; the only fundamental upper limit on noise being the need to identify a quasar and find a redshift. Because the $\mathrm{Ly}\ensuremath{\alpha}$ forest is much closer to linear and generally better understood than galaxies, systematic errors are even less likely to be a problem.

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005).

The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field

Three-dimensional density information of a double free air jet was acquired using optical tomography. The projections of the density field were measured using the background oriented schlieren method (BOS). Preceding the free jet measurements, the sensitivity, accuracy and resolution of the BOS method were investigated. The sensitivity depends mostly on the focal length of the lens used, the relative position of the object between camera and background and the smallest detectable shift in the image plane. The accuracy was found to be sufficiently high to apply a tomographic reconstruction process. The resolution is determined by the transfer function of the BOS-method. It is not constant and depends on the size of the interrogation windows used for the cross-correlation-algorithm. The reconstruction of the free jet was computed, using filtered back projection. The reconstructed 3D density field shows with good resolution the typical diamond structure of the density distribution in under-expanded free jets.

Analysis of Simultaneous Velocity and Density Distributions for High-Speed CO<sub>2</sub> Flow Using Particle Image Velocimetry and Digital Speckle Tomography

Velocity and density distributions of a high-speed and initial CO2 jet flow have been analyzed simultaneously by a developed three-dimensional digital speckle tomography and a particle image velocimetry (PIV). Three high-speed cameras have been used for the tomography and the PIV since a shape of a nozzle for the jet flow is asymmetric and the initial flow is fast and unsteady. The speckle movements between no flow and CO2 jet flow have been obtained by a cross-correlation tracking method so that those distances can be transferred to deflection angles of laser rays for density gradients. The three-dimensional density fields for the high-speed CO2 jet flow have been reconstructed from the deflection angles by the real-time tomography method, and the two-dimensional velocity fields have been calculated by the PIV method simultaneously.

The Irish coastal current: A seasonal jet-like circulation

During 25 July–3 August 2001 a comprehensive cruise was undertaken along the western coast of the Republic of Ireland to resolve the three-dimensional density field and circulation. Towed undulating CTD revealed the strong thermocline beyond the 60 m contour with more diffuse stratification inshore. Argos drifters deployed in the late summer of 1999, 2000 and 2001 demonstrated strongly northward flow, their motion was uncorrelated with wind forcing but was consistent with the predicted geostrophic currents generated by the bottom fronts intersecting the seabed. These flows were evident in the data from the vessel mounted 153.6 kHz acoustic Doppler current profiler (ADCP) although the jets are relatively narrow (15–20 km). This region is heavily influenced by storm events and Atlantic influence with high salinity contributing to strong vertical and horizontal density gradients particularly in the south of the region. However, the seasonal heating cycle coupled with tidal mixing is the dominant force of buoyancy production that ensures that the frontal features occur every year. In combination with similar features found in the Celtic Sea [Brown, J., et al., 2003. Observations of the physical structure and seasonal jet-like circulation of the Celtic Sea and St. George's Channel of the Irish Sea. Continental Shelf Research 23, 533–561] these observations demonstrate the existence of a continuous pathway in summer from the north Cornish coast to Malin Head with average residual velocities >7.5 cm s −1. The data set described here provides the necessary basis for environmental management and knowledge of the pathway for contaminants, the dynamics of nutrients and an understanding of the movement of larvae and juvenile fish, in a geographic location that had previously been little studied.

Interstellar cloud structure: the statistics of centroid velocities

The investigation of the statistical properties of maps of line centroids has been used for almost 50 years, but there is still no general agreement on their interpretation. We try to quantify which properties of underlying turbulent velocity fields can be derived from centroid velocity maps, and we test conditions under which the scaling behaviour of the centroid velocities matches the scaling of the three-dimensional velocity field. Using fractal cloud models we study systematically the relation between three-dimensional density and velocity fields and the statistical properties of the produced line centroid maps. We put special attention to cases with large density fluctuations resembling supersonic interstellar turbulence. Starting from the Delta-variance analysis we derive a new tool to compute the scaling behaviour of the three-dimensional velocity field from observed intensity and centroid velocity maps. We provide two criteria to decide whether the information from the centroid velocities directly reflects the properties of the underlying velocity field. Applying these criteria allows to understand the different results found so far in the literature on the interpretation of the statistics of velocity centroids. A new iteration scheme can be used to derive the three-dimensional velocity scaling from centroid velocity maps for arbitrary density and velocity fields, but it requires an accurate knowledge of the average density of the considered interstellar cloud.

