Chaotic analyses of weakly damped parametrically excited cross waves with surface tension

2005 ◽  
Vol 175 (1-4) ◽  
pp. 139-179
Author(s):  
R. T. Hudspeth ◽  
R. B. Guenther ◽  
S. Fadel
Keyword(s):  
Surface Tension ◽  
Parametrically Excited ◽  
Cross Waves

Long-time evolution and regions of existence of parametrically excited nonlinear cross-waves in a tank

1989 ◽  
Vol 209 ◽  
pp. 249-263 ◽  
Author(s):  
Lev Shemer ◽  
Eliezer Kit
Keyword(s):  
Boundary Condition ◽  
Parametric Excitation ◽  
Wave Breaking ◽  
Model Equation ◽  
Numerical Study ◽  
Parametrically Excited ◽  
Numerical Studies ◽  
Scaling Procedure ◽  
Long Time ◽  
Cross Waves

Results of an experimental and numerical study of parametrically excited nonlinear cross-waves in the vicinity of the cut-off frequency, are reported. Experiments are performed at three cross-wave modes and in the whole range of existence of cross-waves. Numerical studies are based on the solution of the nonlinear Schrödinger equation with a boundary condition at the wavemaker which corresponds to parametric excitation. The validity of the scaling procedure adopted in the model is verified experimentally. Dissipation is incorporated in the model equation and in the wavemaker boundary condition. The influence of the wave breaking on the range of existence of cross-waves is discussed and the relation between the maximum possible steepness of cross-waves and the limits of their existence is obtained.

Parametrically excited, standing cross-waves

1988 ◽  
Vol 186 ◽  
pp. 119-127 ◽  
Author(s):  
John Miles
Keyword(s):  
Surface Waves ◽  
Phase Plane ◽  
Evolution Equations ◽  
Plane Waves ◽  
Wave Problem ◽  
Parametrically Excited ◽  
The Cross ◽  
The Stability ◽  
Cross Waves

Luke's (1967) variational formulation for surface waves is extended to incorporate the motion of a wavemaker and applied to the cross-wave problem. Whitham's average-Lagrangian method then is invoked to obtain the evolution equations for the slowly varying complex amplitude of the parametrically excited cross-wave that is associated with symmetric excitation of standing waves in a rectangular tank of width π/k, length l and depth d for which kl = O(1) and kd [Gt ] 1. These evolution equations are Hamiltonian and isomorphic to those for parametric excitation of surface waves in a cylinder that is subjected to a vertical oscillation, for which phase-plane trajectories, stability criteria and the effects of damping are known (Miles 1984a). The formulation and results differ from those of Garrett (1970) in consequence of his linearization of the boundary condition at the wavemaker and his neglect of self-interaction of the cross-waves in the free-surface conditions (although Garrett does incorporate self-interaction in his calculation of the equilibrium amplitude of the cross-waves). These differences have only a small effect on the criterion for the stability of plane waves, but the self-interaction is crucial for the determination of the stability of the cross-waves.

Gravity–capillary multi-component wave patterns generated by a single-frequency wave-maker oscillation and subsequent resonances

2021 ◽  
Vol 926 ◽  
Author(s):  
Chang Xu ◽  
Marc Perlin
Keyword(s):  
Surface Tension ◽  
Wavelet Transforms ◽  
Fourier Transforms ◽  
Single Frequency ◽  
Two Dimensional ◽  
Frequency Wave ◽  
Wave Patterns ◽  
Surface Patterns ◽  
Wave Maker ◽  
Cross Waves

Cross-waves are standing waves with crests perpendicular to a wave-maker; they are subharmonic waves excited by parametric instability. The modulational and chaotic behaviours of nonlinear cross-waves have been studied widely since the 1970s. Most of the previous work has focused on gravity waves where surface tension can be neglected. In this work we study cross-waves that are highly dependent on surface tension as well as gravity. By oscillating a planar wave-maker either vertically or horizontally with frequencies of 25 Hz through 40 Hz at one end of a rectangular basin, two-dimensional multi-component surface patterns are realized. Using the free-surface synthetic Schlieren technique to measure the surface elevations, multi-dimensional Fourier transforms are utilized to track the evolutionary spectrum of the water surface in both the temporal and spatial domains. Wavelet transforms are implemented to show the development of the various frequency components. Three-wave resonances with and without first subharmonics are observed for small nonlinearity. Three-dimensional oblique propagating cross-waves are generated at higher nonlinearity; unlike most previous cross-wave experiments, this staggered pattern propagates far downstream. Experimental evidence shows that two oblique propagating waves form a two-dimensional short-crested pattern, and that the lateral component of the waves develops into parametric sloshing modes corresponding to the width of the tank. Two regimes of nonlinear wave patterns, resonant triads and oblique propagating cross-waves, are delineated.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

