Initial Density Gradient Research Articles

Three — fluid hydrodynamic simulation of proton beam generation by a subpicosecond laser pulse

The skin-layer ponderomotive acceleration (S-LPA) induced by a short laser pulse is considered to be a promising method of producing dense high-current ion beams having the potential to be applied in high energy density physics or for fast ignition of inertial fusion. In this contribution properties of proton beam generation by S-LPA are studied using a three-fluid relativistic hydrodynamic model of laser-plasma interaction. The numerical calculations were performed for the subpicosecond neodymium-glass laser pulses of intensities up to 1018 W/cm2 interacting with inhomogeneous plasma consisting of three fluids: electron, proton and Au ion fluid. The impact of the initial plasma density gradient and of the different ratio of fluids constituting the plasma slab on proton velocities and proton current densities is presented. In particular, it is shown that the proton velocity increases and the proton current density decreases when the heavy ion fluid content increases. It results in the proton beam intensity having the maximum for the specific ratio of proton and Au ion fluids. The numerical computations were compared to the results of experiment, in which a 1 ps laser pulse of subrelativistic intensity (1017 W/cm2) interacted with a single-layer (plastic) or a double-layer (plastic + Au) thin foil target.

Influence of a finite initial ion density gradient on plasma expansion into a vacuum

The influence of a finite initial ion density gradient on a plasma expansion into a vacuum is studied with a numerical model that takes into account the charge-separation effects and assumes a Boltzmann equilibrium for the electrons. The cases of a semi-infinite plasma and of a finite plasma slab are treated. In both cases it is shown that the finite initial ion density gradient of the plasma surface leads to two phases in the plasma expansion, separated by a wave breaking of the ion flow. An ion front forms after the wave breaking and, in the semi-infinite plasma case, the plasma expansion becomes closer and closer to the initially sharp boundary case, the maximum ion velocity increasing logarithmically with time. In the finite plasma slab case, the energy conservation has to be taken into account, the thermal electron energy being progressively converted into the kinetic energy of the ions. When the initial ion density scale length lss is larger than a few percent of the total plasma slab width, the final maximum ion velocity decreases with lss.

Taylor–Couette flow in a two-layer stratified fluid: instabilities and mixing

In this preliminary experimental study we investigate the mixing of a salt-stratified two-layer fluid in a Taylor–Couette flow. We focus on two flow regimes, one in which waves are present in the pycnocline and vortices in the homogeneous layers, and one with vortices also in the pycnocline. The transition between these two regimes differs significantly compared to the wave–vortex transition found in a uniform stratification, investigated by Caton et al. [Caton, F., Janiaud, B., Hopfinger, E.J., 2000. Stability and bifurcations in stratified Taylor–Couette flow. J. Fluid Mech. 419, 93–124], and is accompanied by a larger jump in fundamental frequency of the density fluc- tuations. Most density gradients show a strong tendency to sharpen with time, with layer formation in the case of an initially thick interface. On a long time-scale, the entrainment of a smooth pycnocline shows cascade-like bifurcations before its transition to chaos. In the latter case, a decrease of the initial density gradient is observed. We discuss the mixing efficiency, measured by the Richardson flux number R i f . Its value is a function of the Reynolds number ∼ R e k , with k = 3 / 2 , and for Reynolds numbers O( 1 0 3 ), the mixing efficiency is of order O( 1 0 − 2 ).

The evolution of planetary nebulae

We investigate and discuss the expansion properties of planetary nebulae by means of 1D radiation-hydrodynamics models computed for different initial envelope configurations and central star evolutionary tracks. In particular, we study how the expansion depends on the initial density gradient of the circumstellar envelope and show that it is possible to derive information on the very last mass-loss episodes during the star's final evolution along and off the asymptotic giant branch. To facilitate the comparison of the models with real objects, we have also computed observable quantities like surface brightness and emission-line profiles. With the help of newly acquired high-resolution emission-line profiles for a sample of planetary nebulae we show that models with initial envelopes based on the assumption of a stationary wind outflow fail to explain the observed expansion speeds of virtually all of the observed planetary nebulae. Instead it must be assumed that during the very last phase of evolution along the final asymptotic giant branch evolution the mass-loss rate increases in strength, resulting in a much steeper slope of the circumstellar radial density distribution. Under these conditions, the expansion properties of the nebular gas differ considerably from the self-similar solutions found for isothermal conditions. Furthermore, the mass loss must remain at a rather high level until the stellar remnant begins to evolve quickly towards the central star regime. Current theoretical computations of dust-driven mass-loss which are restricted to rather low temperatures cannot be applied during the star's departure from the asymptotic giant branch.

