scholarly journals Post-Newtonian properties of EMRI with power law potential

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Chinmay N. Gandevikar ◽  
Divyesh N. Solanki ◽  
Dipanjan Dey
Keyword(s):  
Velocity Profile ◽  
Power Law ◽  
Average Energy ◽  
Mass Ratio ◽  
Matter Distribution ◽  
Energy Radiation ◽  
Newton Potential ◽  
Test Particles ◽  
Orbital Frequency ◽  
Radiation Rate

AbstractThere are many astrophysical scenarios where extreme mass ratio inspiral (EMRI) binaries can be surrounded by inhomogenous matter distribution. The distribution of mass can affect the dynamical properties (e.g. orbital frequency, average energy radiation rate, etc.) of the EMRI. In this matter distribution, instead of Kepler–Newton potential, one may consider a more general form of potential i.e. power law potential. Moreover, due to the power law potential, at the Newtonian order itself, the velocity profile of test particles does not fall as much as that predicted by Kepler–Newton potential and this feature of the velocity profile may be observationally important. In this study, we have obtained the first post-Newtonian (1PN) expressions for dynamical quantities and the average energy radiation rate from the circular orbit EMRI which is surrounded by a matter distribution. We show that the energy radiation rate and orbital frequency of EMRI can be significantly different in the presence of power law potential as compared to that in the Kepler–Newton potential, signatures of which may be observed in gravitational waves from EMRI.

Spatially resolved dust-to-gas mass ratios in nearby galaxies

2019 ◽  
Vol 15 (S341) ◽  
pp. 78-82
Author(s):  
Basilio Solís-Castillo ◽  
Marcus Albrecht
Keyword(s):  
Power Law ◽  
Interstellar Dust ◽  
Conversion Factor ◽  
Strong Impact ◽  
Mass Ratio ◽  
Spatially Resolved ◽  
Nearby Galaxies ◽  
Hierarchical Bayesian Method ◽  
Factor Α ◽  
Infrared Data

AbstractWe analyse the dust-to-gas mass ratio (DGR) in nearby galaxies on kiloparsec scales. We focus on their dependence on metallicity and the CO-to-H2 conversion factor, αco. We use a sample of 25 nearby galaxies from SINGS and combine our data with CO (2-1) and H I observations from the HERACLES and THINGS surveys. We implement a Hierarchical Bayesian method to derive the dust mass via fitting the infrared data from 100 to 500 μm with a single modified blackbody. We find that the DGR-metallicity relation follows a power law and we study its strong dependency on the conversion factor αco. Our results indicate a strong connection between interstellar dust and gas. The resolved DGR-metallicity relation cannot be represented with a single power law. The scatter in this relation shows the strong impact of several processes that take place in every galaxy.

Power Law Velocity Profile in the Turbulent Boundary Layer on Transitional Rough Surfaces

2007 ◽  
Vol 129 (8) ◽  
pp. 1083-1100 ◽  
Author(s):  
Noor Afzal
Keyword(s):  
Boundary Layer ◽  
Functional Equation ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Power Law ◽  
Wall Roughness ◽  
Closure Model ◽  
Log Law

A new approach to scaling of transitional wall roughness in turbulent flow is introduced by a new nondimensional roughness scale ϕ. This scale gives rise to an inner viscous length scale ϕν∕uτ, inner wall transitional variable, roughness friction Reynolds number, and roughness Reynolds number. The velocity distribution, just above the roughness level, turns out to be a universal relationship for all kinds of roughness (transitional, fully smooth, and fully rough surfaces), but depends implicitly on roughness scale. The open turbulent boundary layer equations, without any closure model, have been analyzed in the inner wall and outer wake layers, and matching by the Izakson-Millikan-Kolmogorov hypothesis leads to an open functional equation. An alternate open functional equation is obtained from the ratio of two successive derivatives of the basic functional equation of Izakson and Millikan, which admits two functional solutions: the power law velocity profile and the log law velocity profile. The envelope of the skin friction power law gives the log law, as well as the power law index and prefactor as the functions of roughness friction Reynolds number or skin friction coefficient as appropriate. All the results for power law and log law velocity and skin friction distributions, as well as power law constants are explicitly independent of the transitional wall roughness. The universality of these relations is supported very well by extensive experimental data from transitional rough walls for various different types of roughnesses. On the other hand, there are no universal scalings in traditional variables, and different expressions are needed for various types of roughness, such as inflectional roughness, monotonic roughness, and others. To the lowest order, the outer layer flow is governed by the nonlinear turbulent wake equations that match with the power law theory as well as log law theory, in the overlap region. These outer equations are in equilibrium for constant value of m, the pressure gradient parameter, and under constant eddy viscosity closure model, the analytical and numerical solutions are presented.

