Simple model of microscopic rolling friction

Rolling friction at a microscopic scale is studied with the help of a simple two-dimensional model. Molecular dynamics simulations show that rolling of spherical lubricant molecules exists only for concentrations lower than the concentration of a close-packed layer. At concentrations higher than a critical one due to jamming of lubricant molecules the rolling of nearest neighboring molecules is hindered. An optimal concentration exists which provides the minimum of kinetic friction. Methods for avoiding jamming and increasing the range of operation of rolling mechanism of friction are discussed.     

Statistical basis for physical laws; non-relativistic theory

We extend the constructions of previous papers, showing the equivalence of quantum mechanics and a classical probability formalism with constraints assuring differentiable probability densities without contradictions, to show that these constructions also yield Maxwell's equations and the Lorentz force. These constructions have already yielded Schroedinger's equation for a charged particle in an electromagnetic field, but here it is shown that this statistical construction provides the basis for gauge conditions and defines a specific gauge for this non-relativistic formalism. These constructions also provide new insight into the relationship of Schroedinger quantum mechanics and a classical diffusion process.     

From microscopic interactions to macroscopic laws of cluster evolution

We derive macroscopic governing laws of growth velocity, surface tension, mobility, critical nucleus size, and morphological evolution of clusters, from microscopic scale master equations for a prototype surface reaction system with long range adsorbate-adsorbate interactions.     

Contact area measurements reveal loading-history dependence of static friction

We perform quantitative measurements of the actual area of contact, A, formed by two rough solids that are subjected to different normal loading protocols. We show that microscopic motion, induced by Poisson contraction or expansion, produces a strong memory dependence of on the loading history with a large corresponding influence on the system's frictional strength. These effects, together with accompanying transient dynamics, are independent of humidity, loading rates, and material contrast across the interface.     

Effect of elastoplastic deformation on the static friction force

A study was made of elastoplastic deformation In surface layers caused by normal and tangential forces. A definite relationship is shown to exist between the external friction force and elastoplastic deformation. Maximum elastoplastic deformation arises in the contact zone when static friction is replaced by moving friction. The maximum elastoplastic deformation corresponds to the static friction force.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–37, September, 1969.     

Simple microscopic model for the scalar-isoscalar component of the Landau-Migdal amplitude

A simple microscopic model is proposed that describes the coordinate dependence of the zeroth harmonic f ₀(r) of the scalar-isoscalar component of the Landau-Migdal amplitude. In the theory of finite Fermi systems due to Migdal, such a dependence was introduced phenomenologically. The model presented in this study is based on a previous analysis of the Brueckner G matrix for a planar slab of nuclear matter; it expresses the function f ₀(r) in terms of the off-mass-shell T matrix for free nucleon-nucleon scattering. The result involves the T matrix taken at the negative energy value equal to the doubled chemical potential μ of the nucleus being considered. The amplitude f ₀(r) found in this way is substituted into the condition that, in the theory of finite Fermi systems, ensures consistency of the self-energy operator, effective quasiparticle interaction, and the density distribution. The calculated isoscalar component of the mean nuclear field V(r) agrees fairly well with a phenomenological nuclear potential. Owing to a strong E dependence of the T matrix at low energies, the potential-well depth V(0) depends sharply on μ, increasing as |μ| is reduced. This effect must additionally stabilize nuclei near the nucleon drip line, where μ vanishes.     

Evaluation of functional integrals for an ultralocal static field theory

Exact and perturbative solutions of an ultralocal, static, real φ^m field theory, obtained by functional integral methods are given and discussed. It is shown that this unrenormalizable theory leads to a free one in the local limit, whereas a small non-locality leads to a small effective coupling constant in an effective φ⁴ Lagrangian. It is proved that the usual perturbation seeries is the asymptotic expansion of the exact result.     

Simple versatile shearing interferometer suitable for measurements on a microscopic scale

Micro-electromechanical systems (MEMS) behave differently from massive samples. Conventional testing and inspection techniques usually fail at the microscale. Recently there has been an increasing interest in the application of optical techniques for microstructure testing, because they are high-resolution, non-contact, full-field, fast and relatively inexpensive. New interferometric systems, which are suitable for microscopic optical metrology, are of interest for engineering and industrial applications.A modified electronic speckle pattern shearing interferometer (ESPSI) with a very simple shearing device has been designed for metrology applications on the microscale. The shearing device consists of two partially reflective glass plates. The reflection coefficients of the coatings are 0.3 and 0.7, respectively. The distance and the tilt between the two glass plates control the size of the shear. A long working distance microscope objective is attached to the CCD camera to form a field of view variable over several millimetres in width. The suitability of the system for microscopic measurements is demonstrated. The capability of the system for phase shifting is also demonstrated. The results obtained are promising for future applications of the ESPSI system for testing and characterisation of MEMS.     

“摩擦力是相互作用力”的简捷演示方案

设计了两种简捷演示静摩擦力是一对作用力和反作用力的实验方案。     

Inhomogeneous static model in Brans-Dicke theory

A static universe with position-dependent rest-energy density, pressure, and scalar field is considered in Brans-Dicke theory. A perfect-gas equation of state is obtained with the solution to the field equations for the Euclidean case with Robertson-Walker metric.     

Conservation laws for the Korteweg-de Vries equation and the theory of partitions

We show how the terms appearing in the expressions for the densities and the fluxes for the Korteweg-de Vries equation may be found by combinatorial methods. Our basic device consists in associating partitions and their Ferrers graphs to the first density and to the first flux, and then in proceeding inductively following very simple rules. Furthermore, we use unrestricted partitions and a recurrence relation to specify every term of every integral power of the Sturm-Liouville (or one-dimensional Schrödinger) operator.