Upscaling heterogeneity in aquifer reactivity via exposure-time concept: Forward model

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.

C 2-ray: A new method for photon-conserving transport of ionizing radiation

We present a new numerical method for calculating the transfer of ionizing radiation, called C 2-ray (conservative, causal ray-tracing method). The transfer of ionizing radiation in diffuse gas presents a special challenge to most numerical methods which involve time- and spatial-differencing. Standard approaches to radiative transport require that grid cells must be small enough to be optically-thin while time steps are small enough that ionization fronts do not cross a cell in a single time step. This quickly becomes prohibitively expensive. We have developed an algorithm which overcomes these limitations and is, therefore, orders of magnitude more efficient. The method is explicitly photon-conserving, so the depletion of ionizing photons by bound-free opacity is guaranteed to equal the photoionizations these photons caused. As a result, grid cells can be large and very optically-thick without loss of accuracy. The method also uses an analytical relaxation solution for the ionization rate equations for each time step which can accommodate time steps which greatly exceed the characteristic ionization and ionization front crossing times. Together, these features make it possible to integrate the equation of transfer along a ray with many fewer cells and time steps than previous methods. For multi-dimensional calculations, the code utilizes short-characteristics ray tracing. The method scales as the product of the number of grid cells and the number of sources. C 2-ray is well-suited for coupling radiative transfer to gas and N-body dynamics methods, on both fixed and adaptive grids, without imposing additional limitations on the time step and grid spacing. We present several tests of the code involving propagation of ionization fronts in one and three dimensions, in both homogeneous and inhomogeneous density fields. We compare to analytical solutions for the ionization front position and velocity, some of which we derive here for the first time. As an illustration, we apply C 2-ray to simulate cosmic reionization in three-dimensional inhomogeneous cosmological density field. We also apply it to the problem of I-front trapping in a dense clump, using both a fixed and an adaptive grid.

Analysis of density distribution for unsteady butane flow using three-dimensional digital speckle tomography

Transient and asymmetric density distributions have been investigated by three-dimensional digital speckle tomography. Multiple CCD images captured movements of speckles in three angles of view simultaneously because the flows were asymmetric and transient. The speckle movements between no flow and downward butane flow from a circular half opening have been calculated by a cross-correlation tracking method so that those distances can be transferred to deflection angles of laser rays for density gradients. The three-dimensional density fields have been reconstructed from the deflection angles by a real-time multiplicative algebraic reconstruction technique (MART).

Direct Observations of Along-Isopycnal Upwelling and Diapycnal Velocity at a Shelfbreak Front*

Abstract By mapping the three-dimensional density field while simultaneously tracking a subsurface, isopycnal float, direct observations of upwelling along a shelfbreak front were made on the southern flank of Georges Bank. The thermohaline and bio-optical fields were mapped using a towed undulating vehicle, and horizontal velocity was measured with a shipboard acoustic Doppler current profiler. A subsurface isopycnal float capable of measuring diapycnal flow past the float was acoustically tracked from the ship. The float was released near the foot of the shelfbreak front (95–100-m isobath) and moved 15 km seaward as it rose from 80 to 50 m along the sloping frontal isopycnals over a 2-day deployment. The float's average westward velocity was 0.09 m s−1, while a drifter drogued at 15 m released at the same location moved westward essentially alongfront at 0.18 m s−1. The float measured strong downward vertical velocities (in excess of 0.02 m s−1) associated with propagation of internal tidal solibores in the onbank direction from their formation near the shelf break. The float measured large upward vertical velocities (in excess of 0.001 m s−1 ≃ 100 m day−1) as the pycnocline rebounded adiabatically after the passage of the internal tide solibore. The directly measured mean along-isopycnal vertical velocity was 17.5 m day−1. Intense mixing events lasting up to 2 hours were observed in the shelfbreak front at the boundary between cold, fresh shelf water and warm, salty slope water. Diapycnal velocities of up to 3 × 10−3 m s−1 were measured, implying a diapycnal thermal diffusivity as large as 10−2 m2 s−1, indicative of strong mixing events in this coastal front.