Nonvisual Motor Learning Improves Visual Motion Perception: Evidence From Violating the Two-Thirds Power Law

2010 ◽  
Vol 104 (3) ◽  
pp. 1612-1624 ◽  
Author(s):  
I.A.M. Beets ◽  
F. Rösler ◽  
K. Fiehler
Keyword(s):  
Motor Learning ◽  
Velocity Profile ◽  
Power Law ◽  
Visual Discrimination ◽  
Discrimination Task ◽  
Visual Motion ◽  
Visual Discrimination Task ◽  
Control Group ◽  
Motor Training ◽  
Training Groups

Few studies have reported direct effects of motor learning on visual perception, especially when using novel movements for the motor system. Atypical motor behaviors that violate movement constraints provide an excellent opportunity to study action-to-perception transfer. In our study, we passively trained blindfolded participants on movements violating the 2/3 power law. Before and after motor training, participants performed a visual discrimination task in which they decided whether two consecutive movements were same or different. For motor training, we randomly assigned the participants to two motor training groups or a control group. The motor training group experienced either a weak or a strong elliptic velocity profile on a circular trajectory that matched one of the visual test stimuli. The control group was presented with linear trajectories unrelated to the viewed movements. After each training session, participants actively reproduced the movement to assess motor learning. The group trained on the strong elliptic velocity profile reproduced movements with increasing elliptic velocity profiles while circular geometry remained constant. Furthermore, both training groups improved in visual discrimination ability for the learned movement as well as for highly similar movements. Participants in the control group, however, did not show any improvements in the visual discrimination task nor did participants who did not acquire the trained movement. The present results provide evidence for a transfer from action to perception which generalizes to highly related movements and depends on the success of motor learning. Moreover, under specific conditions, it seems to be possible to acquire movements deviating from the 2/3 power law.

Pipe Flow Measurements of a Transparent Non-Newtonian Slurry

1989 ◽  
Vol 111 (3) ◽  
pp. 331-336 ◽  
Author(s):  
J. T. Park ◽  
R. J. Mannheimer ◽  
T. A. Grimley ◽  
T. B. Morrow
Keyword(s):  
Velocity Profile ◽  
Newtonian Fluid ◽  
Power Law ◽  
Pipe Flow ◽  
Large Scale ◽  
Longitudinal Velocity ◽  
Tangential Velocity ◽  
Turbulent Pipe Flow ◽  
Laser Doppler Velocimeter ◽  
Flow Measurements

An experimental description of the flow structure of non-Newtonian slurries in the laminar, transitional, and full turbulent pipe flow regimes is the primary objective of this research. Experiments were conducted in a large-scale pipe slurry flow facility with an inside pipe diameter of 51 mm. The transparent slurry formulated for these experiments from silica, mineral oil, and Stoddard solvent exhibited a yield-power-law behavior from concentric-cylinder viscometer measurements. The velocity profile for laminar flow from laser Doppler velocimeter (LDV) measurements had a central plug flow region, and it was in agreement with theory. The range of the transition region was narrower than that for a Newtonian fluid. The mean velocity profile for turbulent flow was close to a 1/7 power-law velocity profile. The rms longitudinal velocity profile was also similar to a classical turbulent pipe flow experiment for a Newtonian fluid; however, the rms tangential velocity profile was significantly different.

scholarly journals Analysis of the velocity distribution in different types of ventilation system ducts

2018 ◽  
Vol 180 ◽  
pp. 02081 ◽  
Author(s):  
Kazimierz Peszyński ◽  
Lukasz Olszewski ◽  
Emil Smyk ◽  
Daniel Perczyński
Keyword(s):  
Velocity Profile ◽  
Velocity Distribution ◽  
Cross Section ◽  
Power Law ◽  
Flow Rate ◽  
Fundamental Problem ◽  
Ventilation System ◽  
Different Types ◽  
Actual Profile ◽  
Ventilation Duct

The paper presents the results obtained during the preliminary studies of circular and rectangular ducts before testing the properties elements (elbows, tees, etc.)of rectangular with rounded corners ducts. The fundamental problem of the studies was to determine the flow rate in the ventilation duct. Due to the size of the channel it was decided to determine the flow rate based on the integration of flow velocity over the considered cross-section. This method requires knowledge of the velocity distribution in the cross section. Approximation of the measured actual profile by the classic and modified Prandtl power-law velocity profile was analysed.

