The Puzzling Collapse of Electronic Sliding Friction on a Superconductor Surface

In a recent paper [Phys. Rev. Lett. 80 (1998) 1690], Krim and coworkers have observed that the friction force, acting on a thin physisorbed layer of N_2 sliding on a lead film, abruptly decreases by a factor of ~2 when the lead film is cooled below its superconductivity transition temperature. We discuss the possible mechanisms for the abruptness of the sliding friction drop, and also discuss the relevance of these results to the problem of electronic friction.Comment: 5 pages, no figure

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped f orm, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.Comment: 14 pages, 16 figure

Contact mechanics for randomly rough surfaces

When two solids are squeezed together they will in general not make atomic contact everywhere within the nominal (or apparent) contact area. This fact has huge practical implications and must be considered in many technological applications. In this paper I briefly review basic theories of contact mechanics. I consider in detail a recently developed contact mechanics theory. I derive boundary conditions for the stress probability distribution function for elastic, elastoplastic and adhesive contact between solids and present numerical results illustrating some aspects of the theory. I analyze contact problems for very smooth polymer (PMMA) and Pyrex glass surfaces prepared by cooling liquids of glassy materials from above the glass transition temperature. I show that the surface roughness which results from the frozen capillary waves can have a large influence on the contact between the solids. The analysis suggest a new explanation for puzzling experimental results [L. Bureau, T. Baumberger and C. Caroli, arXiv:cond-mat/0510232] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. I discuss the possibility of testing the theory using numerical methods, e.g., finite element calculations.Comment: Review paper, 29 pages, 31 picture

Asymptotic Freedom from Thermal and Vacuum Magnetization

We calculate the effective Lagrangian for a magnetic field in spinor, scalar and vector QED. Connections are then made to $SU(N_C)$ Yang--Mills theory and QCD. The magnetization and the corresponding effective charge are obtained from the effective Lagrangian. The renormalized vacuum magnetization will depend on the renormalization scale chosen. Regardless of this, the effective charge decreasing with the magnetic field, as in QCD, corresponds to anti- screening and asymptotic freedom. In spinor and scalar QED on the other hand, the effective charge is increasing with the magnetic field, corresponding to screening. Including effects due to finite temperature and density, we comment on the effective charge in a degenerate fermion gas, increasing linearly with the chemical potential. Neglecting the tachyonic mode, we find that in hot QCD the effective charge is decreasing as the inverse temperature, in favor for the formation of a quark-gluon plasma. However, including the real part of the contribution from the tachyonic mode, we find instead an effective charge increasing with the temperature. Including a thermal gluon mass, the effective charge in hot QCD is group invariant (unlike in the two cases above), and decreases logarithmically in accordance to the vacuum renormalization group equation, with the temperature as the momentum scale.Comment: 38 pages. Latex. More sequential treatment of different limits. Thermal gluon mass include

Inhomogeneous potentials, Hausdorff dimension and shrinking targets

Generalising a construction of Falconer, we consider classes of $G_\delta$-subsets of $\mathbb{R}^d$ with the property that sets belonging to the class have large Hausdorff dimension and the class is closed under countable intersections. We relate these classes to some inhomogeneous potentials and energies, thereby providing some useful tools to determine if a set belongs to one of the classes. As applications of this theory, we calculate, or at least estimate, the Hausdorff dimension of randomly generated limsup-sets, and sets that appear in the setting of shrinking targets in dynamical systems. For instance, we prove that for $\alpha \geq 1$, $$\mathrm{dim}_\mathrm{H}\, \{ \, y : | T_a^n (x) - y| < n^{-\alpha} \text{ infinitely often} \, \} = \frac{1}{\alpha},$$ for almost every $x \in [1-a,1]$, where $T_a$ is a quadratic map with $a$ in a set of parameters described by Benedicks and Carleson.Comment: 36 pages. Corrected and reorganised following referee's report. Accepted for publication in Annales Henri Lebesgu

What are the core ideas behind the Precautionary Principle?

The Precautionary Principle is both celebrated and criticized. It has become an important principle for decision making, but it is also subject to criticism. One problem that is often pointed out with the principle is that is not clear what it actually says and how to use it. I have taken on this problem by performing an analysis of some of the most influential formulations of the principle in an attempt to identify the core ideas behind it, with the purpose of producing a formulation of the principle that is clear and practically applicable. It was found that what is called the Precautionary Principle is not a principle that tells us what do to achieve extra precaution or how to handle situations when extra precaution is called for. Instead, it was found to be a list of circumstances that each justify extra precaution. An analysis of some of the most common and influential formulations of the Precautionary Principle identified four such circumstances: (1) When we deal with important values that tend to be systematically downplayed by traditional decision methods – such as human health and the environment. (2) When we suspect that the decision might lead to irreversible and severe consequences and the values at stake are also irreplaceable, (3) When timing is at least as important as being right. (4) When it is more important to avoid false negatives than false positives. This interpretation of the Precautionary Principle does not say anything about what kind of actions to take when extra precaution is called for, but it does provide a clear and practically useful list of circumstances that call for extra precaution and that is not subject to the most common objections to the Precautionary Principle