The effect of the elapsed time between blood draw and processing on the recovery of fetal cells from maternal blood.

To test the hypothesis that a delay in initial fetal cell enrichment processing of maternal blood samples (defined as the time between blood draw and the initial density gradient centrifugation step) compromises the ability to recover fetal cells, we performed a randomized comparison of immediate (within 4 hours of draw) versus delayed (between 18-24 hours of draw) processing. Four centers participated: two centers utilized flow cytometry (FLOW), and two centers utilized magnetic-activated cell sorting (MACS) techniques. Each center collected 34 samples. The outcome was the percentage of gamma positive (gamma(+)) cells for FLOW or the number of nucleated red blood cells (NRBCs) for MACS, found in the final enriched cell population. Both outcomes reflect cell properties that are potentially fetal in origin, thus making them representative of the ability to recover fetal cells. Our results did not support our hypothesis that delay in processing compromises fetal cell recovery. Instead, in MACS processing, we observed an increase in recovered NRBCs when blood sample processing was delayed compared with immediate processing. There was no significant difference in gamma(+) cells with FLOW. Time-related changes in the density of target cells, perhaps associated with their progress towards apoptosis during the delay period, may result in increased intact fetal cells with the study methods utilized.

Numerical modelling of production of ultrahigh-current-density ion beams by short-pulse laser-plasma interaction

The basic features of generation of ion beams of ultrahigh (>109 A/cm2) current densities by the skin-layer subrelativistic interaction of a short (≤1 ps) laser pulse with an inhomogeneous plasma layer are studied with the use of a two-fluid hydrodynamic 1-D computer code. The calculations performed for pico—and subpicosecond 1.05—μm laser pulses of intensity ∼1016∨1017 W/cm2 confirm that non-linear ponderomotive forces induced by the laser pulse accelerate two thin (a few μm) plasma blocks of current densities in the range of 109∨1011 A/cm2, propagating in forward and backward directions. The effect of initial plasma density gradient as well as the laser intensity and the pulse duration on characteristics of ion beams is demonstrated and discussed.

Density profile evolution and nonequilibrium effects in partial and full spreading measurements of surface diffusion

We study the nature of nonequilibrium effects in the collective diffusion coefficient DC(θ) vs the coverage θ as extracted from Boltzmann–Matano analysis of spreading coverage profiles. We focus on the temporal behavior of the profiles and study how the corresponding nonequilibrium effects in DC(θ) depend on the initial density gradient and the initial state from which the spreading starts. To this end, we carry out extensive Monte Carlo simulations for a lattice-gas model of the O/W(110) system. Studies of submonolayer spreading from an initially ordered p(2×1) phase at θ=12 reveal that the spreading and diffusion rates in directions parallel and perpendicular to rows of oxygen atoms are significantly different within the ordered phase. Aside from this effect, we find that the degree of ordering in the initial phase has a relatively small impact on the overall behavior of DC(θ). Also, although we find that nonequilibrium effects are clearly present in submonolayer spreading profiles, DC(θ) determined from such data approaches its asymptotic equilibrium behavior much more rapidly than in the case of full spreading. Nevertheless, in both cases there are noticeable deviations from equilibrium results that persist even at very long times and are strongest in ordered phases and in the vicinity of phase boundaries. These conclusions are confirmed by complementary studies of the temporal behavior of the order parameter φ(θ). Finally, we use DC(θ) and φ(θ) to determine the locations of phase boundaries and find such data to be clearly time dependent during full spreading. We conclude that nonequilibrium effects seem to be an inherent feature in profile evolution studies of surface diffusion in all cases where ordering plays a prominent role. This warrants particular care to be taken with profile spreading experiments.