Flow of Yield Power Law Fluids in Horizontal Pipes-Flow Field Characterization Using Particle Image Velocimetry Technique

2021 ◽  
Author(s):  
Yanxin (Sussi) Sun ◽  
Abdulla Abou-Kassem ◽  
Majid Bizhani ◽  
Ergun Kuru
Keyword(s):  
Experimental Study ◽  
Flow Field ◽  
Velocity Profile ◽  
Yield Stress ◽  
Power Law ◽  
Pipe Flow ◽  
Hydrodynamic Behaviour ◽  
Yield Stress Fluids ◽  
Power Law Fluids ◽  
Flow Field Characteristics

Abstract Yield Power Law (YPL) rheological model is commonly used to describe the pipe and annular flow of drilling fluids. However, the hydrodynamic behaviour of fluids with yield stress are difficult to predict because they exhibit an inherent plug (solid like) region where the velocity gradient is zero. Moreover, it is not easy to identify the transition between this solid like and liquid regions. Theoretical studies have been conducted in the past to describe YPL fluid flow in pipes and annuli. As a result, several models have been proposed for determining flow field characteristics (e.g. velocity profile, plug width, etc.) and frictional pressure losses. However, most of these models have been validated by limited experimental and/or field data. Similar future modeling studies may benefit from more data collected under controlled experimental conditions. Therefore, we have conducted an experimental study to investigate the hydrodynamic behaviour of yield stress fluids under laminar pipe flow conditions and the results are presented in this paper. Water-based Yield Power Law fluids were prepared by using Carbopol® 940, a synthetic high-molecular-weight polyacrylic acid-based cross-linked polymer. Fluids with yield stresses varying from 0.75 Pa (1.56 lb/100 ft2) to 4.37 Pa (9.13 lb/100 ft2) were obtained by using Carbopol concentrations changing from 0.060% w/w to 0.073% w/w. A 9m long horizontal pipeline with, 95 mm diameter (ID) was used for the experiments. Reynolds number range varying from 97 to 1268 confirmed that all flow field characteristics measurements of YPL fluids were conducted under laminar flow regimes. Experimental study provided detailed information about pipe flow characteristics of yield stress fluids, including full annular velocity profile, near wall velocity profile, wall slip velocity and the plug region thickness. The study was concluded by comparing experimental results (i.e. full velocity profile, frictional pressure loss, and plug width) to predictions of models presented in the literature. Practical implications of the results have also been discussed by considering the hydraulic design of some practical field operations such as hole cleaning.

Non-Newtonian Flow in Eccentric Annuli

1990 ◽  
Vol 112 (3) ◽  
pp. 163-169 ◽  
Author(s):  
M. Haciislamoglu ◽  
J. Langlinais
Keyword(s):  
Velocity Profile ◽  
Power Law ◽  
Flow Rate ◽  
Pressure Loss ◽  
Annular Flow ◽  
Flow Behavior ◽  
Drilling Fluids ◽  
Viscosity Term ◽  
Power Law Fluids ◽  
Eccentric Annuli

A common assumption for annular flow used in the petroleum industry is that the inner pipe is concentrically located inside the flow geometry; however, this is rarely the case, even in slightly deviated wells. Considering the increasing number of directional and horizontal wells, the flow behavior of drilling fluids and cement slurries in eccentric annuli is becoming particularly important. In this paper, the governing equation of laminar flow is numerically solved using a finite differences technique to obtain velocity and viscosity profiles of yield-power law fluids (including Bingham plastic and power law fluids). Later, the velocity profile is integrated to obtain flow rate. Results show that the velocity profile is substantially altered in the annulus when the inner pipe is no longer concentric. Stagnant regions of flow were calculated in the low side of the hole. Viscosity profiles predicted for an eccentric annulus show how misleading the widely used single-value apparent viscosity term can be for non-Newtonian fluids. Profiles of velocity and viscosity in concentric and varying eccentric annuli are presented in 3-D and 2-D contour plots for a better visualization of annular flow. Frictional pressure loss gradient versus flow rate relationship data for power law fluids is generated using the computer program. Later, this data is fitted to obtain a simple equation utilizing regressional analysis, allowing for a quick calculation of friction pressure losses in eccentric annuli. For a given flow rate, frictional pressure loss is reduced as the inner pipe becomes eccentric. In most cases, about a 50-percent reduction in frictional pressure loss is predicted when the inner pipe lies on the low side.

Annular Flow—A Note on the Turbulent Velocity Profile

1958 ◽  
Vol 62 (575) ◽  
pp. 830-831 ◽  
Author(s):  
Henry Barrow
Keyword(s):  
Experimental Data ◽  
Velocity Profile ◽  
Velocity Distribution ◽  
Power Law ◽  
Annular Flow ◽  
Turbulent Velocity ◽  
Concentric Annulus ◽  
Annular Section ◽  
Modified Power Law

The Important characteristics of the turbulent velocity profile of a plain concentric annulus and some of the methods of correlating the velocity distribution are briefly reviewed. The average velocities in an annular section are examined and some experimental data is correlated by a modified power law.

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