scholarly journals Analytical and numerical results on the positivity of steady state solutions of a thin film equation

2013 ◽  
Vol 18 (5) ◽  
pp. 1305-1321 ◽  
Author(s):  
Daniel Ginsberg ◽  
◽  
Gideon Simpson ◽  
Keyword(s):  
Thin Film ◽  
Steady State ◽  
Numerical Results ◽  
Thin Film Equation ◽  
Steady State Solutions

scholarly journals Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure

2021 ◽  
pp. 1-25
Author(s):  
ABDULWAHED S. ALSHAIKHI ◽  
MICHAEL GRINFELD ◽  
STEPHEN K. WILSON
Keyword(s):  
Thin Film ◽  
Steady State ◽  
Bifurcation Theory ◽  
Disjoining Pressure ◽  
Thin Film Equations ◽  
Planar Substrate ◽  
Spatially Homogeneous ◽  
The One ◽  
Steady State Solutions ◽  
Average Film Thickness

We consider patterns formed in a two-dimensional thin film on a planar substrate with a Derjaguin disjoining pressure and periodic wettability stripes. We rigorously clarify some of the results obtained numerically by Honisch et al. [Langmuir 31: 10618–10631, 2015] and embed them in the general theory of thin-film equations. For the case of constant wettability, we elucidate the change in the global structure of branches of steady-state solutions as the average film thickness and the surface tension are varied. Specifically we find, by using methods of local bifurcation theory and the continuation software package AUTO, both nucleation and metastable regimes. We discuss admissible forms of spatially non-homogeneous disjoining pressure, arguing for a form that differs from the one used by Honisch et al., and study the dependence of the steady-state solutions on the wettability contrast in that case.

scholarly journals Numerical Investigation of the Steady State of a Driven Thin Film Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
A. J. Hutchinson ◽  
C. Harley ◽  
E. Momoniat
Keyword(s):  
Thin Film ◽  
Steady State ◽  
Thin Liquid Film ◽  
Accurate Solution ◽  
Difference Approximation ◽  
Finite Difference Schemes ◽  
Solution Curve ◽  
Central Difference ◽  
Von Neumann ◽  
Thin Film Equation

A third-order ordinary differential equation with application in the flow of a thin liquid film is considered. The boundary conditions come from Tanner's problem for the surface tension driven flow of a thin film. Symmetric and nonsymmetric finite difference schemes are implemented in order to obtain steady state solutions. We show that a central difference approximation to the third derivative in the model equation produces a solution curve with oscillations. A difference scheme based on a combination of forward and backward differences produces a smooth accurate solution curve. The stability of these schemes is analysed through the use of a von Neumann stability analysis.

scholarly journals Self-Consistent Energy Normalization for Quasistatic Reactor Calculations

2021 ◽  
Vol 2 (2) ◽  
pp. 215-224
Author(s):  
David P. Griesheimer ◽  
Steven J. Douglass ◽  
Mark H. Stedry
Keyword(s):  
Steady State ◽  
Energy Balance ◽  
Energy Release ◽  
Nuclear Energy ◽  
Energy Deposition ◽  
Numerical Results ◽  
Critical Systems ◽  
Self Consistent ◽  
Steady State Solutions

Use of the quasistatic (keff) approximation for producing steady-state solutions for non-critical fission systems is known to result in an imbalance between energy release and deposition within the system. In this paper, we formally quantify this imbalance and present a self-consistent energy normalization technique that preserves nuclear energy release per reaction, as well as enforces energy balance between release and deposition mechanisms, regardless of the criticality state of the system. The proposed technique is straightforward to implement in any type of transport solver through the use of a simple energy rebalance factor. Theoretical and numerical results are presented that demonstrate the energy deposition bias for non-critical systems and the effectiveness of the proposed energy normalization technique.

A Nonlinear Oscillator Lanchester Damper

1987 ◽  
Vol 109 (4) ◽  
pp. 343-347 ◽  
Author(s):  
K. R. Asfar ◽  
A. H. Nayfeh ◽  
K. A. Barrash
Keyword(s):  
Steady State ◽  
Nonlinear Oscillator ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Harmonic Excitation ◽  
Second Order ◽  
Numerical Results ◽  
Nonlinear Spring ◽  
Uniform Expansion ◽  
Steady State Solutions

The method of multiple scales is used to investigate the effect of a nonlinear spring in the main system on the performance of Lanchester-type absorbers. A second-order uniform expansion is obtained for the response of the system to a harmonic excitation. Numerical results for steady-state solutions illustrating the influence of the nonlinearity and damping factors on the response are presented. A softening-type effective nonlinearity dominates the system and considerably improves its damping.

scholarly journals Numerical results on existence and stability of steady state solutions for the reaction-diffusion and Klein–Gordon equations

2014 ◽  
Vol 7 (6) ◽  
pp. 723-742 ◽  
Author(s):  
Miles Aron ◽  
Peter Bowers ◽  
Nicole Byer ◽  
Robert Decker ◽  
Aslihan Demirkaya ◽  
...  
Keyword(s):  
Steady State ◽  
Reaction Diffusion ◽  
Numerical Results ◽  
Existence And Stability ◽  
Klein Gordon ◽  
Steady State Solutions

scholarly journals Smooth zero-contact-angle solutions to a thin-film equation around the steady state

2008 ◽  
Vol 245 (6) ◽  
pp. 1454-1506 ◽  
Author(s):  
Lorenzo Giacomelli ◽  
Hans Knüpfer ◽  
Felix Otto
Keyword(s):  
Thin Film ◽  
Contact Angle ◽  
Steady State ◽  
Thin Film Equation

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.

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