On the Use of Fractional Brownian Motion Simulations to Determine the Three‐dimensional Statistical Properties of Interstellar Gas

Based on fractional Brownian motion (fBm) simulations of three-dimensional gas density and velocity fields, we present a study of the statistical properties of spectroimagery observations (channel maps, integrated emission, and line centroid velocity) in the case of an optically thin medium at various temperatures. The power spectral index ?W of the integrated emission is confirmed to be that of the three-dimensional density field (?n) provided that the medium's depth is at least of the order of the largest transverse scale in the image, and the power spectrum of the centroid velocity map is found to have the same index ?C as that of the velocity field (?v). Further tests with non-fBm density and velocity fields show that this last result holds and is not modified by the effects of density-velocity correlations. A comparison is made with the theoretical predictions of Lazarian & Pogosyan.

Calculation of three-dimensional electromagnetic force field during arc welding

Electromagnetic force is an important driving force for convection in the weld pool during arc welding. Accurate calculation of the electromagnetic force field requires complex numerical calculations of three-dimensional current density and magnetic flux fields. Several simplifying assumptions have been suggested to avoid the complex calculations. The resulting analytical expressions for the electromagnetic force field have been widely used without any critical evaluation of their intrinsic merit, since accurate numerical calculations were difficult in the past because of lack of fast computers. A numerical model has been developed to accurately calculate the current density and magnetic flux fields and the resulting electromagnetic force field in three dimensions in the entire weldment. The model can take into account any current distribution on the work piece surface and evaluate the effects of different arc locations and work piece geometry on the electromagnetic force field. Contributions of the electrode current, arc plasma, and current distribution inside the three-dimensional work piece to the magnetic field and the electromagnetic force field are determined. The electromagnetic force field computed from the model is compared with those obtained from the commonly used simplified expressions of electromagnetic force to examine the accuracy of the commonly used simplifying assumptions. The accuracy of the computed electromagnetic force field can be significantly improved by using the proposed numerical model.

Observations of the physical structure and seasonal jet-like circulation of the Celtic Sea and St. George's Channel of the Irish Sea

During July–September 1998 a comprehensive survey was undertaken of the Celtic Sea and St. George's Channel of the Irish Sea in order to resolve the three-dimensional density field and circulation. Towed undulating CTD data revealed that isolated below the seasonal thermocline was a dense (cold and saline) pool flanked by strong near-bed density gradients. The trajectories of 23 satellite-tracked Argos drifters demonstrated the existence of a cyclonic (anti-clockwise) circulation pattern. This was in accord with persistent and narrow (ca. 20 km) cores of cyclonic flow (dense water to the left) as revealed by geostrophic current estimates and moored acoustic Doppler current profiler data, with velocities >0.1 m s −1 and exceeding 0.3 m s −1 in St. George's Channel. The results are consistent with a seasonal baroclinic circulation that advects saline Atlantic water through the south and west of the region to St. George's Channel. Westward flow across St. George's Channel is directed south into the Celtic Sea and west along the Irish coast. The southward flow, an artefact of the baroclinic circulation, often appears in infrared satellite imagery as a meander in the Celtic Sea front. At the southward extension a secondary clockwise circulation is formed (diameter∼40 km) before water joins westward flow. Fresher water of coastal origin, present in the northern Celtic Sea in late spring, is advected westward by the summer circulation. The advent of summer thermal stratification and associated flow fields reduces exchange between the Celtic and Irish Seas. The understanding provided by such datasets such as those described here provides the necessary basis for environmental management and knowledge of the pathways for contaminants, the dynamics of nutrients and an understanding of the movement of larvae and juvenile fish. It also provides a template against which to test the prognostic capabilities of present and emerging baroclinic numerical models.