The Critical Point Drying Method Applied to Scanning Electron Microscopy of L-929 Cells

1970 ◽  
Vol 28 ◽  
pp. 278-279
Author(s):  
Charles TurnbiLL ◽  
Delbert E. Philpott
Keyword(s):  
Electron Microscopy ◽  
Carbon Dioxide ◽  
Surface Tension ◽  
Critical Point ◽  
Freeze Drying ◽  
Attractive Alternative ◽  
Crystal Formation ◽  
Critical Point Drying ◽  
Time Required ◽  
Scanning Electron

The advent of the scanning electron microscope (SCEM) has renewed interest in preparing specimens by avoiding the forces of surface tension. The present method of freeze drying by Boyde and Barger (1969) and Small and Marszalek (1969) does prevent surface tension but ice crystal formation and time required for pumping out the specimen to dryness has discouraged us. We believe an attractive alternative to freeze drying is the critical point method originated by Anderson (1951; for electron microscopy. He avoided surface tension effects during drying by first exchanging the specimen water with alcohol, amy L acetate and then with carbon dioxide. He then selected a specific temperature (36.5°C) and pressure (72 Atm.) at which carbon dioxide would pass from the liquid to the gaseous phase without the effect of surface tension This combination of temperature and, pressure is known as the "critical point" of the Liquid.

The Use of Styrenes as Embedding Media for Electron Microscopy

1971 ◽  
Vol 29 ◽  
pp. 488-489
Author(s):  
Edward D. De-Lamater ◽  
Eric Johnson ◽  
Thad Schoen ◽  
Cecil Whitaker
Keyword(s):  
Electron Microscopy ◽  
Surface Tension ◽  
Ultraviolet Light ◽  
Methyl Ethyl Ketone Peroxide ◽  
Methyl Ethyl ◽  
Styrene Polymerization ◽  
Radical Initiation ◽  
Tertiary Butyl ◽  
Low Viscosity ◽  
Free Radical Initiation

Monomeric styrenes are demonstrated as excellent embedding media for electron microscopy. Monomeric styrene has extremely low viscosity and low surface tension (less than 1) affording extremely rapid penetration into the specimen. Spurr's Medium based on ERL-4206 (J.Ultra. Research 26, 31-43, 1969) is viscous, requiring gradual infiltration with increasing concentrations. Styrenes are soluble in alcohol and acetone thus fitting well into the usual dehydration procedures. Infiltration with styrene may be done directly following complete dehydration without dilution.Monomeric styrenes are usually inhibited from polymerization by a catechol, in this case, tertiary butyl catechol. Styrene polymerization is activated by Methyl Ethyl Ketone peroxide, a liquid, and probably acts by overcoming the inhibition of the catechol, acting as a source of free radical initiation.Polymerization is carried out either by a temperature of 60°C. or under ultraviolet light with wave lengths of 3400-4000 Engstroms; polymerization stops on removal from the ultraviolet light or heat and is therefore controlled by the length of exposure.

The nucleation of cavities at grain boundaries

1987 ◽  
Vol 45 ◽  
pp. 288-291
Author(s):  
P. J. Goodhew
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Grain Boundaries ◽  
Radiation Damage ◽  
Impurity Concentration ◽  
Driving Force ◽  
Nucleation And Growth ◽  
Phase Boundaries ◽  
Cavity Nucleation ◽  
Spherical Bubble

Cavity nucleation and growth at grain and phase boundaries is of concern because it can lead to failure during creep and can lead to embrittlement as a result of radiation damage. Two major types of cavity are usually distinguished: The term bubble is applied to a cavity which contains gas at a pressure which is at least sufficient to support the surface tension (2g/r for a spherical bubble of radius r and surface energy g). The term void is generally applied to any cavity which contains less gas than this, but is not necessarily empty of gas. A void would therefore tend to shrink in the absence of any imposed driving force for growth, whereas a bubble would be stable or would tend to grow. It is widely considered that cavity nucleation always requires the presence of one or more gas atoms. However since it is extremely difficult to prepare experimental materials with a gas impurity concentration lower than their eventual cavity concentration there is little to be gained by debating this point.

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