Layers Of Different Density Research Articles

Circular restricted three-body problem when both the primaries are heterogeneous spheroid of three layers and infinitesimal body varies its mass

The circular restricted three-body problem, where two primaries are taken as heterogeneous oblate spheroid with three layers of different densities and infinitesimal body varies its mass according to the Jeans law, has been studied. The system of equations of motion have been evaluated by using the Jeans law and hence the Jacobi integral has been determined. With the help of system of equations of motion, we have plotted the equilibrium points in different planes (in-plane and out-of planes), zero velocity curves, regions of possible motion, surfaces (zero-velocity surfaces with projections and Poincare surfaces of section) and the basins of convergence with the variation of mass parameter. Finally, we have examined the stability of the equilibrium points with the help of Meshcherskii space–time inverse transformation of the above said model and revealed that all the equilibrium points are unstable.

Features of Wavelet Analysis in X-Ray Reflectometry of Thin Films

Specific features of the use of wavelet transform for estimating the thickness of layers and their order in a film density profile based on X-ray and synchrotron reflectometry data are considered. Some ways are proposed to reveal the characteristic features of Langmuir film packing by constructing a wavelet transform for the corresponding reflectograms. Dependences of the X-ray attenuation length on the grazing incidence angle are plotted by an example of multilayered box model of film profile; these dependences demonstrate possibilities of mapping the spatial signal delay (which occurs when rays are reflected from layers of different density) in a waveletgram.

Out-of-plane equilibrium points and regions of motion in the photogravitational R3BP when the primaries are heterogeneous spheroid with three layers

The present paper deals with the regions of motion and the out-of-plane equilibrium points in the planar restricted three-body problem when both the primaries are heterogeneous oblate spheroids with three layers of different densities and sources of radiation. We have derived the equations of motion and examined the combine effects of radiation and the effect due to the different layers of primaries on the out-of-plane equilibrium points and regions of motion. It is further observed that the energy constant, the radiation parameter and the effect due to the different layers of primaries have substantial impact on the locations of the out-of-plane equilibrium points and on the regions of motion. Furthermore, we have observed that the out-of-plane equilibrium points are unstable for all mass ratios and other parameters, whereas the infinitesimal mass can move freely around the primaries for smaller values of Jacobi constant. But, when we increase the radiation parameter due to either of the primaries, the forbidden regions increase, where the motion is not possible. Moreover, we have discussed the Newton-Raphson basins of attraction to observe the effect of various perturbation on the topology of basins of convergency on configuration plane.

Ion acceleration in electrostatic collisionless shock: on the optimal density profile for quasi-monoenergetic beams

A numerical study on ion acceleration in electrostatic shock waves is presented, with the aim of determining the best plasma configuration to achieve quasi-monoenergetic ion beams in laser-driven systems. It was recently shown that tailored near-critical density plasmas characterized by a long-scale decreasing rear density profile lead to beams with low energy spread (Fiúza et al 2012 Phys. Rev. Lett. 109 215001). In this work, a detailed parameter scan investigating different plasma scale lengths is carried out. As result, the optimal plasma spatial scale length that allows for minimizing the energy spread while ensuring a significant reflection of ions by the shock is identified. Furthermore, a new configuration where the required profile has been obtained by coupling micro layers of different densities is proposed. Results show that this new engineered approach is a valid alternative, guaranteeing a low energy spread with a higher level of controllability.

Fabrication of multiple-layered gradient cellular metal scaffold via electron beam melting for segmental bone reconstruction

The triple- and double-layered mesh Ti-based alloy scaffolds were successfully fabricated using electron beam melting (EBM). In this study Ti-based alloy cylindrical scaffolds with different 3D architectures intended for the segmental bone defect treatment were systematically compared. All lattice-like scaffolds were additively manufactured using EBM technology from Ti6Al4V to mimic the structures of human trabecular bone. Cylindrically-shaped lattice scaffolds (outer diameter of 15mm and length of 35mm) of five different types were designed and manufactured. Four types were tubular with inner hole diameter of 5mm and two lattice layers of different density. Fifth type was cylindrical with three lattice layers of different density. In all samples outer lattice layer was most dense, and inner layers- least dense. Mechanical properties of scaffolds were determined by conducting uniaxial compression testing. The strain-stress curves for all samples with gradient porosities showed considerable ductility.

