Systematic analysis of Persson's contact mechanics theory of randomly rough elastic surfaces

We systematically check explicit and implicit assumptions of Persson's contact mechanics theory. It casts the evolution of the pressure distribution ${\rm Pr}(p)$ with increasing resolution of surface roughness as a diffusive process, in which resolution plays the role of time. The tested key assumptions of the theory are: (a) the diffusion coefficient is independent of pressure $p$, (b) the diffusion process is drift-free at any value of $p$, (c) the point $p=0$ acts as an absorbing barrier, i.e., once a point falls out of contact, it never reenters again, (d) the Fourier component of the elastic energy is only populated if the appropriate wave vector is resolved, and (e) it no longer changes when even smaller wavelengths are resolved. Using high-resolution numerical simulations, we quantify deviations from these approximations and find quite significant discrepancies in some cases. For example, the drift becomes substantial for small values of $p$, which typically represent points in real space close to a contact line. On the other hand, there is a significant flux of points reentering contact. These and other identified deviations cancel each other to a large degree, resulting in an overall excellent description for contact area, contact geometry, and gap distribution functions. Similar fortuitous error cancellations cannot be guaranteed under different circumstances, for instance when investigating rubber friction. The results of the simulations may provide guidelines for a systematic improvement of the theory.Comment: 27 pages, 16 figures, accepted for publication by Journal of Physics: Condensed Matte

A practical guide for optimal designs of experiments in the Monod model

The Monod model is a classical microbiological model much used in microbiology, for example to evaluate biodegradation processes. The model describes microbial growth kinetics in batch culture experiments using three parameters: the maximal specific growth rate, the saturation constant and the yield coefficient. However, identification of these parameter values from experimental data is a challenging problem. Recently, it was shown theoretically that the application of optimal design theory in this model is an efficient method for both parameter value identification and economic use of experimental resources (Dette et al., 2003). The purpose of this paper is to provide this method as a computational ?tool? such that it can be used by practitioners-without strong mathematical and statistical backgroundfor the efficient design of experiments in the Monod model. The paper presents careful explanations of the principal theoretical concepts, and a computer program for practical optimal design calculations in Mathematica 5.0 software. In addition, analogous programs in Matlab software will be soon available at www.optimal-design.org. --Monod model,microbial growth,biodegradation kinetics,optimal experimental design,D-optimality

Some local--global phenomena in locally finite graphs

In this paper we present some results for a connected infinite graph $G$ with finite degrees where the properties of balls of small radii guarantee the existence of some Hamiltonian and connectivity properties of $G$. (For a vertex $w$ of a graph $G$ the ball of radius $r$ centered at $w$ is the subgraph of $G$ induced by the set $M_r(w)$ of vertices whose distance from $w$ does not exceed $r$). In particular, we prove that if every ball of radius 2 in $G$ is 2-connected and $G$ satisfies the condition $d_G(u)+d_G(v)\geq |M_2(w)|-1$ for each path $uwv$ in $G$, where $u$ and $v$ are non-adjacent vertices, then $G$ has a Hamiltonian curve, introduced by K\"undgen, Li and Thomassen (2017). Furthermore, we prove that if every ball of radius 1 in $G$ satisfies Ore's condition (1960) then all balls of any radius in $G$ are Hamiltonian.Comment: 18 pages, 6 figures; journal accepted versio

Superglass Phase of Helium-four

We study different solid phases of Helium-four, by means of Path Integral Monte Carlo simulations based on a recently developed "worm" algorithm. Our study includes simulations that start off from a high-T gas phase, which is then "quenched" down to T=0.2 K. The low-T properties of the system crucially depend on the initial state. While an ideal hcp crystal is a clear-cut insulator, the disordered system freezes into a "superglass", i.e., a metastable amorphous solid featuring off-diagonal long-range order and superfluidity

Design of experiments for microbiological models

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