Internal Density Gradients Research Articles

Neutron phase contrast imaging of PbWO4 crystals for G experiment test masses using a Talbot-Lau neutron interferometer

The use of transparent test/source masses can benefit future measurements of Newton’s gravitational constant G. Such transparent test mass materials can enable nondestructive, quantitative internal density gradient measurements using optical interferometry and allow in-situ optical metrology methods to be realized for the critical distance measurements often needed in a G apparatus. To confirm the sensitivity of such optical interferometry measurements to internal density gradients it is desirable to conduct a check with a totally independent technique. We present an upper bound on possible internal density gradients in lead tungstate (PbWO4) crystals using a Talbot-Lau neutron interferometer on the Cold Neutron Imaging Facility at NIST. We placed an upper bound on a fractional atomic density gradient in two PbWO4 test crystals of cm−1. This value is about two orders of magnitude smaller than required for G measurements. We discuss the implications of this result and of other nondestructive methods for characterization of internal density inhomogeneties which can be applied to test masses in G experiments.

Imaging of PbWO4 crystals for G experiment test masses using a laser interferometer

It is highly desirable for future measurements of Newton’s gravitational constant G to use test/source masses that allow nondestructive, quantitative internal density gradient measurements. High density optically transparent materials are ideally suited for this purpose since their density gradient can be measured with laser interferometry, and they allow in-situ optical metrology methods for the critical distance measurements often needed in a G apparatus. We present an upper bound on possible internal density gradients in lead tungstate (PbWO4) crystals determined using a laser interferometer. We placed an upper bound on the fractional atomic density gradient in two PbWO4 test crystals of cm−1. This value is more than two orders of magnitude smaller than what is required for G measurements. They are also consistent with but more sensitive than a recently reported measurements of the same samples, using neutron interferometry. These results indicate that PbWO4 crystals are well suited to be used as test masses in G experiments. Future measurements of internal density gradients of test masses used for measurements of G can now be conducted non-destructively for a wide range of possible test masses.

How does three-dimensional canopy geometry affect the front propagation of a gravity current?

Large-eddy simulations are performed to investigate how three-dimensional canopy geometry affects the front propagation of an incoming gravity current under a given initial forcing. A regular array of rigid square cylinders are used to represent the distributed canopy elements. It is shown that the conventional geometrical parameter of submerged canopies in constant-density flows (ah, where a is the frontal area per canopy volume and h is the canopy height) is misleading when applied to buoyancy-driven flows due to the additional complexity arising from the internal density gradients. Instead, the present study suggests a new geometrical framework consisting of a canopy density (ϕ) and a canopy-to-current height ratio (h̃), which can jointly provide an unambiguous description of the state of the current–canopy interaction. Two propagation regimes of the gravity current are identified, either along the channel bed (through-flow) or above the canopy’s top boundary (over-flow). Our analysis reveals that ϕ and h̃ counteract each other’s effect on the transition of flow regimes. Large ϕ implies a strong suppression of horizontal advection within the canopy and thus promotes the through-to-over flow transition; in contrast, large h̃ tends to promote the over-to-through flow transition due to the lack of sufficient potential energy to overcome the height jump. The end product is a complex variation pattern of a propagation regime and front velocity in the two-dimensional ϕ–h̃ parameter space.

Electromotive force in strongly compressible magnetohydrodynamic turbulence

Fully compressible magnetohydrodynamic (MHD) turbulence is investigated in the framework of the multiple-scale direct-interaction approximation. With the aid of the propagators (correlation and Green’s functions), fluctuating fields are solved, and turbulent correlations are estimated in highly compressible turbulence. We focus on the expression of the turbulent electromotive force (EMF). Obliqueness between the mean magnetic field and the mean-density gradient, the mean internal density gradient and the non-equilibrium mean velocity contributes to the EMF in the presence of the density variance, which is ubiquitous in turbulence in strongly variable density flows such as the shock-front region. This density-variance effect is expected to locally enhance the turbulence intensity across the shock front, leading to a fast reconnection.

