Effect Of Density Variation Research Articles

Vibration of rectangle plate with variable density and Poisson’s ratio

The effect of variation in density and Poisson’s ratio is examined, on the vibration of rectangle plate with linear variable thickness. Bi parabolic temperature effect on the plate is also studied and vibrational modes of rectangular plate is calculated by using Rayleigh Ritz method. Authors also compared the present finding with the published results.

Effect of linear variation in density and circular variation in Poisson’s ratio on time period of vibration of rectangular plate

In this paper, a theoretical analysis is carried out to investigate the effect of linear variation in density and circular variation in Poisson’s ratio on time period of frequency modes of rectangular plate with variable thickness under temperature field. The thickness variation is considered to be circular and temperature variation on the plate is assumed to be bi-linear. Rayleigh Ritz method is used to solve the differential equation. All the results (time period for first two modes of vibration) are presented with the help of tables.

On the inertial effects of density variation in stratified shear flows

In this paper, we first revisit the celebrated Boussinesq approximation in stratified flows. Using scaling arguments we show that when the background shear is weak, the Boussinesq approximation yields either (i) At≪O(1) or (ii) Frc2≪O(1), where At is the ratio of density variation to the mean density and Frc is the ratio of the phase speed to the long wave speed. The second clause implies that, in contrast to the commonly accepted notion, a flow with large density variations can also be Boussinesq. Indeed, we show that deep water surface gravity waves are Boussinesq, while shallow water surface gravity waves are not. However, in the presence of moderate/strong shear, the Boussinesq approximation implies the conventionally accepted At≪O(1). To understand the inertial effects of density variation, our second objective is to explore various non-Boussinesq shear flows and study different kinds of stably propagating waves that can be present at an interface between two fluids of different background densities and vorticities. Furthermore, three kinds of density interfaces—neutral, stable, and unstable—embedded in a background shear layer are investigated. Instabilities ensuing from these configurations, which include Kelvin-Helmholtz, Holmboe, Rayleigh-Taylor, and triangular-jet, are studied in terms of resonant wave interactions. The effects of density stratification and the shear on the stability of each of these flow configurations are explored. Some of the results, e.g., the destabilizing role of density stratification, stabilizing role of shear, etc., are apparently counter-intuitive, but physical explanations are possible if the instabilities are interpreted from wave interaction perspective.In this paper, we first revisit the celebrated Boussinesq approximation in stratified flows. Using scaling arguments we show that when the background shear is weak, the Boussinesq approximation yields either (i) At≪O(1) or (ii) Frc2≪O(1), where At is the ratio of density variation to the mean density and Frc is the ratio of the phase speed to the long wave speed. The second clause implies that, in contrast to the commonly accepted notion, a flow with large density variations can also be Boussinesq. Indeed, we show that deep water surface gravity waves are Boussinesq, while shallow water surface gravity waves are not. However, in the presence of moderate/strong shear, the Boussinesq approximation implies the conventionally accepted At≪O(1). To understand the inertial effects of density variation, our second objective is to explore various non-Boussinesq shear flows and study different kinds of stably propagating waves that can be present at an interface between two fluids of different background densities ...

Reconsidering Effective Elastic Thickness Estimates by Incorporating the Effect of Sediments: A Case Study for Europe

AbstractIn the present study we analyzed the influence of density heterogeneity in the sedimentary cover on estimates of the effective elastic thickness (EET) of the lithosphere based on a cross‐spectral analysis of gravity and topography data. The fan wavelet coherence technique was employed to calculate EET for most of Europe and adjoining southern mountain belts. We employed Bouguer gravity anomalies and topography corrected for the effect of density variations within sediments. Correcting for sediments considerably suppresses the effect of unexpressed subsurface loads and substantially reduces EET estimates in areas with negligible topography variations as it was demonstrated for North Europe and East European Platform. The results show a good correspondence between the EET patterns and tectonic fragmentation of Europe and better agree with independent estimates based on the strength model of the lithosphere. Therefore, considering of the effect of sediments is essential for correct determinations of EET in flat areas.

