Macroscopic attractive forces between solid surfaces separated by 10–100 nm II. Experimental determination of attractive forces between mica cylinders by both dynamic-jump and static-jump methods

1982 ◽  
Vol 383 (1785) ◽  
pp. 295-312 ◽  
Keyword(s):  
Equilibrium Point ◽  
Experimental Determination ◽  
Free Vibrations ◽  
Unstable Equilibrium ◽  
Solid Surfaces ◽  
Measuring System ◽  
Unstable Equilibrium Point

Experiments are described that measure macroscopic attractive forces between two mica cylinders. The dynamic-jump method locates the unstable equilibrium point, which is present in the measuring system for a certain régime of separation, and uses the free vibrations of a spring-mounted mica cylinder.

scholarly journals A Four-Zone Model and Nonlinear Dynamic Analysis of Solution Multiplicity of Buoyancy Ventilation in Underground Building

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Yuxing Wang ◽  
Chunyu Wei
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Underground Structure ◽  
Unstable Equilibrium ◽  
Phase Portraits ◽  
Zone Model ◽  
Unstable Equilibrium Point ◽  
Index 2 ◽  
The Stability

The solution multiplicity of natural ventilation in buildings is very important to personnel safety and ventilation design. In this paper, a four-zone model of buoyancy ventilation in typical underground building is proposed. The underground structure is divided to four zones, a differential equation is established in each zone, and therefore, there are four differential equations in the underground structure. By solving and analyzing the equilibrium points and characteristic roots of the differential equations, we analyze the stability of three scenarios and obtain the criterions to determine the stability and existence of solutions for two scenarios. According to these criterions, the multiple steady states of buoyancy ventilation in any four-zone underground buildings for different stack height ratios and the strength ratios of the heat sources can be obtained. These criteria can be used to design buoyancy ventilation or natural exhaust ventilation systems in underground buildings. Compared with the two-zone model in (Liu et al. 2020), the results of the proposed four-zone model are more consistent with CFD results in (Liu et al. 2018). In addition, the results of proposed four-zone model are more specific and more detailed in the unstable equilibrium point interval. We find that the unstable equilibrium point interval is divided into two different subintervals corresponding to the saddle point of index 2 and the saddle focal equilibrium point of index 2, respectively. Finally, the phase portraits and vector field diagrams for the two scenarios are given.

scholarly journals I. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil

1886 ◽  
Vol 40 (242-245) ◽  
pp. 191-203 ◽  
Keyword(s):  
Olive Oil ◽  
Experimental Determination ◽  
Friction And Wear ◽  
Viscous Fluids ◽  
Solid Surfaces ◽  
Fundamental Importance ◽  
Theoretical Treatment ◽  
The Subject

Lubrication, or the action of oils and other viscous fluids to diminish friction and wear between solid surfaces, does not appear to have hitherto formed a subject for theoretical treatment. Such treatment may have been prevented by the obscurity of the physical actions involved, which belong to a class as yet but little known, namely, the boundary or surface actions of fluids; but the absence of such treatment has also been owing to the want of any general laws revealed by experiment. The subject is of such fundamental importance in practical mechanics, and the opportunities of observation so frequent, that it may well be a matter of surprise that any general laws should have for so long escaped detection.

IV. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil

1886 ◽  
Vol 177 ◽  
pp. 157-234 ◽  
Keyword(s):  
Olive Oil ◽  
Experimental Determination ◽  
Friction And Wear ◽  
Viscous Fluids ◽  
Solid Surfaces ◽  
Fundamental Importance ◽  
Theoretical Treatment ◽  
The Subject

1. Lubrication, or the action of oils and other viscous fluids to diminish friction and wear between solid surfaces, does not appear to have hitherto formed a subject for theoretical treatment. Such treatment may have been prevented by the obscurity of the physical actions involved, which belong to a class as yet but little known, namely, the boundary or surface actions of fluids; but the absence of such treatment has also been owing to the want of any general laws discovered by experiment. The subject is of such fundamental importance in practical mechanics, and the opportunities for observation are so frequent, that it may well be a matter of surprise that any general laws should have for so long escaped detection.

scholarly journals High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3130
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed
Keyword(s):  
Equilibrium Point ◽  
Image Encryption ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Unstable Equilibrium ◽  
Phase Portraits ◽  
Time Efficiency ◽  
Unstable Equilibrium Point

Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

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