scholarly journals Elasto-capillary coalescence of multiple parallel sheets

2013 ◽  
Vol 723 ◽  
pp. 692-705 ◽  
Author(s):  
A. D. Gat ◽  
M. Gharib
Keyword(s):  
Energy Analysis ◽  
Minimal Energy ◽  
Common Assumption ◽  
Viscous Forces ◽  
Theoretical Predictions ◽  
The Mean ◽  
The Stability ◽  
Elastic Sheets ◽  
Theoretical Results ◽  
Good Agreement

AbstractWe analyse two-dimensional clamped parallel elastic sheets which are partially immersed in liquid as a model for elasto-capillary coalescence. In the existing literature this problem is studied via minimal energy analysis of capillary and elastic energies of the post-coalescence state, yielding the maximal stable post-coalescence bundle size. Utilizing modal stability analysis and asymptotic analysis, we studied the stability of the configuration before the coalescence occurred. Our analysis revealed previously unreported relations between viscous forces, body forces, and the instability yielding the coalescence, thus undermining a common assumption that coalescence will occur as long as it will not create a bundle larger than the maximal stable post-coalesced size. A mathematical description of the process creating the hierarchical coalescence structure was obtained and yielded that the mean number of sheets per coalesced region is limited to the subset ${2}^{N} $ where $N$ is the set of natural numbers. Our theoretical results were illustrated by experiments and good agreement with the theoretical predictions was observed.

Beam-foil spectroscopy of oxygen in the wavelength region from 270 to 490 Å

1978 ◽  
Vol 56 (5) ◽  
pp. 508-516 ◽  
Author(s):  
Eric H. Pinnington ◽  
Keith E. Donnelly ◽  
J. Anthony Kernahan ◽  
David J. G. Irwin
Keyword(s):  
Satisfactory Agreement ◽  
Wavelength Region ◽  
Theoretical Predictions ◽  
The Mean ◽  
Theoretical Results ◽  
Beam Foil ◽  
Foil Technique ◽  
Good Agreement

We have used the beam-foil technique to study the spectrum of oxygen between 270 and 490 Å. We have measured the mean lives of the 3d2F, 3d4P, 3d4D, 3d′ 2D, 3d′ 2F, 4d4P, and 4d4D terms of O II, the 3s1P0, 3s3P0, 3S5P, 3s′ 3D, 3d3P, 3d3D, 3d3F, and 3d5P terms of O III, and the 3S2S, 3P2P0, and 3s4P0 terms of O IV. All cascade components are adequately explained. Good agreement is found with previous measurements in most cases, but significant discrepancies are found with some earlier results obtained using branches above 2000 Å. Generally satisfactory agreement is also found with theoretical predictions, although disagreement is found for several members of the 2p3–2p23d array in O II f-Values are computed for 18 individual lines, and compared with other experimental and theoretical results. Finally, we discuss briefly the f-value trends along the 2p23P–2p3s3P0 (O III), 2p21D–2p3s1P0 (O III), 2s2p24P–2s2p(3P0)3s4P0 (O IV), and 2p2P0–3s2S (O IV) isoelectronic sequences.

Stability of Water-Lubricated, Hydrostatic, Conical Bearings With Spiral Grooves for High-Speed Spindles

2001 ◽  
Vol 124 (2) ◽  
pp. 398-405 ◽  
Author(s):  
S. Yoshimoto ◽  
S. Oshima ◽  
S. Danbara ◽  
T. Shitara
Keyword(s):  
High Speed ◽  
Water Pressure ◽  
Rotating Shaft ◽  
Pressurized Water ◽  
High Speeds ◽  
Theoretical Predictions ◽  
The Stability ◽  
Stability Of Water ◽  
Spiral Grooves ◽  
Good Agreement

In this paper, the stability of water-lubricated, hydrostatic, conical bearings with spiral grooves for high-speed spindles is investigated theoretically and experimentally. In these bearing types, pressurized water is first fed to the inside of the rotating shaft and then introduced into spiral grooves through feeding holes located at one end of each spiral groove. Therefore, water pressure is increased due to the effect of the centrifugal force at the outlets of the feeding holes, which results from shaft rotation. In addition, water pressure is also increased by the viscous pumping effect of the spiral grooves. The stability of the proposed bearing is theoretically predicted using the perturbation method, and calculated results are compared with experimental results. It was consequently found that the proposed bearing is very stable at high speeds and theoretical predictions show good agreement with experimental data.

