Elastic Force on a Point Defect in or Near a Surface Layer

1996 ◽  
Vol 63 (4) ◽  
pp. 1042-1045 ◽  
Author(s):  
H. Yua ◽  
S. C. Sanday ◽  
D. J. Bacon
Keyword(s):  
Surface Layer ◽  
Free Surface ◽  
Point Defect ◽  
Layer Thickness ◽  
Elastic Constants ◽  
Equilibrium Position ◽  
Stable Equilibrium ◽  
Elastic Force ◽  
Image Method ◽  
Stable Equilibrium Position

The elastic force on a point defect within or near a surface layer is determined by the image method. There is no stable equilibrium position for the point defect in the surface layer, it is attracted either to the free surface or to the interface. When the point defect is in the substrate it is attracted to the interface when the surface layer is softer than the substrate and to an equilibrium position in the substrate when the surface layer is stiffer than the substrate, the equilibrium position being a function of the elastic constants and the layer thickness.

On the equivalent systems for concurrent springs and dampers – Part 1: Small in-plane oscillations

2014 ◽  
Vol 228 (14) ◽  
pp. 2520-2531 ◽  
Author(s):  
Dragi Radomirovic ◽  
Ivana Kovacic
Keyword(s):  
Equilibrium Position ◽  
Stable Equilibrium ◽  
Damping Coefficient ◽  
Viscous Dampers ◽  
Stiffness Coefficients ◽  
Stable Equilibrium Position ◽  
Equivalent Systems ◽  
Stiffness And Damping ◽  
Plane Oscillations

In this work, concurrent linear springs placed in the system that performs small in-plane oscillations around the stable equilibrium position are considered. New theorems defining how they can be replaced by two mutually orthogonal springs are provided. The same concept is applied to find two mutually orthogonal linear viscous dampers that can replace a system of concurrent linear viscous dampers. The directions of such springs and dampers correspond to the principal stiffness and damping axes, respectively. So far unknown invariants related to the sum of stiffness coefficients and damping coefficient of the original and equivalent systems are presented. A few examples are given to illustrate the use and benefits of this approach. In addition, it is shown how the concept of two mutually orthogonal springs can be beneficially used for analysing problems concerned with oscillations of a particle on elastic frames.

scholarly journals EDWIN B. WILSON, MORE THAN A CATALYTIC INFLUENCE FOR PAUL SAMUELSON’S FOUNDATIONS OF ECONOMIC ANALYSIS

2019 ◽  
Vol 41 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Juan Carvajalino
Keyword(s):  
Economic Analysis ◽  
Equilibrium Position ◽  
Differential Calculus ◽  
Stable Equilibrium ◽  
Neoclassical Economics ◽  
Discrete Inequalities ◽  
Stable Equilibrium Position ◽  
Definition Of

This paper is an exploration of the genesis of Paul Samuelson’s Foundations of Economic Analysis (1947) from the perspective of his commitment to Edwin B. Wilson’s mathematics. The paper sheds new light on Samuelson’s Foundations at two levels. First, Wilson’s foundational ideas, embodied in maxims that abound in Samuelson’s book, such as “Mathematics is a Language” or “operationally meaningful theorems,” unified the chapters of Foundations and gave a sense of unity to Samuelson’s economics. Second, Wilson influenced certain theoretical concerns of Samuelson’s economics. Particularly, Samuelson adopted Wilson’s definition of a stable equilibrium position of a system in terms of discrete inequalities. Following Wilson, Samuelson developed correspondences between the continuous and the discrete in order to translate the mathematics of the continuous of neoclassical economics into formulas of discrete magnitudes. In Foundations, the local and the discrete provided the best way of operationalizing marginal and differential calculus. The discrete resonated intuitively with data; the continuous did not.

