scholarly journals Levitation of non-magnetizable droplet inside ferrofluid

2018 ◽  
Vol 857 ◽  
pp. 398-448 ◽  
Author(s):  
Chamkor Singh ◽  
Arup K. Das ◽  
Prasanta K. Das
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Viscosity Ratio ◽  
Temporal Dynamics ◽  
Liquid Droplet ◽  
Droplet Surface ◽  
Two Dimensions ◽  
Projection Algorithm ◽  
The Stability ◽  
The Individual

The central theme of this work is that a stable levitation of a denser non-magnetizable liquid droplet, against gravity, inside a relatively lighter ferrofluid – a system barely considered in ferrohydrodynamics – is possible, and exhibits unique interfacial features; the stability of the levitation trajectory, however, is subject to an appropriate magnetic field modulation. We explore the shapes and the temporal dynamics of a plane non-magnetizable droplet levitating inside a ferrofluid against gravity due to a spatially complex, but systematically generated, magnetic field in two dimensions. The coupled set of Maxwell’s magnetostatic equations and the flow dynamic equations is integrated computationally, utilizing a conservative finite-volume-based second-order pressure projection algorithm combined with the front-tracking algorithm for the advection of the interface of the droplet. The dynamics of the droplet is studied under both the constant ferrofluid magnetic permeability assumption as well as for more realistic field-dependent permeability described by Langevin’s nonlinear magnetization model. Due to the non-homogeneous nature of the magnetic field, unique shapes of the droplet during its levitation, and at its steady state, are realized. The complete spatio-temporal response of the droplet is a function of the Laplace number $La$ , the magnetic Laplace number $La_{m}$ and the Galilei number $Ga$ ; through detailed simulations we separate out the individual roles played by these non-dimensional parameters. The effect of the viscosity ratio, the stability of the levitation path and the possibility of existence of multiple stable equilibrium states is investigated. We find, for certain conditions on the viscosity ratio, that there can be developments of cusps and singularities at the droplet surface; we also observe this phenomenon experimentally and compare with the simulations. Our simulations closely replicate the singular projection on the surface of the levitating droplet. Finally, we present a dynamical model for the vertical trajectory of the droplet. This model reveals a condition for the onset of levitation and the relation for the equilibrium levitation height. The linearization of the model around the steady state captures that the nature of the equilibrium point goes under a transition from being a spiral to a node depending upon the control parameters, which essentially means that the temporal route to the equilibrium can be either monotonic or undulating. The analytical model for the droplet trajectory is in close agreement with the detailed simulations.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

1998 ◽  
Vol 60 (3) ◽  
pp. 529-539 ◽  
Author(s):  
RENU BAJAJ ◽  
S. K. MALIK
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Thermal Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

Stability properties of cold mantle systems for current-driven modes

1980 ◽  
Vol 23 (3) ◽  
pp. 383-400
Author(s):  
D. Ohlsson
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Stability Diagrams ◽  
Neutral Gas ◽  
Transverse Current ◽  
Laboratory Plasmas ◽  
State Models ◽  
The Stability ◽  
Moderate Magnetic Field ◽  
Parameter Ranges

The stability problem of the boundary regions of cold blanket systems with induced currents parallel to the lines of force is formulated. Particular interest is focused on two types of mode: first electrostatic modes driven by the combined effects of a transverse resistivity gradient due to a spatially non-uniform electron temperature and a longitudinal current, second electromagnetic kink-like modes driven by the torque arising from a transverse current density gradient and magnetic field perturbations. It is found that the combination of various dissipative and neutral gas effects introduces strong stabilizing effects within specific parameter ranges. For particular steady-state models investigated it is shown that these effects become of importance in laboratory plasmas at relatively high densities, low temperatures and moderate magnetic field strengths. Stability diagrams based on specific steady-state cold plasma blanket models will be presented.

Stability of an anisotropic plasma jet

1971 ◽  
Vol 6 (2) ◽  
pp. 237-248 ◽  
Author(s):  
M. R. Raghavachar
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Infinite Number ◽  
Plasma Jet ◽  
Plasma Pressure ◽  
Magnetic Pressure ◽  
Anisotropic Plasma ◽  
Parallel Component ◽  
Perpendicular Component ◽  
The Stability

The stability of an anisotropic plasma jet has been investigated using equations of Chew, Goldberger & Low (1965) in both plane and cylindrical geometries. The main conclusions are as follows:(i) For waves of small wavelength, when λ (the ratio of plasma density to the density of surrounding non-conducting medium) is much greater than unity, the plasma jet is stable only if 1/6(1 + σ) <p∥/p⊥ < 1 + 2σ, where p∥ and p⊥ denote the components of pressure parallel and perpendicular to the direction of magnetic field in the steady state, and σ denotes the ratio of magnetic pressure to the perpendicular component of plasma pressure.(ii) When λ ≫ 1, the plasma jet is unstable if the parallel component of pressure exceeds the sum of the perpendicular component of pressure and twice the magnetic pressure of the plasma.(iii) For long waves, we find that there exists an infinite number of growing and decaying waves. Expressions for the growth rates have been obtained.