Combination of shape and X-ray inspection for apple internal quality control: in silico analysis of the methodology based on X-ray computed tomography

Multisensor inspection allows for inline detection of internal defects of products with variable shapes, such as fruit and vegetables, by combining X-ray radiography with 3D shape recognition and modelling. For products with a complex internal structure such as apple fruit, inspection must also account for the corresponding internal density gradients that can affect X-ray radiographic images. Apple fruit consist of different tissues with spatially varying differences and gradients in porosity, resulting in corresponding density gradients. Development of internal browning disorders during storage of apples result in damage to tissue structure and associated changes of density distribution. In this paper, a method is developed and evaluated to account for density gradients in apple to improve detection success of defected apples. Experiments were conducted with 26 ‘Braeburn’ apples that were subjected to storage conditions in which internal browning develops. X-ray CT images of each apple were taken at 5 time points over a period of 9 months to obtain a reference dataset of 130 apples with varying levels of defects that could be accurately characterized. The fruit were additionally subjected to multisensory inspection. Using the images of healthy fruit, an internal density distribution model was created and used in the image processing pipeline of the proposed technique to correct for internal gradients. Accounting for a non-uniform internal density distribution increased the R2adj value from 0.73 to 0.86 for prediction of the degree of browning in a fruit. A receiver operator characteristic analysis found that accounting for non-uniform samples reduced the number of false positives from 14 to 5% at a true positive rate of 90%. It was demonstrated that the multisensor inspection approach requires relatively simple hardware of combined with prior knowledge in the form of a statistical shape model and associated density distribution. It is also flexible, since no specific segmentation and detection methods have to be developed for different types of defects.

Spreading of sediment due to underwater blasting and dredging: Field observations from quay construction in Sisimiut, Greenland

The primary objectives of this study were to quantify the spreading of suspended sediment from underwater blasting and subsequent dredging of bedrock and to understand the physical processes governing the spreading of suspended sediment due to underwater blasting. The investigations were carried out in connection with the construction of a new quay at the existing harbour of Sisimiut, Greenland. Subsequent to the largest of a series of underwater blasts, the distribution of suspended sediment in the water column at and around the construction site was observed using a CTD (Conductivity, Temperature, Depth) equipped with a turbidity meter. The observations show that sediment was brought into suspension near the surface and at internal density gradients in the water column, where it became subject to prevailing flow conditions. The observations further show what was probably a turbidity current, flowing down the steeply sloping seabed away from the construction site. The spreading of sediment due to this turbidity current could not be assessed, but could have been considerable. Observations made using sediment traps over much of the period of construction show that the total spreading of sediment was roughly the same for blasting of bedrock and dredging of the blasted material and that much of the sediment that was brought into suspension settled near the construction site. Furthermore, these observations indicate that blasting leads to a wider spreading of sediment, but that dredging leads to a wider spreading of the organic part of the sediment. Almost all material less than 2 μm, including surficial clay minerals and much organic material, was transported away from the construction site and its vicinity, which could imply mobilization and export of pollutants. Environmental impacts of suspended sediment from underwater blasting, which could include coverage of the benthos or increased turbidity, can be managed by timing the blast favourably relative to currents, waves and stratification. It is argued that the environmental impact of blasting can be minimized by decreasing or maybe even increasing the spreading of sediment, depending on, e.g., the resilience of the flora and fauna and the surficial sediment and the pollution therein.

Ichnofossil morphology as a response to resource distribution: Insights from modern invertebrate foraging

A number of surficial horizontal ichnofossils have non-random, simple geometric morphologies such as spirals or meanders. These paths may result from an organism's interactive response to the perceived spatial distribution of resources on the seafloor. This hypothesis was tested by examining the movements of foraging invertebrates in response to the location, shape and internal density gradient of food patches in a controlled laboratory environment. Freshwater pond snails ( Planorbis planorbis), marine intertidal crabs ( Hemigrapsus nudus) and microscopic soil nematodes ( Caenorhabditis elegans) were placed in experimental arenas free of competitors and containing food patches of varying shapes and density distributions, and allowed to move and forage freely. Their movements were recorded at 1-minute intervals, and any visible tracks and trails were photographed. Pathways were digitally reconstructed using the recorded movement data, and along with the photographs were digitally analyzed. The total path length, path tortuosity, polygon area, step number, average step length and average turning radius within the resource patches were compared to the values for movement outside the resource patches. All three invertebrates engaged in area-restricted searching when within patches, consisting of a larger step number, higher path tortuosity, larger polygon area, greater turning radius, and a shorter step length. The behavior of these three invertebrate species suggests that resource distribution, in terms of patch morphology, acts as a strong control on forager movement and path morphology. Area-restricted searching as a distinct movement style may have evolved in response to the appearance of patchy resource distributions on the seafloor during the Cambrian substrate revolution.

