Application of Boltzmann Statistical Mechanics in the Validation of the Gaussian Summit-Height Distribution in Rough Surfaces

1997 ◽  
Vol 119 (4) ◽  
pp. 846-850 ◽  
Author(s):  
M. Leung ◽  
C. K. Hsieh ◽  
D. Y. Goswami
Keyword(s):  
Surface Roughness ◽  
Statistical Mechanics ◽  
Theoretical Basis ◽  
Rough Surfaces ◽  
Electrical Contact ◽  
Height Distribution ◽  
Probable Distribution ◽  
Theoretical Predictions ◽  
Most Probable Distribution ◽  
Roughness Measurements

In theoretical modeling of contact mechanics, a homogeneously, isotropically rough surface is usually assumed to be a flat plane covered with asperities of a Gaussian summit-height distribution. This assumption yields satisfactory results between theoretical predictions and experimental measurements of the physical characteristics, such as thermal/electrical contact conductance and friction coefficient. However, lack of theoretical basis of this assumption motivates further study in surface modeling. This paper presents a theoretical investigation by statistical mechanics to determine surface roughness in terms of the most probable distribution of surface asperities. Based upon the surface roughness measurements as statistical constraints, the Boltzmann statistical model derives a distribution equivalent to Gaussian. The Boltzmann statistical mechanics derivation in this paper provides a rigorous validation of the Gaussian summit-height assumption presently in use for study of rough surfaces.

Influence of surface roughness on the wetting angle

1995 ◽  
Vol 10 (8) ◽  
pp. 1984-1992 ◽  
Author(s):  
X.B. Zhou ◽  
J.Th.M. De Hosson
Keyword(s):  
Surface Roughness ◽  
Gaussian Distribution ◽  
Rough Surfaces ◽  
Contact Angles ◽  
Wetting Angle ◽  
Experimental Results ◽  
Solid Surfaces ◽  
Roughness Measurements

A this paper the influence of surface roughness on contact angles in the system of liquid Al wetting solid surfaces of Al2O3 has been studied. It was observed that contact angles of liquid Al vary significantly on different rough surfaces of Al2O3. A model is proposed to correlate contact angles with conventional roughness measurements and wavelengths by assuming a cosine profile of rough grooves with a Gaussian distribution of amplitudes. In comparison with the experimental results, the model provides a good estimate for describing the influence of surface roughness on contact angles of liquid Al on Al2O3.

Boltzmann Entropy & Equilibrium in Non-Isolated Systems

2017 ◽  
pp. 74-92 ◽  
Author(s):  
Alberto Gianinetti
Keyword(s):  
Statistical Mechanics ◽  
Stable Condition ◽  
Microscopic Level ◽  
Boltzmann Entropy ◽  
Microscopic Approach ◽  
Macroscopic Level ◽  
Probable Distribution ◽  
Isolated Systems ◽  
Most Probable Distribution

The microscopic approach of statistical mechanics has developed a series of formal expressions that, depending on the different features of the system and/or process involved, allow for calculating the value of entropy from the microscopic state of the system. This value is maximal when the particles attain the most probable distribution through space and the most equilibrated sharing of energy between them. At the macroscopic level, this means that the system is at equilibrium, a stable condition wherein no net statistical force emerges from the overall behaviour of the particles. If no force is available then no work can be done and the system is inert. This provides the bridge between the probabilistic equilibration that occurs at the microscopic level and the classical observation that, at a macroscopic level, a system is at equilibrium when no work can be done by it.

Boltzmann: the probabilistic interpretation of entropy

2020 ◽  
pp. 570-595
Author(s):  
Robert T. Hanlon
Keyword(s):  
Probability Theory ◽  
Statistical Mechanics ◽  
Gas Phase ◽  
Probabilistic Interpretation ◽  
Atoms And Molecules ◽  
Collective Work ◽  
Novel Approach ◽  
Probable State ◽  
Probable Distribution ◽  
Most Probable Distribution

Boltzmann’s collective work was a mathemetical tour de force. Building on Clausius and Maxwell, he demonstrated that the distribution of gas phase atoms and molecules follows from probability theory. Atoms and molecules distribute themselves in space and momentum to the most probable distribution. Boltzmann used probability theory to quantify the most probable state and then demonstrated the connection between this state and its entropy. This novel approach, later validated by Sackur–Tetrode, led to the creation of statistical mechanics.

Statistical Thermodynamics Concepts and Mathematical Tools for a Multi-Agent Ecosystem

2014 ◽  
Vol 20 (2) ◽  
pp. 237-270
Author(s):  
Javier Segovia
Keyword(s):  
Statistical Mechanics ◽  
Mathematical Problem ◽  
Statistical Thermodynamics ◽  
Economic Systems ◽  
Global Behavior ◽  
Probable Distribution ◽  
Or Economics ◽  
Artificial Ecosystems ◽  
Multi Agent ◽  
Most Probable Distribution

Finding the distribution of systems over their possible states is a mathematical problem. One possible solution is the method of the most probable distribution developed by Boltzmann. This method has been instrumental in developing statistical mechanics and explaining the origin of many thermodynamics concepts, like entropy or temperature, but is also applicable in many other fields like ecology or economics. Artificial ecosystems have many features in common with ecological or economic systems, but surprisingly the method does not appear to have been very successful in this field of application. The hypothesis of this article is that this failure is due to the incorrect interpretation of the method's concepts and mathematical tools. We propose to review and reinterpret the method so that it can be correctly applied and all its potential exploited in order to study and characterize the global behavior of an artificial multi-agent ecosystem.

scholarly journals Radar Imaging Statistics of Non-Gaussian Rough Surface: A Physics-Based Simulation Study

2022 ◽  
Vol 14 (2) ◽  
pp. 311
Author(s):  
Cheng-Yen Chiang ◽  
Kun-Shan Chen ◽  
Ying Yang ◽  
Yang Zhang ◽  
Lingbing Wu
Keyword(s):  
Surface Roughness ◽  
Rough Surface ◽  
Rough Surfaces ◽  
Parameters Estimation ◽  
Statistical Characteristics ◽  
Height Distribution ◽  
Sar Imaging ◽  
Non Gaussian ◽  
Physics Based Simulation ◽  
Gaussian Surface

This paper investigates the radar image statistics of rough surfaces by simulating the scattered signal’s dependence on the surface roughness. Statistically, the roughness characteristics include the height probability density (HPD) and, to the second-order, the power spectral density (PSD). We simulated the radar backscattered signal by computing the far-field scattered field from the rough surface within the antenna beam volume in the context of synthetic aperture radar (SAR) imaging. To account for the non-Gaussian height distribution, we consider microscopic details of the roughness on comparable radar wavelength scales to include specularly, singly, and multiply scatterers. We introduce surface roughness index (RSI) to distinguish the statistical characteristics of rough surfaces with different height distributions. Results suggest that increasing the RMS height does not impact the Gaussian HPD surface but significantly affects the Weibull surface. The results confirm that as the radar frequency increases, or reaches a relatively larger roughness, the surface’s HPD causes significant changes in incoherent scattering due to more frequent multiple scattering contributions. As a result, the speckle move further away from the Rayleigh model. By examining individual RSI, we see that the Gaussian HPD surface is much less sensitive to RMS height than the Weibull HPD surface. We demonstrate that to retrieve the surface parameters (both dielectric and roughness) from the estimated RCS, less accuracy is expected for the non-Gaussian surface than the Gaussian surface under the same conditions. Therefore, results drawn from this study are helpful for system performance evaluations, parameters estimation, and target detection for SAR imaging of a rough surface.

Surface roughness measurements of vanadium-contaminated fluidized cracking catalysts by atomic force microscopy

1996 ◽  
Vol 54 ◽  
pp. 866-867
Author(s):  
H. Kinney ◽  
M.L. Occelli ◽  
S.A.C. Gould
Keyword(s):  
Surface Roughness ◽  
Zeolite Y ◽  
Atomic Level ◽  
Microporous Structure ◽  
Contact Mode ◽  
Force Microscopy ◽  
Atomic Force ◽  
Before And After ◽  
Roughness Measurements ◽  
Cracking Catalysts

For this study we have used a contact mode atomic force microscope (AFM) to study to topography of fluidized cracking catalysts (FCC), before and after contamination with 5% vanadium. We selected the AFM because of its ability to well characterize the surface roughness of materials down to the atomic level. It is believed that the cracking in the FCCs occurs mainly on the catalysts top 10-15 μm suggesting that the surface corrugation could play a key role in the FCCs microactivity properties. To test this hypothesis, we chose vanadium as a contaminate because this metal is capable of irreversibly destroying the FCC crystallinity as well as it microporous structure. In addition, we wanted to examine the extent to which steaming affects the vanadium contaminated FCC. Using the AFM, we measured the surface roughness of FCCs, before and after contamination and after steaming.We obtained our FCC (GRZ-1) from Davison. The FCC is generated so that it contains and estimated 35% rare earth exchaged zeolite Y, 50% kaolin and 15% binder.

scholarly journals Atomic force microscopy comparative analysis of the surface roughness of two posterior chamber phakic intraocular lens models: ICL versus IPCL

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Juan Gros-Otero ◽  
Samira Ketabi ◽  
Rafael Cañones-Zafra ◽  
Montserrat Garcia-Gonzalez ◽  
Cesar Villa-Collar ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Atomic Force Microscopy ◽  
Intraocular Lenses ◽  
Posterior Chamber ◽  
Anterior Surface ◽  
Contact Mode ◽  
Force Microscopy ◽  
Atomic Force ◽  
Phakic Intraocular Lenses ◽  
Roughness Measurements

Abstract Background To compare the anterior surface roughness of two commercially available posterior chamber phakic intraocular lenses (IOLs) using atomic force microscopy (AFM). Methods Four phakic IOLs were used for this prospective, experimental study: two Visian ICL EVO+ V5 lenses and two iPCL 2.0 lenses. All of them were brand new, were not previously implanted in humans, were monofocal and had a dioptric power of − 12 diopters (D). The anterior surface roughness was assessed using a JPK NanoWizard II® atomic force microscope in contact mode immersed in liquid. Olympus OMCL-RC800PSA commercial silicon nitride cantilever tips were used. Anterior surface roughness measurements were made in 7 areas of 10 × 10 μm at 512 × 512 point resolution. The roughness was measured using the root-mean-square (RMS) value within the given regions. Results The mean of all anterior surface roughness measurements was 6.09 ± 1.33 nm (nm) in the Visian ICL EVO+ V5 and 3.49 ± 0.41 nm in the iPCL 2.0 (p = 0.001). Conclusion In the current study, we found a statistically significant smoother anterior surface in the iPCL 2.0 phakic intraocular lenses compared with the VISIAN ICL EVO+ V5 lenses when studied with atomic force microscopy.

Testing the Accuracy of Surface Roughness Measurements Carried out with a Portable Profilometer

2015 ◽  
Vol 637 ◽  
pp. 69-73 ◽  
Author(s):  
Krzysztof Stępień
Keyword(s):  
Surface Roughness ◽  
Measurement Accuracy ◽  
Environmental Changes ◽  
Experimental Tests ◽  
Evaluation Procedure ◽  
Human Errors ◽  
Modern Manufacturing ◽  
Machine Parts ◽  
Roughness Measurements

Surface roughness is a factor that has a vital influence on overall quality of machine parts. This is the reason why proper measurements of surface roughness are a matter of great importance in modern manufacturing technology. Nowadays portable profilometers are common instruments to be used under industrial conditions. Measurements with such instruments can be affected by numerous factors, for example environmental changes, human errors of an operator, etc. This paper discusses problem of an evaluation of measurement accuracy of portable profilometers. It also describes the evaluation procedure and presents results experimental tests.

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