Correction of low-Reynolds number turbulence model to hydrocarbon fuel at supercritical pressure

At supercritical pressure, due to the drastic change of thermophysical property near the pseudo-critical temperature, the density fluctuation and density variation, along with buoyancy, play an important role in supercritical turbulence modelling. Based on the original LS (Launder–Sharma) low-Reynolds number turbulence model, the buoyancy modification, the density fluctuation modification, the density variation modification and the empirical coefficients modification are considered and the corresponding correction terms are derived and applied in the governing equations. Numerical simulation of heat transfer to hydrocarbon fuel flowing through the uniformly heated round pipe at supercritical pressure has been performed by the modified LS turbulence model incorporated into the in-house numerical code. Inlet temperature varied from 373 K to 473 K, with heat flux varying from 241 kW/m2 to 470 kW/m2. Inlet mass flux was 736 kg/(m2⋅s) and operating pressure was 4 MPa. The flow directions included upflow and downflow. Compared with the original LS turbulence model, the modified LS turbulence model leads to the better agreement with the experimental results, with 41.16% improvement in computation accuracy in the current study. The consideration of density fluctuation and density variation effects makes the turbulence model more suitable for thermophysical property variation at supercritical pressure.

MHD Fluid Flow of an Exponentially Varying Plasma Density in a Radiating and Slowly Rotating Hot Sphere

The study presents the effect of density variation on the flow structure of a plasma gas in a slowly rotating and radiating hot sphere. The problem which is solved by general perturbation method shows that the plasma temperature decreases to a minimum at a radial distance of 1.4 solar radii and then increased to a maximum value at a radial distance of 3.5 solar radii, for various radiation parameters, N2. The sudden increase in temperature profile when the radial distance is 1.4 solar radii, indicates the heating up of the upper regions of the solar atmosphere.

Density variation effect on multi-ions with kinetic Alfven wave around cusp region—a kinetic approach

The kinetic Alfven waves in the presence of homogeneous magnetic field plasma with multi-ions effect are investigated. The dispersion relation and normalised damping rate are derived for low- $\beta$ plasma using kinetic theory. The effect of density variation of $\text{H}^{+}$ , $\text{He}^{+}$ and $\text{O}^{+}$ ions is observed on frequency and damping rate of the wave. The variation of frequency ( $\omega$ ) and normalised damping rate ( $\gamma / \varOmega_{H^{ +}} $ ) of the wave are studied with respect to $k_{ \bot} \rho_{j}$ , where $k_{ \bot} $ is the perpendicular wave number, $\rho_{j}$ is the ion gyroradius and $j $ denotes $\text{H}^{+}$ , $\text{He}^{+}$ and $\text{O}^{+}$ ions. The variation with $k_{ \bot} \rho_{j}$ is considered over wide range. The parameters appropriate to cusp region are used for the explanation of results. It is found that with hydrogen and helium ions gyration, the frequency of wave is influenced by the density variation of $\text{H}^{+}$ and $\text{He}^{+}$ ions but remains insensitive to the change in density of $\text{O}^{+}$ ions. For oxygen ion gyration, the frequency of wave varies over a short range only for $\text{O}^{+}$ ion density variation. The wave shows damping at lower altitude due to variation in density of lighter $\text{H}^{+}$ and $\text{He}^{+}$ ions whereas at higher altitude only heavy $\text{O}^{+}$ ions contribute in wave damping. The damping of wave may be due to landau damping or energy transfer from wave to particles. The present study signifies that the both lighter and heavier ions dominate differently to change the characteristics of kinetic Alfven wave and density variation is also an important parameter to understand wave phenomena in cusp region.

Influence of the Ambient Electric Field on Measurements of the Actively Controlled Spacecraft Potential by MMS

AbstractSpace missions with sophisticated plasma instrumentation such as Magnetospheric Multiscale, which employs four satellites to explore near‐Earth space benefit from a low electric potential of the spacecraft, to improve the plasma measurements and therefore carry instruments to actively control the potential by means of ion beams. Without control, the potential varies in anticorrelation with plasma density and temperature to maintain an equilibrium between the plasma current and the one of photoelectrons produced at the surface and overcoming the potential barrier. A drawback of the controlled, almost constant potential is the difficulty to use it as convenient estimator for plasma density. This paper identifies a correlation between the spacecraft potential and the ambient electric field, both measured by double probes mounted at the end of wire booms, as the main responsible for artifacts in the potential data besides the known effect of the variable photoelectron production due to changing illumination of the surface. It is shown that the effect of density variations is too weak to explain the observed correlation with the electric field and that a correction of the artifacts can be achieved to enable the reconstruction of the uncontrolled potential and plasma density in turn. Two possible mechanisms are discussed: the asymmetry of the current‐voltage characteristic determining the probe to plasma potential and the fact that a large equipotential structure embedded in an electric field results in asymmetries of both the emission and spatial distribution of photoelectrons, which results in an increase of the spacecraft potential.