Topography on the D′′ region from analysis of a thin dense layer beneath a convecting cell

In this study, we examine the development of topography on a thin dense layer at the base of the lower mantle. The effect of the convecting mantle above is represented as a traction acting on the upper surface of the layer. Topography on the layer boundaries is predicted by a balance of dynamic flow stress and external traction. The nature of boundary topography depends on the magnitude of the driving tractions and the density variation within the layer. If we assume that the layer density is greatest beneath areas of mantle downwelling and decreases to a minimum beneath areas of mantle upwelling (the layer is thermally coupled to the convection in the overlying mantle) then its upper boundary develops a cusp-like peak beneath the upwelling mantle. The height of this peak is potentially much greater than the layer thickness. If, however, the layers are effectively coupled by viscous shear then internal density gradients of the opposite sign may be established. In this case, we observe solutions where the layer is completely swept away beneath areas of mantle downwelling leaving steep-sided ‘islands’ of dense material. This mechanism therefore provides a possible explanation for steep-sided anomalously slow regions at the base of the mantle observed by seismic methods (e.g. beneath south Africa) or for discrete ultralow velocity zones detected at the core–mantle boundary beneath locations of surface hotspots. The magnitude of the upper boundary driving tractions compared to the density gradient within the layer is the key parameter that determines the nature of flow in, and consequently boundary topography of, the layer. The deflection of the core–mantle boundary is small compared with that of the top of the dense layer, but a change in sign of the ratio of these deflections is observed as the magnitude of the driving tractions changes relative to the magnitude of the internal density gradient. We compare seismic measurements of core–mantle boundary topography and D′′ topography with the predictions of this model in an attempt to constrain model parameters, but no clear correlation seems to exist between D′′ thickness and CMB topography.

The growth and structure of double-diffusive cells adjacent to a cooled sidewall in a salt-stratified environment

Observations and measurements are reported on the patterns and rates of growth in time of the double-diffusive cells that form adjacent to a cooled sidewall in a salt-stratified environment. Fluid near the wall is cooled and sinks a distance h where its density, increased by cooling, matches that of the salt-stratified ambient. The fluid separates from the wall, moving outwards as a cool, fresher layer beneath a warmer, more saline region. This leads to growing double-diffusive cells that advance outward at a rate, found by dimensional reasoning, to initially be proportional to N(0)h, where N-0 is the initial buoyancy frequency in the ambient and h is the intrusion's vertical thickness. Near the wall at the top of each cell, the sinking colder fluid is continually replaced by selective withdrawal from the ambient 'far field'. The fluid being withdrawn from the ambient is always the least dense in the cell, and as the experiment proceeds, the straining of the fluid in the ambient region reduces the stratification. The vertical density gradient inside the cell relaxes by continuous hydrostatic adjustment (CHA) to match the ambient and the speed of advance reduces. Measurements of the rate of advance of the cell nose were made in tanks of different lengths L with a range of initial salinity gradients and temperature differences. A simple two-dimensional model is developed to describe the rate of extension of the cells and the internal density gradient as functions of time in which the tank length appears as an important variable. This effect does not seem to have been recognized previously. The rates of evolution in each run involve the time scale tau = L/(C(H)hN(0)), where C-H approximate to 10(-2) is a heat transfer coefficient. The mean length of the cells (l) over bar (t) and the internal buoyancy frequency as functions of time are given by(l) over bar (t)/L = t/tau - (t/2tau)(2), N = N-0(1 - t/2tau).Inversion of the first of these expressions results in t/tau = 2 - 2{1 - ((l) over bar (t)/L)}(1/2) from which a time scale tau(-1) can be estimated. The measurements from individual runs when plotted in this way generally produce accurate straight lines as the model predicts, from which C-H is found. This should be approximately the same for each run; the mean over all runs was found to be 9.3 x 10(-3) with standard deviation 2.4 x 10(-3). The velocity scale of the intrusions at the beginning of an experiment is of order 10(-2) cm s(-1), for typical parameters of water at temperature 20 degreesC, cooled wall temperature of 0 degreesC and mean salinity of 5%.