Temperature and entropy in molecular system

2022 ◽  
pp. 1-11
Author(s):  
Leyu Wang ◽  
James D. Lee
Keyword(s):  
Kinetic Energy ◽  
Gaussian Distribution ◽  
Equilibrium Position ◽  
Velocity Vector ◽  
Stable Equilibrium ◽  
Molecular System ◽  
Solid Material ◽  
Thermal Velocity ◽  
Global Motion ◽  
Stable Equilibrium Position

The irreversibility, temperature, and entropy are identified for an atomic system of solid material. Thermodynamics second law is automatically satisfied in the time evolution of molecular dynamics (MD). The irreversibility caused by an atom spontaneously moves from a non-stable equilibrium position to a stable equilibrium position. The process is dynamic in nature associated with the conversion of potential energy to kinetic energy and the dissipation of kinetic energy to the entire system. The forward process is less sensitive to small variation of boundary condition than reverse process, causing the time symmetry to break. Different methods to define temperature in molecular system are revisited with paradox examples. It is seen that the temperature can only be rigorously defined on an atom knowing its time history of velocity vector. The velocity vector of an atom is the summation of the mechanical part and the thermal part, the mechanical velocity is related to the global motion (translation, rotation, acceleration, vibration, etc.), the thermal velocity is related to temperature and is assumed to follow the identical random Gaussian distribution for all of its [Formula: see text], [Formula: see text] and [Formula: see text] component. The [Formula: see text]-velocity (same for [Formula: see text] or [Formula: see text]) versus time obtained from MD simulation is treated as a signal (mechanical motion) corrupted with random Gaussian distribution noise (thermal motion). The noise is separated from signal with wavelet filter and used as the randomness measurement. The temperature is thus defined as the variance of the thermal velocity multiply the atom mass and divided by Boltzmann constant. The new definition is equivalent to the Nose–Hover thermostat for a stationary system. For system with macroscopic acceleration, rotation, vibration, etc., the new definition can predict the same temperature as the stationary system, while Nose–Hover thermostat predicts a much higher temperature. It is seen that the new definition of temperature is not influenced by the global motion, i.e., translation, rotation, acceleration, vibration, etc., of the system. The Gibbs entropy is calculated for each atom by knowing normal distribution as the probability density function. The relationship between entropy and temperature is established for solid material.

Interaction Between an Edge Dislocation and a Lamellar Inhomogeneity With a Slipping Interface

1992 ◽  
Vol 59 (1) ◽  
pp. 215-217 ◽  
Author(s):  
L. Stagni ◽  
R. Lizzio
Keyword(s):  
Elastic Constants ◽  
Edge Dislocation ◽  
Stable Equilibrium ◽  
Finite Thickness ◽  
Elastic Field ◽  
Image Force ◽  
Plane Elasticity ◽  
Matrix Interface ◽  
Stable Equilibrium Position ◽  
Plane Elasticity Problem

The plane elasticity problem of an internal stress source located near a lamellar inhomogeneity is considered. It is assumed that the lamella-matrix interface does not transmit tangential displacements or shear tractions (slipping interface). The elastic field is given in terms of the source bulk field and one parameter formed from the elastic constants. The image force on an edge dislocation near the lamella is calculated and discussed. A dislocation stable-equilibrium position exists in a domain of elastic constants and Burgers vector directions. This result is characteristic of the interaction with a slipping lamellar inhomogeneity having finite thickness.

scholarly journals Experimental Analysis of the Influence of Factors Acting on the Layer Thickness Formed by Anodic Oxidation of Aluminium

Coatings ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 57 ◽  
Author(s):  
Miroslav Gombár ◽  
Alena Vagaská ◽  
Marta Harničárová ◽  
Jan Valíček ◽  
Milena Kušnerová ◽  
...  
Keyword(s):  
Surface Layer ◽  
Layer Thickness ◽  
Anodic Oxidation ◽  
Current Practice ◽  
Oxidation Process ◽  
Influence Factors ◽  
Basic Criterion ◽  
Electrolysis Method ◽  
Current Densities ◽  
Anodic Oxidation Process