Numerical study of variable density turbulence interaction with a normal shock wave

Accurate numerical simulations of shock–turbulence interaction (STI) are conducted with a hybrid monotonicity-preserving–compact-finite-difference scheme for a detailed study of STI in variable density flows. Theoretical and numerical assessments of data confirm that all turbulence scales as well as the STI are well captured by the computational method. Linear interaction approximation (LIA) convergence tests conducted with the shock-capturing simulations exhibit a similar trend of converging to LIA predictions to shock-resolving direct numerical simulations (DNS). The effects of density variations on STI are studied by comparing the results corresponding to an upstream multi-fluid mixture with the single-fluid case. The results show that for the current parameter ranges, the turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations exist. Turbulent mixing enhancement by the shock is also increased and stronger mixing asymmetry in the postshock region is observed when there is significant density variation. The turbulence structure is strongly modified by the shock wave, with a differential distribution of turbulent statistics in regions having different densities. The dominant mechanisms behind the variable density STI are identified by analysing the transport equations for the Reynolds stresses, vorticity, normalized mass flux and density specific volume covariance.

The Parametric Decay Instability of Alfvén Waves in Turbulent Plasmas and the Applications in the Solar Wind

Abstract We perform three-dimensional ideal magnetohydrodynamic (MHD) simulations to study the parametric decay instability (PDI) of Alfvén waves in turbulent plasmas and explore its possible applications in the solar wind. We find that, over a broad range of parameters in background turbulence amplitudes, the PDI of an Alfvén wave with various amplitudes can still occur, though its growth rate in turbulent plasmas tends to be lower than both the theoretical linear theory prediction and that in the non-turbulent situations. Spatial–temporal FFT analyses of density fluctuations produced by the PDI match well with the dispersion relation of the slow MHD waves. This result may provide an explanation of the generation mechanism of slow waves in the solar wind observed at 1 au. It further highlights the need to explore the effects of density variations in modifying the turbulence properties as well as in heating the solar wind plasmas.

Elastic-plastic transition on rotating spherical shells in dependence of compressibility

The purpose of this paper is to establish the mathematical model on the elastic-plastic transitions occurring in the rotating spherical shells based on compressibility of materials. The paper investigates the elastic-plastic stresses and angular speed required to start yielding in rotating shells for compressible and incompressible materials. The paper is based on the non-linear transition theory of elastic-plastic shells given by B.R. Seth. The elastic-plastic transition obtained is treated as an asymptotic phenomenon at critical points & the solution obtained at these points generates stresses. The solution obtained does not require the use of semi-empirical yield condition like Tresca or Von Mises or other certain laws. Results are obtained numerically and depicted graphically. It has been observed that Rotating shells made of the incompressible material are on the safer side of the design as compared to rotating shells made of compressible material. The effect of density variation has been discussed numerically on the stresses. With the effect of density variation parameter, rotating spherical shells start yielding at the internal surface with the lower values of the angular speed for incompressible/compressible materials.

Thinned crustal structure and tectonic boundary of the Nansha Block, southern South China Sea

The southern South China Sea margin consists of the thinned crustal Nansha Block and a compressional collision zone. The Nansha Block’s deep structure and tectonic evolution contains critical information about the South China Sea’s rifting. Multiple geophysical data sets, including regional magnetic, gravity and reflection seismic data, reveal the deep structure and rifting processes. Curie point depth (CPD), estimated from magnetic anomalies using a windowed wavenumber-domain algorithm, enables us to image thermal structures. To derive a 3D Moho topography and crustal thickness model, we apply Oldenburg algorithm to the gravity anomaly, which was extracted from the observed free air gravity anomaly data after removing the gravity effect of density variations of sediments, and temperature and pressure variations of the lithospheric mantle. We found that the Moho depth (20 km) is shallower than the CPD (24 km) in the Northwest Borneo Trough, possibly caused by thinned crust, low heat flow and a low vertical geothermal gradient. The Nansha Block’s northern boundary is a narrow continent–ocean transition zone constrained by magnetic anomalies, reflection seismic data, gravity anomalies and an interpretation of Moho depth (about 13 km). The block extends southward beneath a gravity-driven deformed sediment wedge caused by uplift on land after a collision, with a contribution from deep crustal flow. Its southwestern boundary is close to the Lupar Line defined by a significant negative reduction to the pole (RTP) of magnetic anomaly and short-length-scale variation in crustal thickness, increasing from 18 to 26 km.

