4,670 research outputs found
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
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
, (b) the diffusion process is drift-free at any value of , (c) the point
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 , 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 with
finite degrees where the properties of balls of small radii guarantee the
existence of some Hamiltonian and connectivity properties of . (For a vertex
of a graph the ball of radius centered at is the subgraph of
induced by the set of vertices whose distance from does not
exceed ). In particular, we prove that if every ball of radius 2 in is
2-connected and satisfies the condition for
each path in , where and are non-adjacent vertices, then
has a Hamiltonian curve, introduced by K\"undgen, Li and Thomassen (2017).
Furthermore, we prove that if every ball of radius 1 in satisfies Ore's
condition (1960) then all balls of any radius in 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
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