Emptying filling boxes – free turbulent versus laminar porous media plumes

We examine the transient evolution of a negatively buoyant, laminar plume in an emptying filling box containing a uniform porous medium. In the long time limit, $\unicode[STIX]{x1D70F}\rightarrow \infty$, the box is partitioned into two uniform layers of different densities. However, the approach towards steady state is characterized by a lower contaminated layer that is continuously stratified. The presence of this continuous stratification poses non-trivial analytical challenges; we nonetheless demonstrate that it is possible to derive meaningful bounds on the range of possible solutions, particularly in the limit of large $\unicode[STIX]{x1D707}$, where $\unicode[STIX]{x1D707}$ represents the ratio of the draining to filling time scales. The validity of our approach is confirmed by drawing comparisons against the free turbulent plume case where, unlike with porous media plumes, an analytical solution that accounts for the time-variable continuous stratification of the lower layer is available (Baines & Turner, J. Fluid Mech., vol. 37, 1969, pp. 51–80; Germeles, J. Fluid Mech., vol. 71, 1975, pp. 601–623). A separate component of our study considers time-variable forcing where the laminar plume source strength changes abruptly with time. When the source is turned on and off with a half-period, $\unicode[STIX]{x0394}\unicode[STIX]{x1D70F}$, the depth and reduced gravity of the contaminated layer oscillate between two extrema after the first few cycles. Different behaviour is seen when the source is merely turned up or down. For instance, a change of the source reduced gravity leads to a permanent change of interface depth, which is a qualitative point of difference from the free turbulent plume case.

Seismic Surface Wave Cloaking by Acoustic Wave Refraction

Recently two seismic cloaking methods of earthquake engineering have been suggested. One is the seismic wave deflection method that makes the seismic wave bend away and the other is the shadow zone method that makes an area that seismic waves cannot pass through. It is called as seismic cloaking. The fundamental principles of the seismic cloaking by variable refractive index were explained. A two-dimensional cylindrical model which was composed of 40 layers of different density and modulus was tested by numerical simulation. The center region of the model to be protected is called 'cloaked area' and the outer region of it to deflect the incoming wave is called 'cloaking area' or 'cloak area.' As the incoming surface wave is approaching to the cloaking area, the refractive index is decreasing and, therefore, the velocity and impedance are increasing. Then, the wave bends away the cloaked area instead of passing it. Three cases are tested depending on the comparison between the seismic wavelength and the diameter of the cloaked region. The advantage and disadvantage of the method were compared with conventional earthquake engineering method. Some practical requirements for realization in fields were discussed.

Dynamics of the thermocline in the equatorial region of the Pacific ocean

This paper is devoted to the subsurface current dynamics in equatorial regions, where the hallmark of a strong stratification is a sharp interface (thermocline), separating two layers of different density, and whose depth is dependent upon the strength of the winds above the ocean's surface. We give here a few monotonicity results concerning the dynamics of the thermocline in the equatorial region. The most important one asserts that the level of the thermocline decreases as the strength of the wind at ten meters above the ocean surface, denoted |Uw|, increases. Moreover, the strength of the current at the thermocline decreases as |Uw| increases.

Fluctuations and local ice structure in model supercooled water.

Large-scale simulations (up to 32,000 molecules) are used to analyze local structures and fluctuations for the TIP4P/2005 and TIP5P water models, under deeply supercooled conditions, near previously proposed liquid-liquid critical points. Bulk freezing does not occur in our simulations, but correlations between molecules with local ice-like structure (ice-like molecules) are strong and long ranged (∼4 nm), exceeding the shortest dimension of smaller simulation cells at the lowest temperatures considered. Correlations between ice-like molecules decay slowly at low temperature, on the order of a hundred nanoseconds. Local ice-like structure is strongly correlated with highly tetrahedral liquid structure at all times, both structures contribute to density fluctuations, and to the associated anomalous scattering. For the TIP4P/2005 and TIP5P models, we show that the apparent spontaneous liquid-liquid phase separations, recently reported [T. Yagasaki, M. Matsumoto, and H. Tanaka, Phys. Rev. E 89, 020301 (2014)] for small rectangular simulation cells below the proposed critical points, exhibit strong system size dependence and do not occur at all in the largest systems we consider. Furthermore, in the smaller rectangular systems where layers of different densities do occur, we find that the appearance of a region of low density is always accompanied simultaneously by an excess of local ice density, with no separation in time. Our results suggest that the density differences observed in direct simulations for the two models considered here are likely due to long-range correlations between ice-like molecules and do not provide strong evidence of liquid-liquid phase separation.

