Study on abundant explicit wave solutions of the thin-film Ferro-electric materials equation

2021 ◽  
Vol 54 (1) ◽  
Author(s):  
Emad H. Zahran ◽  
Seyed M. Mirhosseini-Alizamini ◽  
Maha S. M. Shehata ◽  
Hadi Rezazadeh ◽  
Hijaz Ahmad
Keyword(s):  
Thin Film ◽  
Wave Solutions ◽  
Electric Materials

Traveling-wave solutions to thin-film equations

1993 ◽  
Vol 48 (6) ◽  
pp. 4423-4431 ◽  
Author(s):  
Stefanella Boatto ◽  
Leo P. Kadanoff ◽  
Piero Olla
Keyword(s):  
Thin Film ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Thin Film Equations

scholarly journals Analysis and computations of a non-local thin-film model for two-fluid shear driven flows

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190367 ◽  
Author(s):  
D. T. Papageorgiou ◽  
S. Tanveer
Keyword(s):  
Thin Film ◽  
Viscous Fluid ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Large Wave ◽  
Film Model ◽  
Bifurcation Points ◽  
Wave Solutions ◽  
Thin Film Model ◽  
Non Local

This paper is concerned with analysis and computations of a non-local thin-film model developed in Kalogirou & Papageorgiou ( J. Fluid Mech. 802 , 5–36, 2016) for a perturbed two-layer Couette flow when the thickness of the more viscous fluid layer next to the stationary wall is small compared to the thickness of the less viscous fluid. Travelling wave solutions and their stability are determined numerically, and secondary bifurcation points are identified in the process. We also determine regions in parameter space where bistability is observed with two branches being linearly stable at the same time. The travelling wave solutions are mathematically justified through a quasi-solution analysis in a neighbourhood of an empirically constructed approximate solution. This relies in part on precise asymptotics of integrals of Airy functions for large wave numbers. The primary bifurcation about the trivial state is shown rigorously to be supercritical, and the dependence of bifurcation points, as a function of Reynolds number R and the primary wavelength 2 πν −1/2 of the disturbance, is determined analytically.

scholarly journals Rigorous asymptotics of traveling-wave solutions to the thin-film equation and Tanner’s law

Nonlinearity ◽  
2016 ◽  
Vol 29 (9) ◽  
pp. 2497-2536 ◽  
Author(s):  
Lorenzo Giacomelli ◽  
Manuel V Gnann ◽  
Felix Otto
Keyword(s):  
Thin Film ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Thin Film Equation

scholarly journals On the stability of traveling wave solutions to thin-film and long-wave models for film flows inside a tube

2021 ◽  
Vol 415 ◽  
pp. 132750 ◽  
Author(s):  
Roberto Camassa ◽  
Jeremy L. Marzuola ◽  
H. Reed Ogrosky ◽  
Sterling Swygert
Keyword(s):  
Thin Film ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Wave Models ◽  
The Stability ◽  
Film Flows

Clean Electron Microscope Substrate Films Used for Micrometeorite Collection and Study

1967 ◽  
Vol 25 ◽  
pp. 366-367
Author(s):  
D. M. Davies ◽  
R. Kemner ◽  
E. F. Fullam
Keyword(s):  
Thin Film ◽  
Electron Microscope ◽  
High Altitude ◽  
Amyl Acetate ◽  
Temperature Variations ◽  
Film Forming ◽  
Film Specimen ◽  
Particulate Contaminants

All serious electron microscopists at one time or another have been concerned with the cleanliness and freedom from artifacts of thin film specimen support substrates. This is particularly important where there are relatively few particles of a sample to be found for study, as in the case of micrometeorite collections. For the deposition of such celestial garbage through the use of balloons, rockets, and aircraft, the thin film substrates must have not only all the attributes necessary for use in the electron microscope, but also be able to withstand rather wide temperature variations at high altitude, vibration and shock inherent in the collection vehicle's operation and occasionally an unscheduled violent landing.Nitrocellulose has been selected as a film forming material that meets these requirements yet lends itself to a relatively simple clean-up procedure to remove particulate contaminants. A 1% nitrocellulose solution is prepared by dissolving “Parlodion” in redistilled amyl acetate from which all moisture has been removed.