Density gradients and springback: environmental influences

Laser dilatometry was combined with X-ray computed tomography (XRCT) to investigate the relationship between springback and internal density gradients in dry-pressed alumina compacts. Compacts were prepared using the same binder and binder content but different states of plasticization to examine these effects on dimensions and final density distribution. Both density gradients and microstructural-level characteristics exert control over differential springback behavior; the expansion of the low-density (LD) zone is larger than that of the high-density (HD) zone. For these submicron alumina powders, the concentration of binder associated with density gradients leads to potential loss of final dimensional tolerance. A sinusoidal dimensional response, dependent upon the state of the binder, is noted, which changes dramatically with time and environmental exposure. In some cases, dimensional changes occurred due to moisture absorption/desorption in compacts prepared at relative humidities different from ambient conditions.

Effect of the stratified ocean of the core upon the Chandler wobble

It is supposed that a stably stratified layer exists at the top of the fluid core; we call it the stratified ocean of the core (SOC). The assumed model of the SOC has a sharp density drop at the boundary with the bulk of the core, and a uniform internal density gradient. The influence of the SOC upon the Chandler wobble is considered. It is shown that the action of Archimedean buoyancy forces in the SOC creates inside this layer an additional fluid velocity of order of ( C H/2 σ)v τ . Here C H is the relative density deficit in the SOC, v τ is the velocity associated with the Chandler wobble without the SOC, and σ∼1/400 is the frequency of the Chandler wobble measured in cycles per day. The effect of the SOC on the Chandler wobble is small: it increases the wobble period by ∼0.1 day, and its contribution to the dissipation of the wobble energy is about six orders of magnitude smaller than the observed dissipation. A change of seismic velocity in the SOC due to the greater concentration of the light admixture is discussed. A comparison of the conditions in the SOC with the conditions at the inner core boundary shows that the extra amount of the light fluid in the layer increases the seismic velocity; therefore, the SOC is a high-velocity layer.

Onset of 3D collective response in bimetallic jellium films: Surface and mode sensitivity.

We use experimental and calculated excitation spectra of bimetallic jellium films with widths of up to a few Fermi wavelengths to explore how excitations of a thin metal with internal density gradients evolve into surface plasmons of a three-dimensional layer. We find that the onset of 3D plasmons is mode specific, and sensitive to surface potentials, even for small surface wave vectors

Geostrophic adjustment over submarine canyons

The geostrophic adjustment of a stratified coastal current in the presence of a submarine canyon is considered with a mathematical model in which the vertical structure of the fluid is handled with a “level” technique that represents vertical gradients by finite differences. Two situations are investigated in detail: a two‐level system where one level represents the shelf and one the canyon, and a three‐level system with two levels over the shelf and one in the canyon. There are four important length scales in the adjustment process: the initial width of the coastal current, the width of the canyon, and the internal and external radii of deformation. For each vertical mode, the shorter of the radius of deformation for that mode and the width of the coastal current determines the distance over which the perturbing influence of the canyon decays. For typical shelf situations, the external mode decays with the width of the coastal current, while the internal modes decay with the internal radius of deformation. The width of the canyon determines the strength of the cross‐canyon flow and thus, the strength of the canyon's effect on the overlying coastal current, with the interaction becoming smaller as the canyon width becomes smaller than the current width or the radius of deformation. As the cross‐canyon flow becomes small, the importance of the geostrophic balance decreases and the internal density gradients become more important in balancing pressure gradients. Therefore even in the case of flow over a narrow canyon, the isopycnals at the top of the canyon are distorted and there will be some residual circulation on the shelf that is forced by the presence of the canyon.

The Effect of Stellar Structure on Supernova Remnant Evolution

1. AbstractOne-dimensional hydrodynamic calculations have been done of 1E51 erg explosions in 15M⊙ stars. We have appended a steep external density gradient to the pre-supernova model of Weaver et al and find: (1) the outer shock wave decelerates throughout the pre-Sedov phase, (2) the expanding stellar envelope and the shocked interstellar material are Rayleigh-Taylor stable until the Sedov phase, and (3) steep internal density gradients are R-T unstable during the early expansion and may be the source of high velocity knots seen in Cas A.

The effect of Stellar structure on supernova remnant evolution

One-dimensional hydrodynamic calculations have been done of 1E51 erg explosions in 15M⊙ stars. We have appended a steep external density gradient to the pre-supernova model of Weaver et al and find: (1) the outer shock wave decelerates throughout the pre-Sedov phase, (2) the expanding stellar envelope and the shocked interstellar material are Rayleigh-Taylor stable until the Sedov phase, and (3) steep internal density gradients are R-T unstable during the early expansion and may be the source of high velocity knots seen in Cas A.