Numerical simulation of the inner structure of a two-phase plume formed in a stratification environment

The inner structure of a two-phase plume, driven by air bubble buoyancy and formed in a stratification ambient fluid in a rectangular tank, is numerically simulated by means of two-phase flow theory and Large-eddy simulation technology. Focusing on the discrete nature of the buoyant dispersed phase and on the role of momentum exchange between two phases during plume formation, we investigated the phenomena of mass "entraining-in" and "peeling-out" that occurs inside the stratified ambient plume. These phenomena are thought to result from an intricate interplay among phase interaction, static stability of the stratification ambient fluid itself, and dynamic stability due to turbulence. Numerical simulations show that there exists an inner-out structure of the stratified ambient plume, while at the same time predicting that the re-entraining-in mass flux is on the same order of magnitude as that of the inner peeling-out mass flux within the annular region centered around the plume. This further explains the mechanism underlying the formation of multi-scale eddies at the edge of the air bubble plume, which also constitutes the boundary between the inner and outer zones of this inner-out stratified fluid plume. Within the inner part of the plume, the mass entraining-in and peeling-out appeared as a spatial discontinuity. The numerically visualized three-dimensional density fields are consistent with the two-phase plume characteristics.

An electrically conducting sphere in a three-dimensional, alternating magnetic field

The electrical vector and scalar potential as well as the underlying induced eddy current density of a conducting sphere exposed to an external, time-varying magnetic field are calculated. The external magnetic field is assumed to be generated by sinusoidally alternating current density distributions. Admitting arbitrary three-dimensional current density fields, this paper extends previous results on this subject. Among other things, these calculations prove that in a sphere there is no radial component of the induced eddy current density field. As an application of these results the impedance and power absorption of the sphere are derived. The impedance is the key for the contactless, inductive measurement of the electrical conductivity of metallic melts.

Numerical visualization of two-phase plume formation in a stratification flow environment.

Evolution of two-phase plumes driven by air bubble buoyancy in a stratification ambient in a rectangular tank is visualized numerically by means of two-phase flow theory and large-eddy simulation technology. With a focus on the discrete nature of the buoyant dispersed phase and the role of momentum exchange between two phases in plume formation, we investigated the phenomena of mass entraining-in and peeling-out for continuous phase plume, which may result from a complicated and intricate interplay with phase interaction and dynamic stability of the stratification ambient, respectively. Numerical simulations show that although mass entraining-in and peeling-out appear to be distinguished entirely in the vertical direction, they interact or couple locally within inner of the plume and present a discontinuity in nature. The numerically visualized three-dimensional density field also indicates the same plume characteristics.

Maximum Entropy Reconstruction of the Interstellar Medium. I. Theory

We have developed a technique to map the three-dimensional structure of the local interstellar medium using a maximum entropy reconstruction technique. A set of column densities to stars of known distance can in principle be used to recover a three-dimensional density field , since the two quantities are related by simple geometry through the equation = , where is a matrix characterizing the stellar spatial distribution. In practice, however, there are an infinite number of solutions to this equation. We use a maximum entropy reconstruction algorithm to find the density field containing the least information which is consistent with the observations. The solution obtained with this technique is, in some sense, the model containing the minimum structure. We apply the algorithm to several simulated data sets to demonstrate its feasibility and success at recovering "real" density contrasts. This technique can be applied to any set of column densities whose endpoints are specified. In a subsequent paper we shall describe the application of this method to a set of stellar color excesses in order to derive a map of the dust distribution and to soft X-ray absorption columns to hot stars in order to derive a map of the total density of the interstellar medium.

B207 Digital Specklegram Tomography for Reconstruction of Transient Three-Dimensional Density Distributions

Transient and asymmetric density distributions have been investigated by digital specklegram tomography. Multiple CCD images captured movements of speckles in three angles of view simultaneously because the flows were asymmetric and transient. The speckle movements between no flow and downward carbon dioxide flow from a circular small opening with a vertical partition have been calculated by a cross-correlation tracking method so that those distances can be transferred to deflection angles of laser rays for density gradients. The transient three-dimensional density fields have been reconstructed from the deflection angles by a tomography method.