The current practice in the field of anodic oxidation of aluminium and its alloys is based mainly on a set of partial empirical experiences of technologists obtained during surface treatment. The aim of the presented paper is deeper and more complex identification of the influence of chemical and technological factors acting during the anodic oxidation process especially on the thickness of the formed surface layer by the electrolysis method in a sulfuric acid solution. The current density was selected as the basic criterion for verification evaluation and analysis of experimentally obtained data, in accordance with Faraday’s laws. For current densities of 1 to 5 A·dm−2, the synergy of significant influence factors was identified, and mathematical and statistical models were then developed to predict the thickness of the surface layer with a relative accuracy of up to 10%. The presented paper does not only focus on the observation of the thickness of the surface layer desired by the customer, but also on the monitoring of this thickness in relation to the overall layer thickness of the coating.

scholarly journals The effect of the titanium surface layer thickness on the characteristics of a layered composite material

2019 ◽  
Vol 1281 ◽  
pp. 012057 ◽  
Author(s):  
E O Nasakina ◽  
M A Sudarchikova ◽  
K Yu Demin ◽  
M A Gol’dberg ◽  
M I Baskakova ◽  
...  
Keyword(s):  
Composite Material ◽  
Surface Layer ◽  
Layer Thickness ◽  
Titanium Surface ◽  
Layered Composite ◽  
Layered Composite Material ◽  
Surface Layer Thickness

scholarly journals Efek Tegangan Listrik dan Waktu Proses Elektroplating Krom Keras terhadap Tebal Lapisan

2019 ◽  
Vol 12 (2) ◽  
pp. 75
Author(s):  
Ketut Suarsana ◽  
I M. Astika ◽  
D.N.K Putra Negara
Keyword(s):  
Surface Layer ◽  
Layer Thickness ◽  
Coating Process ◽  
Electrical Voltage ◽  
Wear And Corrosion ◽  
Chrome Coating ◽  
Time Variations ◽  
Coating Time ◽  
Hard Chrome ◽  
Wear And Corrosion Resistance

Proses pelapisan krom keras merupakan proses akhir atau tahap penyelesaian pada kebanyakan pembuatan komponen agar tidak cepat aus, seperti pada poros, pasak, ring piston, silinder, bearing dan crank shaf. Dalam bidang industri sifat mekanik yang banyak diperlukan pada logam yang dipergunakan adalah kemampuannya untuk tahan aus dan tahan korosi yang mana kita ketahui logam mempunyai reaksi yang sangat aktif terhadap perubahaan temperatur dan cuaca, maka perlu dilakukan pelapisan sehingga kemungkinan suatu bahan logam terkena korosi bisa dihambat. Bahan spesimen yang di gunakan adalah Baja St 60 (C 0.40%; Mn 7%; Si 0.28%; P+S 0.09%; Fe 98,53%) dengan variasi tegangan listrik: 4, 6, dan 8 volt, untuk variasi waktu elektroplating krom keras 30, 45, dan 60 menit. Pengujian yang dilakukan dengan pengukuran ketebalan lapisan menggunakan skala foto mikro dan menghitung ketebalan lapisan permukaan. Hasil penelitian menunjukkan bahwa semakin tinggi tegangan listrik yang digunakan dan semakin lama waktu proses pelapisan krom keras maka meningkat ketebalan lapisannya. Ketebalan lapisan permukaan yang paling tebal didapatkan pada tegangan 8 volt dengan waktu pelapisan 60 menit dengan ketebalan lapisannya sebesar 89,37 ?m, sedangkan ketebalan lapisan permukaan tipis didapat pada tegangan 4 volt dengan waktu pelapisan 30 menit ketebalan lapisannya sebesar 20,18 ?m. Jadi tegangan listrik dan waktu electroplating dapat mempengaruhi dan memberikan efek terhadap ketebalan lapisan yang terjadi pada Baja St.60. The hard chrome coating process is the final process or completion stage in most parts making so as not to wear out quickly, such as on the shaft, pegs, piston rings, cylinders, bearings and crank shafts. In the industrial field of mechanical properties that are much needed in the metal used is its ability to withstand wear and corrosion resistance which we know metals have a very active reaction to changes in temperature and weather, coating is necessary so that the possibility of a metal being corroded can be inhibited. The specimens used were Baja St 60 (C 0.40%; Mn 7%; Si 0.28%; P + S 0.09%; Fe 98.53%) with variations in electrical voltage: 4, 6 and 8 volts, for time variations hard chrome electroplating 30, 60 and 90 minutes. Tests carried out by measuring the thickness of the layer use a micro photo scale and calculate the thickness of the surface layer. The results showed that the higher the voltage used and the longer the coating process was hard chrome, the thickness of the layer increased. The thickest surface layer thickness was obtained at 8 volts with a coating time of 60 minutes with a layer thickness of 89.37 ?m, while the thickness of the thin surface layer was obtained at a voltage of 4 volts with a coating time of 30 minutes layer thickness of 20.18 ?m. So the electrical voltage and time of electroplating can affect and give effect to the thickness of the coating that occurs in Steel St.60