Nonlinear Study of Stratified Fluid Through Porous Media

An analysis is presented to describe the effects of Darcy resistance, fluid inertia, and horizontal density gradient on a heterogeneous Boussinesq fluid saturated porous medium in the presence of the vertical gravitational field using the Forchheimer-Lapwood extended Darcy (DLF) equation. The fluid is initially at rest, and sets in motion owing to two forms of the initial density gradients. One is the constant initial horizontal density gradient and the other is the piecewise constant density gradient. In the case of the uniform initial horizontal density gradient a purely horizontal motion develops satisfying the nonlinear Forchheimer extended Darcy (FD) equation. Analytical solution of this equation is obtained and limiting solutions valid for the Darcy regime and for a nonviscous fluid in the absence of porous media are derived. A measure of the stability of the flow is discussed briefly using the Richardson number. A comparison between the nature of solutions satisfying the nonlinear and linear initial value problems is made. We found that the vertical density gradient varies continuously both with space z and time t but the horizontal density gradient remains unchanged. In the case of a piecewise constant initial density gradient with continuous distribution of density, stream function formulation is used and the solutions are obtained using time-series analysis. In this case the solution shows crowding of the density profiles in the lower half of the channel, reflecting an increase in density gradient and incipient frontogenesis there, because of the increase in circulation of the flow due to the piecewise initial density gradient. Copyright © 2001 by Begell House, Inc.

Material versus local incompressibility and its influence on glacial-isostatic adjustment

SUMMARY We present an analytical form of the layer propagator matrix for the response of a locally incompressible, layered, linear-viscoelastic sphere to an external load assuming that the initial density stratification ϱ0(r) within each layer is parametrized by Darwin's law. From this, we show that the relaxation of a sphere consisting of locally incompressible layers is governed by a discrete set of viscous modes. The explicit dependence of the layer propagator matrix on the Laplace transform variable allows us to determine the amplitudes of the viscous modes analytically. Employing Darwin's parametrization, we construct three simplified earth models with different initial density gradients that are used to compare the effects of the local incompressibility constraint, div (ϱ0u)=0, and the material incompressibility constraint, div u=0, on viscoelastic relaxation. We show that a locally incompressible earth model relaxes faster than a materially incompressible model. This is a consequence of the fact that the perturbations of the initial density are zero during viscoelastic relaxation of a locally incompressible medium, so that there are no internal buoyancy forces associated with the continuous radial density gradients, only the buoyancy forces generated by internal density discontinuities. On the other hand, slowly decaying internal buoyancy forces in a materially incompressible earth model cause it to reach the hydrostatic equilibrium after a considerably longer time than a locally incompressible model. It is important to note that the approximation of local incompressibility provides a solution for a compressible earth model that is superior to the conventional solutions for a compressible earth with homogeneous layers because it is based on an initial state that is consistent with the assumption of compressibility.

Density Gradients and Sintered Dimensional Tolerance in Compacts Formed from Spray‐Dried Alumina

This study proves that initial density gradients have lasting detrimental effects on final dimensional tolerances. X‐ray computed tomography has been used to quantify changes in density following sintering; associated dimensional changes have been monitored using a laser micrometer. Nonuniformities present in the green state are still present at an overall relative density of ∼73%; in fact, these nonuniformities are exaggerated. Major losses of dimensional tolerance are triggered by the initial density gradients.

Relative competitiveness of nine early-successional boreal forest species associated with planted jack pine and black spruce seedlings

Differences in yield-density models derived from an additive experimental design were used to compare the relative competitiveness of nine early-successional boreal forest plants (aster, grass, fireweed, fern, raspberry, willow, alder, birch, and aspen) on jack pine (Pinus banksiana Lamb.) and black spruce (Picea mariana (Mill.) BSP). A randomized complete block split-split-plot design with three replications blocked on soil type was used. Initial density gradients were 0-4 plants/m2 for woody and 0-8 plants/m2 for herbaceous species. An a priori analytical approach that compared a full model (using linear regression analysis of 4th-year stem diameter of conifers under increasing cover and height of competitors) to various reduced models was used to assess competition. Increasing cover and (or) height of all competitors (except fern) significantly (P < 0.05) decreased conifer stem diameter. The final regression model (based on visual estimates of cover and differences in initial conifer size) accounted for 89% of the variation in stem diameter. During the years studied, both conifers responded similarly to competition, and herbaceous species were on average 28.9% more competitive than woody species. Under different growing conditions (e.g., a natural forest) the relative competitiveness of herbaceous and woody species may vary from these results.