Microtomy of spherical Al2O3 powders

1983 ◽  
Vol 41 ◽  
pp. 74-75
Author(s):  
E.J. Jenkins ◽  
D.S. Tucker ◽  
J.J. Hren
Keyword(s):  
Thin Film ◽  
Size Range ◽  
Particle Aggregation ◽  
Ion Milling ◽  
Thin Sections ◽  
Α Phase ◽  
Convenient Means ◽  
Van Der Waals Attraction ◽  
Negative Feature ◽  
Film Substrate

The size range of mineral and ceramic particles of one to a few microns is awkward to prepare for examination by TEM. Electrons can be transmitted through smaller particles directly and larger particles can be thinned by crushing and dispersion onto a substrate or by embedding in a film followed by ion milling. Attempts at dispersion onto a thin film substrate often result in particle aggregation by van der Waals attraction. In the present work we studied 1-10 μm diameter Al2O3 spheres which were transformed from the amprphous state to the stable α phase.After the appropriate heat treatment, the spherical powders were embedded in as high a density as practicable in a hard EPON, and then microtomed into thin sections. There are several advantages to this method. Obviously, this is a rapid and convenient means to study the microstructure of serial slices. EDS, ELS, and diffraction studies are also considerably more informative. Furthermore, confidence in sampling reliability is considerably enhanced. The major negative feature is some distortion of the microstructure inherent to the microtoming operation; however, this appears to have been surprisingly small. The details of the method and some typical results follow.

Studies on Water in the Hydration Chamber of a Modified Electron Microscope

1970 ◽  
Vol 28 ◽  
pp. 544-545
Author(s):  
R. C. Moretz ◽  
G. G. Hausner ◽  
D. F. Parsons
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Electron Microscope ◽  
Steady State ◽  
Room Temperature ◽  
Small Mass ◽  
Equilibrium Pressure ◽  
Biological Objects ◽  
Mechanical Pump ◽  
Differential Pumping

Use of the electron microscope to examine wet objects is possible due to the small mass thickness of the equilibrium pressure of water vapor at room temperature. Previous attempts to examine hydrated biological objects and water itself used a chamber consisting of two small apertures sealed by two thin films. Extensive work in our laboratory showed that such films have an 80% failure rate when wet. Using the principle of differential pumping of the microscope column, we can use open apertures in place of thin film windows.Fig. 1 shows the modified Siemens la specimen chamber with the connections to the water supply and the auxiliary pumping station. A mechanical pump is connected to the vapor supply via a 100μ aperture to maintain steady-state conditions.

Imaging of platinum-shadowed macromolecular complexes in dark field

1984 ◽  
Vol 42 ◽  
pp. 146-147
Author(s):  
D.W. Andrews ◽  
F.P. Ottensmeyer
Keyword(s):  
Thin Film ◽  
Three Dimensional ◽  
Average Diameter ◽  
Dark Field ◽  
Bright Field ◽  
Field Mode ◽  
Macromolecular Complexes ◽  
Average Mass ◽  
Topological Features ◽  
Projection Images

Shadowing with heavy metals has been used for many years to enhance the topological features of biological macromolecular complexes. The three dimensional features present in directionaly shadowed specimens often simplifies interpretation of projection images provided by other techniques. One difficulty with the method is the relatively large amount of metal used to achieve sufficient contrast in bright field images. Thick shadow films are undesirable because they decrease resolution due to an increased tendency for microcrystalline aggregates to form, because decoration artefacts become more severe and increased cap thickness makes estimation of dimensions more uncertain.The large increase in contrast provided by the dark field mode of imaging allows the use of shadow replicas with a much lower average mass thickness. To form the images in Fig. 1, latex spheres of 0.087 μ average diameter were unidirectionally shadowed with platinum carbon (Pt-C) and a thin film of carbon was indirectly evaporated on the specimen as a support.

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