Analysis of Dispersion of Small Spherical Particles in a Random Velocity Field

1990 ◽  
Vol 112 (1) ◽  
pp. 114-120 ◽  
Author(s):  
H. Ounis ◽  
G. Ahmadi
Keyword(s):  
Particle Velocity ◽  
Digital Simulation ◽  
Density Ratio ◽  
Spherical Particles ◽  
Theoretical Predictions ◽  
The Mean ◽  
Analysis Of Dispersion ◽  
Gradient Effects ◽  
Analytical Expressions ◽  
Good Agreement

The equation of motion of a small spherical rigid particle in a turbulent flow field, including the Stokes drag, the Basset force, and the virtual mass effects, is considered. For an isotropic field, the lift force and the velocity gradient effects are neglected. Using the spectral method, responses of the resulting constant coefficient stochastic integrao-differential equation are studied. Analytical expressions relating the Lagrangian energy spectra of particle velocity to that of the fluid are developed and the results are used to evaluate various response statistics. Variations of the mean-square particle velocity and particle diffusivity with size, density ratio and response time are studied. The theoretical predictions are compared with the digital simulation results and the available data and good agreement is observed.

Vibration of a Rotating Asymmetric Shaft Supported in Asymmetric Bearings

1968 ◽  
Vol 10 (3) ◽  
pp. 252-261 ◽  
Author(s):  
H. F. Black ◽  
A. J. McTernan
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Forced Vibrations ◽  
Variation Method ◽  
Approximate Theory ◽  
Cross Sectional ◽  
Mass Unbalance ◽  
The Mean ◽  
Theoretical Results ◽  
Good Agreement

The parametrically excited vibrations of this system with assumed small asymmetry of the shaft cross-section are discussed in terms of the motion of a symmetric shaft having the mean cross-sectional flexibility, and the equations of motion are solved by the approximate perturbation-variation method of Hsu. Both features yield a more lucid appreciation of the motions expected than previous treatments: in particular, simpler explicit expressions for unstable bounds are given and forced vibrations due to mass unbalance are discussed with greater facility. The practically important case of nearly coincident natural frequencies is examined. The theoretical results are compared with analogue computation: good agreement with the approximate theory is found even for quite large shaft asymmetry.

Thermal Behavior and Friction in Journal Bearings

1970 ◽  
Vol 92 (3) ◽  
pp. 373-380 ◽  
Author(s):  
Al. Nica
Keyword(s):  
Experimental Data ◽  
Thermal Behavior ◽  
Heat Dissipation ◽  
Journal Bearings ◽  
Friction Torque ◽  
Operating Characteristics ◽  
Lubricant Flow ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Good Agreement

This paper deals with friction and the field of temperature in the lubricant film of journal bearings. Theoretical results regarding the thermal behavior are checked with experimental data and good agreement is found. Emphasis is put on the variation of temperature and lubricant flow with the operating characteristics of the bearing and it is seen that theoretical predictions for minima of friction torque are backed by temperature measurements. Further on, the friction torque and the mechanism of heat dissipation in bearings are dealt with, in order to verify the assumptions used in the calculation schemes. The means of efficiently cooling the bearing are also discussed, as well as the part played by the divergent zone in this process.

scholarly journals The Dynamics of the S(1D)+H2/D2 Reactions at Low Temperature via Statistical Simulations

2020 ◽  
Vol 3 (1) ◽  
pp. 9-16
Author(s):  
Tomas Gonzalez-Lezana ◽  
Pascal Larrégaray ◽  
Laurent Bonnet
Keyword(s):  
Cross Sections ◽  
Quantum Model ◽  
Space Theory ◽  
Collisional Energy ◽  
Energy Regime ◽  
Phase Space Theory ◽  
The Mean ◽  
Statistical Approaches ◽  
Theoretical Results ◽  
Good Agreement

Two different statistical approaches, the statistical quantum model (SQM) and the mean potential phase space theory (MPPST), have been employed to calculate the integral cross sections for the reactive collisions between S(1D) and H2/ D2  in the low energy regime (below 0.3 eV collisional energy). The rate constant for the S(1D) + H2 → SH + H reaction has been also obtained and compared with previously reported experimental and theoretical results. The good agreement shows the capability of these two methods to study the dynamics of these complex-forming atom-diatom processes in the present energy regime.