scholarly journals SURFACE TENSION OF SERUM

1922 ◽  
Vol 35 (5) ◽  
pp. 707-735 ◽  
Author(s):  
P. Lecomte du Noüy
Keyword(s):  
Surface Tension ◽  
Surface Layer ◽  
Free Surface ◽  
Organic Compounds ◽  
Sodium Oleate ◽  
Mean Value ◽  
Physiological Solution ◽  
Optimum Concentration ◽  
Initial Value ◽  
Ring Method

The application of the ring method to the measurement of solutions of serum and of certain organic compounds has brought forth new facts, mainly the decrease of the surface tension of such solutions in function of time. 1. In serum diluted at such a low concentration as 1:1,000,000 in NaCl, physiological solution, the surface tension of the liquid is lowered by 3 or 4 dynes in 2 hours; at 1:100,000, by about 11 dynes (mean value) in 2 hours, and by 20 dynes in 24 hours; at 1:10,000 by about 13 to 16 dynes in 2 hours. 2. The drop in surface tension is much more rapid in the first 30 minutes and follows generally the law of adsorption in the surface layer in function of the time. 3. Stirring or shaking after the drop causes the surface tension to rise, but generally below its initial value. 4. The same phenomena occur when using sodium oleate, glycocholate, or saponin instead of serum. 5. For every serum, as well as for the substances mentioned above a maximum drop occurs in certain conditions at a given optimum concentration. 6. Not only are the substances which lower the surface tension adsorbed in the surface layer, in the case in which they are present with crystalloids, but also the crystalloids themselves, in contradiction to Gibbs' statement. This is plainly shown by the evaporation of such solutions in watch-glasses which, instead of a small group of sharp, large, well defined crystals at the bottom, leaves a white disc almost as large as the initial free surface itself, due to the liberation of the salt by the surface layer as it crawls down the concave surface of the glass. 7. In these conditions, solutions of serum are characterized by a very peculiar periodic and concentric distribution of the crystals, at a concentration of 1:100 only. The same ring-like aspect is observed with sodium oleate, glycocholate, and saponin, but not at the same concentration, as was to be expected, since serum is a solution in itself.

An Edge Dislocation in a Three-Phase Composite Cylinder Model

1991 ◽  
Vol 58 (1) ◽  
pp. 75-86 ◽  
Author(s):  
H. A. Luo ◽  
Y. Chen
Keyword(s):  
Edge Dislocation ◽  
Stable Equilibrium ◽  
Phase Model ◽  
Composite Cylinder ◽  
Two Phase ◽  
Trapping Mechanism ◽  
Three Phase ◽  
Cylinder Model ◽  
Stable Equilibrium Position ◽  
The Stability

An exact solution is given for the stress field due to an edge dislocation embedded in a three-phase composite cylinder. The force on the dislocation is then derived, from which a set of simple approximate formulae is also suggested. It is shown that, in comparison with the two-phase model adopted by Dundurs and Mura (1964), the three-phase model allows the dislocation to have a stable equilibrium position under much less stringent combinations of the material constants. As a result, the so-called trapping mechanism of dislocations is more likely to take place in the three-phase model. Also, the analysis and calculation show that in the three-phase model the orientation of Burgers vector has only limited influence on the stability of dislocation. This behavior is pronouncedly different from that predicted by the two-phase model.

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