A General Approach to Casimir Force Problems Based on Local Reflection Amplitudes and Huygen's Principle

In this paper we describe an approach to Casimir Force problems that is ultimately generalizable to all fields, boundary conditions, and cavity geometries. This approach utilizes locally defined reflection amplitudes to express the energy per unit area of any Casimir interaction. To demonstrate this approach we solve a number of Casimir Force problems including the case of uniaxial boundary conditions in a parallel-plate cavity.Comment: 9 pages, 5 figures, Equation 18 has been corrected, [v1] contained a typ

Transition rates for slip-avalanches in soft athermal disks under quasi-static simple shear deformations

We study slip-avalanches in two-dimensional soft athermal disks by quasi-static simulations of simple shear deformations. Sharp drops in shear stress, or slip-avalanches, are observed intermittently during steady state. Such the stress drop is caused by restructuring of the contact networks, accompanied by drastic changes of the interaction forces. The changes of the forces happen heterogeneously in space, indicating that collective non-affine motions of the disks are most pronounced when slip-avalanches occur. We analyze and predict statistics for the force changes, by transition rates of the force and contact angle, where slip-avalanches are characterized by their wide power-law tails. We find that the transition rates are described as a q-Gaussian distribution regardless of the area fraction of the disks. Because the transition rates quantify structural changes of the force-chains, our findings are an important step towards a microscopic theory of slip-avalanches in the experimentally accessible quasi-static regime.Comment: 5 pages, 6 figure

Atomic Scale Sliding and Rolling of Carbon Nanotubes

A carbon nanotube is an ideal object for understanding the atomic scale aspects of interface interaction and friction. Using molecular statics and dynamics methods different types of motion of nanotubes on a graphite surface are investigated. We found that each nanotube has unique equilibrium orientations with sharp potential energy minima. This leads to atomic scale locking of the nanotube. The effective contact area and the total interaction energy scale with the square root of the radius. Sliding and rolling of nanotubes have different characters. The potential energy barriers for sliding nanotubes are higher than that for perfect rolling. When the nanotube is pushed, we observe a combination of atomic scale spinning and sliding motion. The result is rolling with the friction force comparable to sliding.Comment: 4 pages (two column) 6 figures - one ep

Force-displacement relation in a tangential frictional contact with adhesion

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 2051, 020244 (2018) and may be found at https://doi.org/10.1063/1.5083487.We consider tangential contact between a rigid cylinder and elastic half-space in the presence of adhesion and Coulomb’s frictional force. In the limit of very small range of adhesive interaction, the main governing dimensionless parameters are identified and it is shown that the shape of the relation between the normalized force and normalized displacement is function of only one system parameter closely related to the Tabor parameter. However, the qualitative behavior is the same for arbitrary values of the Tabor parameter: the force monotonously increases from zero to the maximum value corresponding to the complete sliding. This behavior is qualitatively different from that known in the case of non-adhesive contact where—in the case of flat-ended cylindrical punch—the whole contact area remains in stick state until the displacement achieves some critical value, after which complete sliding starts

Global vs local Casimir effect

This paper continues the investigation of the Casimir effect with the use of the algebraic formulation of quantum field theory in the initial value setting. Basing on earlier papers by one of us (AH) we approximate the Dirichlet and Neumann boundary conditions by simple interaction models whose nonlocality in physical space is under strict control, but which at the same time are admissible from the point of view of algebraic restrictions imposed on models in the context of Casimir backreaction. The geometrical setting is that of the original parallel plates. By scaling our models and taking appropriate limit we approach the sharp boundary conditions in the limit. The global force is analyzed in that limit. One finds in Neumann case that although the sharp boundary interaction is recovered in the norm resolvent sense for each model considered, the total force per area depends substantially on its choice and diverges in the sharp boundary conditions limit. On the other hand the local energy density outside the interaction region, which in the limit includes any compact set outside the strict position of the plates, has a universal limit corresponding to sharp conditions. This is what one should expect in general, and the lack of this discrepancy in Dirichlet case is rather accidental. Our discussion pins down its precise origin: the difference in the order in which scaling limit and integration over the whole space is carried out.Comment: 32 pages, accepted for publication in Ann. H. Poincar

Impact of wheel shape on the vertical damage of cast crossing panels in turnouts

Impact forces generated in the load transfer area of railway crossing panels lead to a range of degradation modes from wear and fatigue of the contacting materials, fatigue of supporting components to ballast/subgrade deterioration. A simplified modelling approach has been developed to first analyse the geometrical problem of the axle rolling through the crossing geometry, and in a second step to predict the vertical dynamic force produce from the interaction between the wheel unsprung mass and the track system. The force is analysed in the frequency domain to estimate the level of damage in different parts of the track system. A parametric analysis of wheel shapes was carried out showing that the axle lateral displacement has a significant influence on the produced level of damage and also that characteristics such as the wheel flange thickness and the equivalent slope in the area of contact also leads to increased damage. It is suggested that such a measure in combination with the simplified algorithms developed here could be used, possibly in combination with track side monitoring system, to highlight traffic instances leading to increased asset damage

On the Mechanics of Disc-Soil-Planter Interaction

The main objective of this research project was to understand the disc-soil-planter interaction in order to provide the lowest draft force for robotic planters. For that purpose, an analytical investigation was conducted and the mathematical model of the interaction was developed. Then a series of experimental tests were completed and reported. This constitutes the thesis’ contribution to research in this area. Finally, optimization of parameters was investigated to minimize the drag force

Contacts With Negative Work of “Adhesion” and Superlubricity

Van der Waals forces between solids in vacuum are always attractive and are considered as the main source of adhesion. However, in the presence of an intermediate medium, they can also be repelling (Dzyaloshinskii et al., 1961) which means that the “work of adhesion” becomes negative. Similarly to the case of adhesion, the interaction range of these forces can be either comparable (or larger) than the minimum characteristic length scale of the contact problem or it can be negligible compared with all characteristic length scales. We call this latter case the “JKR-approximation,” as the JKR theory of adhesion (Johnson et al., 1971) is also valid in this limit. The repelling interaction can also be due to the presence (and squeezing out) of a thin fluid layer between solids as considered in Müser (2014). In the papers Popov and Hess (2018) and Heß and Popov (2019), it was shown that the contact of two oppositely charged surfaces at a constant voltage is equivalent to the adhesive contact with an effective van der Waals interaction. Similarly, the contact of the bodies with the same charge would be equivalent to repelling van der Waals forces with a negative work of adhesion. Further kinds of repelling forces may be solvation, structural, and hydration forces (Israelachvili, 2011). In the following, we speak about van der Waals forces, but they are thought as representative for a larger class of long range repelling forces. We argue that in the JKR approximation, the Hertz' solution of the contact problem with a repelling van der Waals interaction, remains practically unchanged. However, the contact area falls apart into the area of “weak (van der Waals) interaction” and “strong (rigid wall) interaction.” It is speculated that if the normal force is smaller than a critical value at which the core region of strong interaction disappears, a macroscopic superlubricity state of the contact may be observed.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli