Analytical expressions for the kinetic friction in the Prandtl-Tomlinson model

2012 ◽  
Vol 86 (3) ◽  
Author(s):  
Enrico Gnecco ◽  
Raphael Roth ◽  
Alexis Baratoff
Keyword(s):  
Kinetic Friction ◽  
Tomlinson Model ◽  
Analytical Expressions

Atomistic Origins of Friction

2019 ◽  
pp. 348-388
Author(s):  
C. Mathew Mate ◽  
Robert W. Carpick
Keyword(s):  
Atomic Structure ◽  
Real Life ◽  
Static Friction ◽  
Electronic Excitations ◽  
Kinetic Friction ◽  
Dynamic Simulations ◽  
Tomlinson Model ◽  
Current State ◽  
Friction Models ◽  
Kontorova Model

This chapter covers the current state of knowledge about how the shear strength (the force needed to slide one surface over another) originates at the atomic level. For adhesive friction, friction originates from the forces needed to move the atoms on one surface over the atomic structure of the opposing surface; the simplest model for adhesive friction is the cobblestone model. The Frenkel–Kontorova model, the Prandtl–Tomlinson model, and molecular dynamic simulations are typically used to show how the atomic structure of the surfaces leads to static friction. One exciting aspect of these friction models is the prediction of superlubricity or negligible friction for incommensurate sliding surfaces, which is now being realized in experiments. Also discussed is why superlubricity is not observed in real-life situations. As atoms and molecules slide over surfaces, kinetic friction originates from phonon and electronic excitations, which are typically studied using the quartz crystal microbalance (QCM).

Numerical Investigation of Atomic Scale Kinetic Friction in Ambient Condition With a Novel Extended Prandtl-Tomlinson Model

2014 ◽  
Author(s):  
Birahima Gueye ◽  
Chenfei Sun ◽  
Yan Zhang ◽  
Yujuan Wang ◽  
Yunfei Chen
Keyword(s):  
Relative Humidity ◽  
Adhesion Force ◽  
Normal Load ◽  
Analytical Data ◽  
Two Dimensions ◽  
Atomic Scale ◽  
Kinetic Friction ◽  
Capillary Bridge ◽  
Mode Operation ◽  
Tomlinson Model

A more adequate extended Prandtl-Tomlinson model in two dimensions (2D) analysis is proposed in the aim to thoroughly investigate the interplay between kinetic friction, relative humidity (RH), normal load, and temperature in both contact and tapping mode atomic force microscopic (AFM). In contact mode operation, results firstly show that for various applied normal loads highly wetted surface in contrast to partially wetted surface exhibits lower friction at finite temperature range. This phenomenon is attributed to the film layer acting as a lubricant. Secondly, two different regimes when varying the relative humidity were further observed with increasing temperature. The first one shows the thermolubricity’s effect at low RH (RH 20%) while the second regime remarkably confirms an increase of friction with temperature at higher RH (RH60%) which is inconsistent with common observation. The latter regime is characterized by the thermally activated capillary bridge formation leading to an increase of the total adhesion force. Thirdly we demonstrated that both regimes also hold in ac mode operation and regardless to the humidity level, either low or high RH, friction force decreases with increasing amplitude modulation. Good agreement was found with measurement and analytical data reported previously. In the model treatment, however, only effects of capillary force which dominate in AFM measurement were considered.

Layered and ion implantation specimens as possible reference materials for the electron-probe microanalysis

1992 ◽  
Vol 50 (2) ◽  
pp. 1652-1653
Author(s):  
G. Remond ◽  
R.H. Packwood ◽  
C. Gilles ◽  
S. Chryssoulis
Keyword(s):  
Ion Implantation ◽  
Reference Materials ◽  
Analytical Techniques ◽  
Thin Film Deposition ◽  
Film Deposition ◽  
X Ray ◽  
Spatially Resolved ◽  
Analytical Expressions ◽  
Original Approach ◽  
Depth Concentration

Merits and limitations of layered and ion implanted specimens as possible reference materials to calibrate spatially resolved analytical techniques are discussed and illustrated for the case of gold analysis in minerals by means of x-ray spectrometry with the EPMA. To overcome the random heterogeneities of minerals, thin film deposition and ion implantation may offer an original approach to the manufacture of controlled concentration/ distribution reference materials for quantification of trace elements with the same matrix as the unknown.In order to evaluate the accuracy of data obtained by EPMA we have compared measured and calculated x-ray intensities for homogeneous and heterogeneous specimens. Au Lα and Au Mα x-ray intensities were recorded at various electron beam energies, and hence at various sampling depths, for gold coated and gold implanted specimens. X-ray intensity calculations are based on the use of analytical expressions for both the depth ionization Φ (ρz) and the depth concentration C (ρz) distributions respectively.

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 64-65
Author(s):  
D. Van Dyck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Direct Method ◽  
Real Space ◽  
Zone Axis ◽  
Phase Object ◽  
High Resolution Images ◽  
The Many ◽  
Analytical Expressions ◽  
Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

KINEMATIC FEATURES OF THE LAPPING PROCESS AND DETERMINATION OF ITS BASIC PARAMETERS

2020 ◽  
Vol 7 (3) ◽  
pp. 23-28
Author(s):  
EZIZ SARVAN SHIRVAN ◽  
Keyword(s):  
Dynamic Properties ◽  
Cutting Speed ◽  
Equilibrium System ◽  
Technological Parameters ◽  
Kinematic Characteristics ◽  
Angular Velocities ◽  
Basic Parameters ◽  
Grinding Tool ◽  
Mathematical Relationships ◽  
Analytical Expressions

This paper discusses the kinematic characteristics of lapping process and the main parameters of the process. It was determined that the influencing degree of technological parameters to the forming surface and processes. It was projected the construction of the lapping head for processing of internal cylindrical surfaces, scheme of the lapping operation and graphic description of the forces influencing. The relationships between the axial, radial and tangential cutting forces and the effect of the combined force thereof are determined in order to ensure the necessary surface pressure. During the analysis geometric and mathematical relationships were obtained. The extracted analytical expressions can be realized by further experimental researches and can be used in engineering calculations of technological parameters of processing by lapping. Angular velocity, friction force, linear velocity, also the length of the tactile curve and the radius of the part can be considered the main kinematic and dynamic parameters of the process that the formation of the surface, also the course of the process depends on these parameters. Depending on the kinematic parameters, the wear nature of the tool changes and this changes the linear and angular velocities, which have a significant impact on the accuracy, quality and productivity of processing. When examining the technological capabilities of the process, the nature of the movement between the part and the grinding tool, also changes in cutting speed are often considered as a main factor. Analytical expressions were obtained to determine the main parameters of the process, taking into account the kinematic characteristics of the friction process. These expressions can be used in engineering calculations and allow to determine the optimal values of the processing mode. In order to obtain the required micrometric surface cleanliness and measurement accuracy, correlation relationships were established between the main parameters of the process, equations of the equilibrium system of shear forces were compiled and analytical expressions were obtained based on the analysis of kinematic and dynamic properties of the system.

Evaluation of the Power Transformer Magnetizing Inrush Currents

2020 ◽  
Vol 10 (10) ◽  
pp. 20-32
Author(s):  
Aleksey A. KUVSHINOV ◽  
◽  
Vera V. VAKHNINA ◽  
Aleksey N. CHERNENKO ◽  
◽  
...  
Keyword(s):  
Power Transformer ◽  
Geomagnetic Disturbance ◽  
Inrush Current ◽  
Geomagnetic Disturbances ◽  
Disturbance Intensity ◽  
Magnetizing Inrush Current ◽  
Inrush Currents ◽  
Instantaneous Values ◽  
The Mathematical Model ◽  
Analytical Expressions

The mathematical model of a shell-core power transformer’s magnetization branch is substantiated. By using the model, analytical expressions for the magnetizing current instantaneous values under the conditions of geomagnetic disturbances can be obtained. Quantitative assessments of the magnetizing inrush current amplitudes and durations versus the geomagnetic disturbance intensity are obtained. The dynamics of the power transformer magnetic system saturation transient and changes in the magnetization inrush current amplitudes and durations after a sudden occurrence of geomagnetic disturbances are shown. The error of estimating the magnetizing inrush current amplitudes under geomagnetic disturbances is determined based on comparison with experimental data.

Extended electric power sources

2018 ◽  
Author(s):  
T.A. Konev ◽  
V.A. Kuzmin ◽  
E. Yu. Mutovina ◽  
R.D. Puzhaykin ◽  
Vladimir Salomatov
Keyword(s):  
Electric Power ◽  
Electric Current ◽  
Load Resistance ◽  
Active Power ◽  
Operating Voltage ◽  
Power Sources ◽  
Distributed Parameters ◽  
Analytical Expressions ◽  
Characteristic Resistance ◽  
Length Effects

Chemical sources of current are investigated as lines with distributed parameters. Analytical expressions are obtained for the voltage and active power values of the source at different distances from the beginning of the cell as well as dependences of the working voltage and active power on the source length. Effects of a reduction in the operating voltage and active power are due to the flow of electric current along the source during operation. The magnitude of these effects depends not only on the length of the source, but also on the ratio of characteristic resistance to the load resistance.<br>

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