The instability of the thin vortex ring of constant vorticity

1977 ◽  
Vol 287 (1344) ◽  
pp. 273-305 ◽  
Keyword(s):  
Stability Analysis ◽  
Vortex Ring ◽  
Mean Flow ◽  
Bending Waves ◽  
Constant Vorticity ◽  
Ring Radius ◽  
Amplification Rate ◽  
The Mean ◽  
The Stability ◽  
Good Agreement

A theoretical investigation of the instability of a vortex ring to short azimuthal bending waves is presented. The theory considers only the stability of a thin vortex ring with a core of constant vorticity (constant /r) in an ideal fluid. Both the mean flow and the disturbance flow are found as an asymptotic solution in e = a /R, the ratio of core radius to ring radius. Only terms linear in wave amplitude are retained in the stability analysis. The solution to 0 (e 2 ) is presented, although the details of the stability analysis are carried through completely only for a special class of bending waves that are known to be unstable on a line filament in the presence of strain (Tsai & Widnall 1976) and have been identified in the simple model of Widnall, Bliss & Tsai (1974) as a likely mode of instability for the vortex ring: these occur at certain critical wavenumbers for which waves on a line filament of the same vorticity distribution would not rotate (w 0 = 0). The ring is found to be always unstable for at least the lowest two critical wavenumbers ( ka = 2.5 and 4.35). The amplification rate and wavenumber predicted by the theory are found to be in good agreement with available experimental results.

scholarly journals Generalized Softened Variable Angle Truss Model for RC Hollow Beams under Torsion

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2209
Author(s):  
Luís Bernardo
Keyword(s):  
Solution Procedure ◽  
Pure Torsion ◽  
Specific Behavior ◽  
Torsional Response ◽  
Truss Model ◽  
Variable Angle ◽  
Theoretical Predictions ◽  
Hollow Beams ◽  
Theoretical Results ◽  
Good Agreement

In recent studies, a new softened truss model called Generalized Softened Variable Angle Truss Model (GSVATM) has been proposed to compute the full torsional response of reinforced concrete (RC) rectangular solid beams under pure torsion. In this article, the GSVATM is extended to cover RC hollow beams under torsion. The modification of the calculation procedure, in order to account for the specific behavior of RC hollow beams for low loading levels, as well as the final solution procedure, is presented. The theoretical predictions from the extended GSVATM are compared with experimental results of RC hollow beams under torsion found in the literature. Good agreement is observed between the experimental and theoretical results, for both high and low loading levels.

On the computation of dipole transitions in the HD molecule. Part II

1976 ◽  
Vol 54 (6) ◽  
pp. 672-679 ◽  
Author(s):  
L. Wolniewicz
Keyword(s):  
Ground State ◽  
Wave Functions ◽  
Nonadiabatic Coupling ◽  
Transition Moments ◽  
The Mean ◽  
Variational Wave Functions ◽  
Theoretical Results ◽  
Variational Wave ◽  
Electronic Ground ◽  
Good Agreement

The nonadiabatic coupling with Πu states in the electronic ground state of the HD molecule is discussed. Formulas are given that facilitate the evaluation of Πu contributions to the energies and transition moments. Numerical computations are performed for all ν ≤ 4 vibrational and J ≤ 4 rotational levels yielding the Πu and Σu nonadiabatic corrections. The variational wave functions are employed to compute the transition moments for the 0–ν bands with ν ≤ 4. The results are in good agreement with experimental data except in the case of the 0–ν band where the theoretical results are larger than the mean experimental moment by a factor of about 1.4.

Comparison Between Theoretical Predictions of Wave Resistance and Experimental Data for the Wigley Hull

1983 ◽  
Vol 27 (04) ◽  
pp. 215-226
Author(s):  
C. Y. Chen ◽  
F. Noblesse
Keyword(s):  
Experimental Data ◽  
Froude Number ◽  
Resistance Coefficient ◽  
Wave Resistance ◽  
Number Range ◽  
Theoretical Predictions ◽  
Wigley Hull ◽  
Sinkage And Trim ◽  
Theoretical Results ◽  
Good Agreement

A number of theoretical predictions of the wave-resistance coefficient of the Wigley hull are compared with one another and with available experimental data, to which corrections for sinkage and trim are applied. The averages of eleven sets of experimental data (corrected for sinkage and trim) and of eleven sets of theoretical results for large values of the Froude number, specifically for F 0.266, 0.313, 0.350, 0.402, 0.452, and 0.482, are found to be in fairly good agreement, in spite of considerable scatter in both the experimental data and the numerical results. Furthermore, several sets of theoretical results are fairly close to the average experimental data and the average theoretical predictions for these large values of the Froude number. Discrepancies between theoretical predictions and experimental measurements for small values of the Froude number, specifically for F = 0.18, 0.20, 0.22, 0.24, and 0.266, generally are much larger than for the above-defined high-Froude-number range. However, a notable exception to this general finding is provided by the first-order slender-ship approximation evaluated in Chen and Noblesse [1],3 which is in fairly good agreement with the average experimental data over the entire range of values of Froude number considered in this study.

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