NUMERICAL INVESTIGATION OF INSULATION FECT ON SOLAR POND

Solar energy is one of the most important renewable energy sources. Solar heat generation is widely used. Solar pond collects and stores solar energy in the form of heat. Solar pond consists of layers of different density from top to bottom. Salt gradient in the solar pond prevents heat loss by convection in this structure. As well as the heat losses from side and bottom walls are very important to minimize heat losses. In this study, insulated and non-insulated solar ponds were modeled at the same dimensions and summer months. The temperature distributions of the solar pond were obtained during three months (e.g. June, July, August). Furthermore, the temperature distributions were compared for insulated and non-insulated solar ponds. According to calculations, insulated solar pond was found to be much more efficient

A note on axisymmetric supercritical coning in a porous medium

The steady response of a fluid with two layers of different density in a porous medium is considered during extraction through a point sink. Supercritical withdrawal in which both layers are being withdrawn is investigated using a spectral method. We show that for each withdrawal rate, there is a single entry angle of the interface into the point sink. As the flow rate decreases the angle of entry steepens until it becomes almost vertical, at which point the method fails. This limit is shown to correspond to the upper bound on sub-critical (single-layer) flow. doi:10.1017/S1446181114000170

Structure of internal solitary waves in two-layer fluid at near-critical situation

A new model equation describing weakly nonlinear long internal waves at the interface between two thin layers of different density is derived for the specific relationships between the densities, layer thicknesses and surface tension between the layers. The equation derived and dubbed here the Gardner–Kawahara equation represents a natural generalisation of the well-known Korteweg–de Vries (KdV) equation containing the cubic nonlinear term as well as fifth-order dispersion term. Solitary wave solutions are investigated numerically and categorised in terms of two dimensionless parameters, the wave speed and fifth-order dispersion. The equation derived may be applicable to wave description in other media.

The Photo-Gravitational R3BP when the Primaries are Heterogeneous Spheroid with Three Layers

The present paper deals with the stationary solution of the planar restricted three body problem when both the primaries are heterogeneous oblate spheroid with three layers of different densities and sources of radiation as well. It derives equations of motion and examines the existence and the linear stability of libration points. It is seen that there are five libration points, two triangular points and three collinear ones. It is further observed that the collinear points are unstable, while the triangular points are stable for the mass parameter 0 ≤ μ < μcrit. Here μcrit (the critical mass parameter) depends upon the combined effects of radiation and that due to the three different layers in the primaries. It is further seen that long or short periodic elliptical orbits emanate from the triangular points in the aforementioned range of μ.

An experimental study of the dynamic response of cylindrical sandwich shells with metallic foam cores subjected to blast loading

The deformation/failure modes and blast resistance of cylindrical sandwich shells comprising two aluminum face-sheets and an aluminum foam core, subjected to air blast loading, were investigated experimentally. Specimens of two different radii of curvature and geometrical configurations, clamped along their peripheries, were studied. A four-cable ballistic pendulum system was employed to measure the impulse imparted to the specimens. Typical deformation/failure modes were classified and analyzed; the effects of face-sheet thickness, core relative density, arrangement of foam core layers of different densities, specimen curvature and mass of charge on the structural response were also examined. The results indicate that both the deformation/failure modes and the structural response of the shells are sensitive to the geometrical configurations and blast impulse. Various failure modes – indentation or tearing of the front face-sheet, collapse of the core, severe inelastic deformation or tearing of the rear face-sheet, and failure between the face-sheets and foam core, were observed. The findings are useful for validating theoretical predictions, as well as to guide application of cellular metal sandwich structures for blast protection purposes.

A NOTE ON AXISYMMETRIC SUPERCRITICAL CONING IN A POROUS MEDIUM

AbstractThe steady response of a fluid with two layers of different density in a porous medium is considered during extraction through a point sink. Supercritical withdrawal in which both layers are being withdrawn is investigated using a spectral method. We show that for each withdrawal rate, there is a single entry angle of the interface into the point sink. As the flow rate decreases the angle of entry steepens until it becomes almost vertical, at which point the method fails. This limit is shown to correspond to the upper bound on sub-critical (single-layer) flow.