scholarly journals On the small redshift limit of steady states of the spherically symmetric Einstein–Vlasov system and their stability

2015 ◽  
Vol 159 (3) ◽  
pp. 529-546 ◽  
Author(s):  
MAHIR HADŽIĆ ◽  
GERHARD REIN
Keyword(s):  
Steady State ◽  
Steady States ◽  
Spherically Symmetric ◽  
Second Variation ◽  
Speed Of Light ◽  
Limiting Behavior ◽  
Adm Mass ◽  
The Stability ◽  
The Individual ◽  
The Second Variation

AbstractFamilies of steady states of the spherically symmetric Einstein–Vlasov system are constructed, which are parametrised by the central redshift. It is shown that as the central redshift tends to zero, the states in such a family are well approximated by a steady state of the Vlasov–Poisson system, i.e., a Newtonian limit is established where the speed of light is kept constant as it should be and the limiting behavior is analysed in terms of a parameter which is tied to the physical properties of the individual solutions. This result is then used to investigate the stability properties of the relativistic steady states with small redshift parameter in the spirit of recent work by the same authors, i.e., the second variation of the ADM mass about such a steady state is shown to be positive definite on a suitable class of states.

Nonlinear Kelvin—Helmholtz instability in magnetic fluids of finite thickness: effects of a tangential magnetic field

1994 ◽  
Vol 51 (3) ◽  
pp. 451-465 ◽  
Author(s):  
Abdel Raouf F. Elhefnawy
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Second Harmonic ◽  
Wave Train ◽  
Finite Thickness ◽  
Magnetic Fluids ◽  
Two Dimensions ◽  
Stability And Instability ◽  
Regions Of Stability ◽  
The Stability

The nonlinear stability of a horizontal interface separating two streaming magnetic fluids of finite thickenss is investigated in two dimensions. The fluids are considered to be inviscid and incompressible. The magnetic field is applied along the direction of streaming. The method of multiple scales, in both space and time, is used to examine the stability properties of the system arising from second-harmonic resonance. A pair of partial differential equations for the amplitude of the wave and its second harmonic are derived. These describe the evolution of the wave train up to cubic order, and may be regarded as the counterparts of the single nonlinear Schrödinger equation that occurs in the non-resonant case. The stability condition of this equation is discussed both analytically and numerically, and stability diagrams are obtained. Regions of stability and instability are identified. The nonlinear cut-off wavenumber separating the regions of stability from those of instability is obtained. The equation governing the evolution of the amplitude at the critical point is also obtained, which leads to a nonlinear Klein—Gordon equation.

Implications of Person Fluctuation for the Stability and Validity of Test Scores

Methodology ◽  
2006 ◽  
Vol 2 (4) ◽  
pp. 142-148 ◽  
Author(s):  
Pere J. Ferrando
Keyword(s):  
Item Response ◽  
Test Scores ◽  
Temporal Stability ◽  
Person Fit ◽  
Item Parameters ◽  
Individual Trait ◽  
The Stability ◽  
The Individual ◽  
Different Levels ◽  
Fluctuation Model

In the IRT person-fluctuation model, the individual trait levels fluctuate within a single test administration whereas the items have fixed locations. This article studies the relations between the person and item parameters of this model and two central properties of item and test scores: temporal stability and external validity. For temporal stability, formulas are derived for predicting and interpreting item response changes in a test-retest situation on the basis of the individual fluctuations. As for validity, formulas are derived for obtaining disattenuated estimates and for predicting changes in validity in groups with different levels of fluctuation. These latter formulas are related to previous research in the person-fit domain. The results obtained and the relations discussed are illustrated with an empirical example.

Magnetic Field Imaging on Stacked Flash Memories by Laser Probing and SQUID Scanning

2017 ◽  
Author(s):  
K. Sanchez ◽  
G. Bascoul ◽  
F. Infante ◽  
N. Courjault ◽  
T. Nakamura
Keyword(s):  
Magnetic Field ◽  
Failure Analysis ◽  
Two Dimensions ◽  
Analysis Tool ◽  
Active Device ◽  
Current Path ◽  
3D Packaging ◽  
Magnetic Field Imaging ◽  
The Magnetic Field ◽  
Field Imaging

Abstract Magnetic field imaging is a well-known technique which gives the possibility to study the internal activity of electronic components in a contactless and non-invasive way. Additional data processing can convert the magnetic field image into a current path and give the possibility to identify current flow anomalies in electronic devices. This technique can be applied at board level or device level and is particularly suitable for the failure analysis of complex packages (stacked device & 3D packaging). This approach can be combined with thermal imaging, X-ray observation and other failure analysis tool. This paper will present two different techniques which give the possibility to measure the magnetic field in two dimensions over an active device. Same device and same level of current is used for the two techniques to give the possibility to compare the performance.

The Stability of Steady-State Depth Distributions of Marine Phytoplankton

1974 ◽  
Vol 108 (963) ◽  
pp. 679-687 ◽  
Author(s):  
W. O. Criminale, ◽  
D. F. Winter
Keyword(s):  
Steady State ◽  
Marine Phytoplankton ◽  
The Stability ◽  
Depth Distributions
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