A comparison of predictions and measurements of kinematic mixing of two fluids in a 2D enclosure

Buoyancy driven mixing of two fluids in a 2D closed cavity is simulated with a two-fluid model. The predictions are compared with a set of experimental data. The experiment involves flow visualization of the mixing process and application of the image processing technique to determine the mixing characteristics. The measurements and predictions include the interface evolution, interface elongation, and mixing width. Two Grashof numbers based on the initial density gradient, Gr=3.7×10 5, 3.7×10 3 and two valve speeds, 0 and 5 cm/s are considered. The predictions are generally in good agreement with the experimental data.

Relative competitiveness of nine early-successional boreal forest species associated with planted jack pine and black spruce seedlings

Differences in yield-density models derived from an additive experimental design were used to compare the relative competitiveness of nine early-successional boreal forest plants (aster, grass, fireweed, fern, raspberry, willow, alder, birch, and aspen) on jack pine (Pinus banksiana Lamb.) and black spruce (Picea mariana (Mill.) BSP). A randomized complete block split-split-plot design with three replications blocked on soil type was used. Initial density gradients were 0-4 plants/m2 for woody and 0-8 plants/m2 for herbaceous species. An a priori analytical approach that compared a full model (using linear regression analysis of 4th-year stem diameter of conifers under increasing cover and height of competitors) to various reduced models was used to assess competition. Increasing cover and (or) height of all competitors (except fern) significantly (P < 0.05) decreased conifer stem diameter. The final regression model (based on visual estimates of cover and differences in initial conifer size) accounted fo...

Effects due to compressional and compositional density stratification on load-induced Maxwell viscoelastic perturbations

SUMMARY Calculations of viscoelastic perturbations of an incompressible £uid earth initially in hydrostatic equilibrium have been conventionally based on models consisting of isocompositional layers. A special case is the incompressible, isocompositional half-space, for which the initial density distribution is spatially uniform. One of the de¢ciencies of this model is that it ignores the increase of the initial density with depth in the earth’s interior due to compressional and compositional strati¢cation. The presentstudy is concernedwith load-induced Maxwellviscoelastic perturbations of a half-space with a compressional and compositional initial density gradient. Analytic solutions to this problem are deduced for the limiting cases of purely compressional strati¢cation (earth model P) and purely compositional strati¢cation (earth model C). The comparison of the solutions for these earth models with that for the special case of no density strati¢cation (earth model R) shows that eiects due to the initial density gradient become important for perturbations whose lateral scale length exceeds about 10 3 km. Using axisymmetric models of the Pleistocene Fennoscandian and Canadian ice sheets and considering the vertical surface displacements near the load axes, the maximum diierences are found to be about 10 m (Fennoscandia) or 35 m (Canada) at the beginning of relaxation for earth models P and R and about 50 m (Fennoscandia) or 150 m (Canada) at intermediate times of relaxation for earth models C and R.

Development, Characterization, and Use of Monoclonal Antibodies Made to Antigens Expressed on the Surface of Fetal Nucleated Red Blood Cells

Current methods for obtaining fetal cells for prenatal diagnosis are invasive and carry a small (0.5-1.0%) but definite risk of miscarriage. An attractive alternative would be isolation of fetal cells from peripheral maternal blood using antibodies with high specificity and avidity. To generate antibodies, we purified nucleated red blood cells (NRBCs) from fetal livers and used them as the immunogen to generate monoclonal antibodies (mAbs) directed against surface antigens. The four antibodies recognized at least two conformationally sensitive epitopes of the transferrin receptor. Isolation of NRBCs from 252 maternal blood samples using these antibodies in magnetic activated cell sorting after an initial density gradient centrifugation yielded 0-419 NRBCs per 25 mL of maternal blood. One antibody, 2B7.4, not only isolated the highest number of NRBCs (>10 in 90% of the samples) but also isolated these NRBCs in 78 consecutive maternal samples. Antibody 2B7.4 shows promise for the isolation of NRBCs from maternal blood and should allow studies concerning the source of these cells, fetal vs maternal, and the factors controlling their prevalence.