Kelvin–Helmholtz instability in the presence of variable viscosity for mudflow resuspension in estuaries

The temporal stability of a parallel shear flow of miscible fluid layers of different density and viscosity is investigated through a linear stability analysis and direct numerical simulations. The geometry and rheology of this Newtonian fluid mixing can be viewed as a simplified model of the behavior of mudflow at the bottom of estuaries for suspension studies. In this study, focus is on the stability and transition to turbulence of an initially laminar configuration. A parametric analysis is performed by varying the values of three control parameters, namely the viscosity ratio, the Richardson and Reynolds numbers, in the case of initially identical thickness of the velocity, density and viscosity profiles. The range of parameters has been chosen so as to mimic a wide variety of real configurations. This study shows that the Kelvin–Helmholtz instability is controlled by the local Reynolds and Richardson numbers of the inflection point. In addition, at moderate Reynolds number, viscosity stratification has a strong influence on the onset of instability, the latter being enhanced at high viscosity ratio, while at high Reynolds number, the influence is less pronounced. In all cases, we show that the thickness of the mixing layer (and thus resuspension) is increased by high viscosity stratification, in particular during the non-linear development of the instability and especially pairing processes. This study suggests that mud viscosity has to be taken into account for resuspension parameterizations because of its impact on the inflection point Reynolds number and the viscosity ratio, which are key parameters for shear instabilities.

Исследование деформационного поведения фрагмента кости при осевом сжатии, содержащего компактный и губчатый слои разной плотности

Исследование деформационного поведения фрагмента кости при осевом сжатии, содержащего компактный и губчатый слои разной плотности

Anorogenic plateau formation: The importance of density changes in the lithosphere

Away from active plate boundaries the relationships between spatiotemporal variations in density and geothermal gradient are important for understanding the evolution of topography in continental interiors. In this context the classic concept of the continental lithosphere as comprising three static layers of different densities (upper crust, lower crust, and upper mantle) is not adequate to assess long‐term changes in topography and relief in regions associated with pronounced thermal anomalies in the mantle. We have therefore developed a one‐dimensional model, which is based on thermodynamic equilibrium assemblage computations and deliberately excludes the effects of melting processes like intrusion or extrusions. Our model calculates the “metamorphic density” of rocks as a function of pressure, temperature, and chemical composition. It not only provides a useful tool for quantifying the influence of petrologic characteristics on density, but also allows the modeled “metamorphic” density to be adjusted to variable geothermal gradients and applied to different geodynamic environments. We have used this model to simulate a scenario in which the lithosphere‐asthenosphere boundary is subjected to continuous heating over a long period of time (130 Ma), and demonstrate how an anorogenic plateau with an elevation of 1400 m can be formed solely as a result of heat transfer within the continental lithosphere. Our results show that, beside dynamic topography (of asthenospheric origin), density changes within the lithosphere have an important impact on the evolution of anorogenic plateaus.

Numerical simulation of mass transport in internal solitary waves

A computational study of mass transport by large-amplitude, mode-2 internal solitary waves propagating on a pycnocline between two layers of different densities was conducted. The numerical model is based on the simulation of a vorticity-based formulation of the two-dimensional Navier-Stokes equations in the Boussinesq limit. Numerical experiments are conducted of the collapse of an initially mixed region, which leads to the generation of a train of internal solitary waves. The peak wave amplitude, a, is achieved by the leading wave, which encloses an intrusional bulge. The wave amplitude decays as it moves away from the collapsing mixing region. When the amplitude drops below a critical value, the wave is no longer able to transport mass and sharp-nosed intrusion is left behind. Mass transport by the leading wave, and by the trailing wave train and intrusion, is analyzed by tracking the motion of Lagrangian particles initially concentrated in the mixed region. Results indicate that for moderate wave amplitudes, a gradual decay in the wave amplitude occurs as the wave propagates, but the structure of the bulge is essentially maintained during this process. In contrast, for large-amplitude waves, the motion around the bulge is substantially more complex, exhibiting periodic shedding of vortex structures in the wake of the bulge and entrainment of external fluid into its core. It is shown that these motions have substantial impact on mass transport by the wave train, which is quantified through detailed analysis of the Lagrangian particle distributions.

Numerical study of the effects occurring near a circular cylinder in stratified fluid flows with short buoyancy periods

Flow around a two-dimensional circular cylinder of a stratified fluid with periods buoyancy Tb = 25.2 and 6.28 sec is studied numerically over a wide range of Reynolds and Froude numbers. It is found that in the presence of a perturbation ahead of a cylinder which moves downstream with increasing Reynolds number, the salinity isolines have the shape of a semi-circular comb with sharp teeth. The shape change of the attached waves and the occurrence of fluid layers of different densities in the cylinder wake are studied. In flows with a buoyancy period Tb = 6.28 sec at Reynolds numbers Re 60, these zones are absent.