The effect of density variation on photon dose calculation and its impact on intensity modulated radiotherapy and stereotactic body radiotherapy.

Inaccurate density information may introduce dose calculation errors when inhomogeneity correction is applied. The aim of the present study was to examine the effect of density variation on photon dose calculation accuracy using the convolution/superposition (CS) algorithm with the focus on newer treatment technologies including intensity modulated radiotherapy, volumetric modulated arc radiotherapy, and stereotactic body radiotherapy (SBRT). Calculations were first performed using simple inhomogeneity phantoms in order to determine clinically relevant tolerance levels for different tissue types. The clinical validity of these tolerance levels was then demonstrated by evaluating their dosimetric impact on clinical treatment plans. The dose difference was examined by comparing the dose-volume histogram statistics and the spatial distribution of dose errors calculated on a voxel-by-voxel basis. In order to gain some insight into this issue for the Monte Carlo (MC) algorithm, the authors also performed additional validation using a MC dose calculation system. For soft tissue and bone, the tolerance levels determined from this study appear to be consistent with the values previously calculated using simpler inhomogeneity correction methods. However, the tolerance level for low density lung tissue has been found to be much smaller than what previous studies had reported. The results from this study also suggest that if density variation is restricted within ±0.02, ±0.03, and ±0.10 g/cm3 for lung, soft tissue, and bone, respectively, the resulting dose error in target volumes can be limited to <2% for most clinical cases and <3% for more challenging lung SBRT cases. When the same amount of density variation is introduced, MC algorithm yields ∼0.3%-0.9% and ∼0.0%-1.2% smaller dose errors for the target and organs-at-risk as compared to CS. It is important to include lung substitute material into the periodic quality assurance of CT simulators and treatment planning systems. This study suggests that the tolerance value of CT number for lung material is ∼ ± 20 HU in order to keep the associated dose uncertainty at 2%-3% or less. Further studies with larger number of lung cases are warranted to validate this new tolerance value before it can be applied to clinical practice.

Consistency of Geoid Models, Radar Altimetry, and Hydrodynamic Modelling in the North Sea

ABSTRACTRadar altimetry, when corrected for tides, atmospheric forcing of the sea surface, and the effects of density variations and mean and time-variable currents, provides an along-track realization of the marine geoid. In this study we investigate whether and how such an ‘altimetric-hydrodynamic’ geoid over the North Sea can serve for validating satellite-gravimetric geoids. Our results indicate that, using ERS-2 and ENVISAT along-track altimetry and water levels from the high-resolution operational circulation model BSHcmod, we do find distinct differences in RMS fits for various state-of-the art satellite-only models (beyond degree 145 for GRACE-only, and beyond degree 185 for GOCE models) and for combined geoid models, very similar as seen in GPS-levelling validations over land areas. We find that, at spectral resolution of up to about 200, an RMS fit as low as about 7 cm can be obtained for the most recent GOCE-derived models such as GOCO05S. This is slightly above what we expect from budgeting individual errors. Key to the validation is a proper treatment of the spectral mismatch between satellite-gravimetric and altimetric-hydrodynamic geoids. Comparison of data fits and error budget suggests that geoid truncation errors residual to EGM2008 (i.e. EGM2008 commission and omission error) may amount up to few cm.

High velocity impact mitigation with gradient cellular solids

The dynamic behavior of gradient cellular solids subjected to high velocity impact is investigated, with shock theory and rigid-perfectly-plastic-locking idealization. The impact is induced by the fragments of a cased charge explosion in near field, sufficiently high to progressively crush the cellular solids from the loading part, regardless of the density variation of the cellular solids. The dynamic response and energy absorption are examined for different gradient cellular solid layers with the same mass and thickness, but different density variation. The cellular solids with larger density gradient lead to smaller crushed distance and higher energy absorption compared to those with smaller density gradients, when subjected to the same impact, provided that the cellular solid is not fully densified. However, when the cellular layer is fully crushed, the effect of density variation on energy absorption vanishes.

Effect of inter-trials variability on the estimation of cortical connectivity by Partial Directed Coherence.