Nonlinear evolution of a nonneutral electron gas-discharge plasma with nonzero electron temperature

The nonlinear evolution of a nonneutral electron gas-discharge plasma density in crossed E⊥ B fields taking into account nonelastic electron-neutral collisions and a low electron temperature has been considered. It is shown that the temperature effect depends on the sign of the initial density gradient and accelerates or decelerates the process of relaxation and flattening of the electron density equilibrium profile.

Relaxation of equilibrium density profiles in nonneutral electron plasma due to electron-neutral collisions

Under the assumption of constant frequency of electron-neutral collisions and constant electron temperature, analytical expressions are obtained for equilibrium space-time distributions of the electron density of a cylindrically symmetric, strongly magnetized, nonneutral electron plasma. It is found that the effect of nonzero electron temperature accelerates or slows down the relaxation and flattening of equilibrium density profiles depending on the initial density gradient sign.

An analytical and numerical study of surface and bottom boundary layers with variable forcing and application to the North Sea

A study is made concerning the evolution of a tidally generated bottom layer and a wind-driven surface layer with a time-dependent surface stress in view of its application to thermal stratification problems in shelf seas. Three test cases are defined. In the first two a linear stratification is assumed initially while a stress is applied either at the bottom or at the surface. Analytical solutions can then be derived using simplifying assumptions. They show how the evolution depends on the forcing parameters, i.e. initial density gradient, rotation, forcing period, amplitude of the tidal current or magnitude of the wind stress, ellipticity and polarisation of the tidal or surface (stress) ellipse. It is shown that the analytical theory is in good agreement with results obtained using a numerical model incorporating a turbulence closure scheme. An important result is the occurrence of a resonance and an increased growth of the surface layer when the time scale of the surface stress is comparable with the rotation period. No such resonance has been found for the bottom layer forced by the semi-diurnal tide, In a third test case a simulation is made of the seasonal cycle at station CS in the North Sea, The results are compared with the temperature data from the North Sea Project, A series of numerical experiments is performed to verify parts of the theoretical analysis.

Geostrophic Adjustment: Frontogenesis and Energy Conversion

Abstract Nonlinear geostrophic adjustment is examined with a Boussinesq model. The motion is restricted to a two-dimensional channel in the horizontal and vertical (x, z) plane; the fluid is in uniform rotation, is stably stratified, inviscid, and incompressible. The flows considered fall under two classes: zero and uniform potential vorticity flows. Steady geostrophic flow fields are determined from initial man imbalances, represented by both symmetric and antisymmetric density anomalies that vary along the x axis. The distinguishing characteristic of these solutions is the development of a front, defined as a zero-order discontinuity in both density and geostrophic velocity at one or both vertical boundaries. Frontal formation occurs, as previously discovered by Ou for zero potential vorticity flow, when the initial horizontal density gradient is sufficiently large. The critical values are displayed for different cases in terms of the initial amplitude and initial scale of the density anomaly. The conve...

Cavity flow induced by a fluctuating acceleration field

Buoyancy driven convection induced by a fluctuating acceleration field is studied in a two dimensional square cavity. This is a simplified model of, for example, fluid flow in a directional solidification cell subject to external accelerations, such as those encountered in a typical microgravity environment (g-jitter). The effect of both deterministic and stochastic acceleration modulations normal to the initial density gradient are considered. In the latter case, the acceleration field is modeled by narrow band noise defined by a characteristic frequency Ω, a correlation time τ, and an intensity G2. If the fluid is quiescent at t=0 when the acceleration field is initiated, the ensemble average of the vorticity at the center of the cavity remains zero for all times. The mean squared vorticity 〈ξ2〉, however, is seen to exhibit two distinct regimes: For t≪τ, 〈ξ2〉 oscillates in time with frequency Ω. For t≫τ, 〈ξ2〉 grows linearly in time with an amplitude equal to R2Pr/(1+(Ωτ))2, where R is a new dimensionless number which reduces to the Rayleigh number in the case of a constant gravity, and Pr is Prandtl number. At yet later times, viscous dissipation at the walls of the cavity leads to saturation, with 〈ξ2〉sat={(Pr τ+1)R2/[(Pr τ+1)2+Ω2τ2]}.