Partial Directed Coherence (PDC) is a powerful estimator of effective connectivity. In neuroscience it is used in different applications with the aim to investigate the communication between brain regions during the execution of different motor or cognitive tasks. When multiple trials are available, PDC can be computed over multiple realizations, provided that the assumption of stationarity across trials is verified. This allows to improve the amount of data, which is an important constraint for the estimation accuracy. However, the stationarity of the data across trials is not always guaranteed, especially when dealing with patients. In this study we investigated how the inter-trials variability of an EEG dataset affects the PDC accuracy. Effects of density variations and of changes of connectivity values across trials were first investigated with a simulation study and then tested on real EEG data collected from two post-stroke patients during a motor imagery task and characterized by different inter-trials variability. Results showed the effect of different factors on the PDC accuracy and the robustness of such estimator in a range of conditions met in practical applications.

Toward fracture porosity assessment by gravity forward modeling for geothermal exploration (Sankt Gallen, Switzerland)

Fracture porosity is a crucial parameter in hydrocarbon and geothermal reservoir exploration and a major challenge in the absence of nearby exploration wells. The Sankt Gallen geothermal project targets a fault zone that affects Mesozoic sediments at a depth of about 4500m. Spatial extension of these sediments, a major fault zone and indication for graben structures in the crystalline basement are observed in 3D seismic. Both the graben and the fault zone coincide with negative gravity anomalies acquired and analyzed during this study. Forward modeling of gravity anomalies based on a 3D seismic survey is used to estimate possible fracture porosity. After stripping gravity effects of geothermally irrelevant geological units from the residual anomaly, most likely only local structures related to the fault zone account for remaining anomalies. Synthetic case study on the effect of density variation and considerable gas content in the well support possible fracture porosity between about 4% and 8%.

Mixed Convective Heat and Mass Transfer Flow of Nanofluids in Concentric Annulus

This paper studies the non-Darcy natural convective heat transfer flow of nanofluid flow through a porous medium in a co-axial cylindrical duct where the boundaries are maintained at constant temperature and concentration. The flow in the porous material is given by a linear Brinkman-Forchheimer-extended Darcy equation. The Boussinesq approximation is invoked so that the effect of density variation is combined to the buoyancy forces. The equations of momentum, energy and diffusion are coupled and linear. Galerkin finite element analysis is employed with quadratic polynomial approximations. At different axial positions, analysis is conducted for the behaviour of velocity, temperature and concentration.

On a Molecular Based Q-Tensor Model for Liquid Crystals with Density Variations

In this article, we study the new Q-tensor model previously derived from Onsager's molecular theory by Han \textit{et al.} [Arch. Rational Mech. Anal., 215.3 (2014), pp. 741-809] for static liquid crystal modeling. Taking density and Q-tensor as order parameters, the new Q-tensor model not only characterizes important phases while capturing density variation effects, but also remains computationally tractable and efficient. We report the results of two numerical applications of the model, namely the isotropic--nematic--smectic-A--smectic-C phase transitions and the isotropic--nematic interface problem, in which density variations are indispensable. Meanwhile, we show the connections of the new Q-tensor model with classical models including generalized Landau-de Gennes models, generalized McMillan models, and the Chen-Lubensky model. The new Q-tensor model is the pivot and an appropriate trade-off between the classical models in three scales.

Model and Test Methods for Stability of Fresh Cement Paste

Abstract The stability of fresh cement paste can be described as its ability to remain homogeneous over time. Instability in the form of sedimentation and bleeding occurs for various reasons related to the material composition. In this study, the relevant mechanisms for quantifying stability are reviewed, and a conceptual model is proposed describing the sedimentation progress in terms of bleeding (supernatant), the homogeneous zone, the variable concentration zone, and the compressible sediment zone. A sensitive hydrostatic pressure test (HYSPT) with good repeatability and without influence from evaporation was developed to describe the sedimentation process of fresh cement paste. HYSPT relies on the fact that the mainly restricted Stokesian settlement of particles causes changes in the solid fraction and the fresh density at a given height and time. The influence of the pressure detection direction and position were investigated by changing the inlet design of glass pipes. The pressure drop due to cement dissolution, chemical shrinkage, and paste structural buildup also was investigated but was found to be negligible compared to the effect of density variation due to sedimentation before setting. The sedimentation rates obtained from HYSPT measurements were found to coincide with the volume fraction variation detected via in situ measurements. The solid fraction and bleeding results were in alignment with the conceptual model.