Stochastic Properties of Static Friction

The onset of frictional motion is mediated by rupture-like slip fronts, which nucleate locally and propagate eventually along the entire interface causing global sliding. The static friction coefficient is a macroscopic measure of the applied force at this particular instant when the frictional interface loses stability. However, experimental studies are known to present important scatter in the measurement of static friction; the origin of which remains unexplained. Here, we study the nucleation of local slip at interfaces with slip-weakening friction of random strength and analyze the resulting variability in the measured global strength. Using numerical simulations that solve the elastodynamic equations, we observe that multiple slip patches nucleate simultaneously, many of which are stable and grow only slowly, but one reaches a critical length and starts propagating dynamically. We show that a theoretical criterion based on a static equilibrium solution predicts quantitatively well the onset of frictional sliding. We develop a Monte-Carlo model by adapting the theoretical criterion and pre-computing modal convolution terms, which enables us to run efficiently a large number of samples and to study variability in global strength distribution caused by the stochastic properties of local frictional strength. The results demonstrate that an increasing spatial correlation length on the interface, representing geometric imperfections and roughness, causes lower global static friction. Conversely, smaller correlation length increases the macroscopic strength while its variability decreases. We further show that randomness in local friction properties is insufficient for the existence of systematic precursory slip events. Random or systematic non-uniformity in the driving force, such as potential energy or stress drop, is required for arrested slip fronts. Our model and observations..

Streaming Kernelization

Kernelization is a formalization of preprocessing for combinatorially hard problems. We modify the standard definition for kernelization, which allows any polynomial-time algorithm for the preprocessing, by requiring instead that the preprocessing runs in a streaming setting and uses $\mathcal{O}(poly(k)\log|x|)$ bits of memory on instances $(x,k)$. We obtain several results in this new setting, depending on the number of passes over the input that such a streaming kernelization is allowed to make. Edge Dominating Set turns out as an interesting example because it has no single-pass kernelization but two passes over the input suffice to match the bounds of the best standard kernelization

Welding-base metal investigation Final report, 27 Jun. 1964 - 28 Jul. 1965

Weld defects associated with aluminum alloys - monitoring weld shielding gas purit

Oral Region Homologies in Paleozoic Crinoids and Other Plesiomorphic Pentaradial Echinoderms

The phylogenetic relationships between major groups of plesiomorphic pentaradial echinoderms, the Paleozoic crinoids, blastozoans, and edrioasteroids, are poorly understood because of a lack of widely recognized homologies. Here, we present newly recognized oral region homologies, based on the Universal Elemental Homology model for skeletal plates, in a wide range of fossil taxa. The oral region of echinoderms is mainly composed of the axial, or ambulacral, skeleton, which apparently evolved more slowly than the extraxial skeleton that forms the majority of the body. Recent phylogenetic hypotheses have focused on characters of the extraxial skeleton, which may have evolved too rapidly to preserve obvious homologies across all these groups. The axial skeleton conserved homologous suites of characters shared between various edrioasteroids and specific blastozoans, and between other blastozoans and crinoids. Although individual plates can be inferred as homologous, no directly overlapping suites of characters are shared between edrioasteroids and crinoids. Six different systems of mouth (peristome) plate organization (Peristomial Border Systems) are defined. These include four different systems based on the arrangement of the interradially-positioned oral plates and their peristomial cover plates, where PBS A1 occurs only in plesiomorphic edrioasteroids, PBS A2 occurs in plesiomorphic edrioasteroids and blastozoans, and PBS A3 and PBS A4 occur in blastozoans and crinoids. The other two systems have radially-positioned uniserial oral frame plates in construction of the mouth frame. PBS B1 has both orals and uniserial oral frame plates and occurs in edrioasterid and possibly edrioblastoid edrioasteroids, whereas PBS B2 has exclusively uniserial oral frame plates and is found in isorophid edrioasteroids and imbricate and gogiid blastozoans. These different types of mouth frame construction offer potential synapomorphies to aid in parsimony-based phylogenetics for exploring branching order among stem groups on the echinoderm tree of life

On the Propagation of Slip Fronts at Frictional Interfaces

The dynamic initiation of sliding at planar interfaces between deformable and rigid solids is studied with particular focus on the speed of the slip front. Recent experimental results showed a close relation between this speed and the local ratio of shear to normal stress measured before slip occurs (static stress ratio). Using a two-dimensional finite element model, we demonstrate, however, that fronts propagating in different directions do not have the same dynamics under similar stress conditions. A lack of correlation is also observed between accelerating and decelerating slip fronts. These effects cannot be entirely associated with static local stresses but call for a dynamic description. Considering a dynamic stress ratio (measured in front of the slip tip) instead of a static one reduces the above-mentioned inconsistencies. However, the effects of the direction and acceleration are still present. To overcome this we propose an energetic criterion that uniquely associates, independently on the direction of propagation and its acceleration, the slip front velocity with the relative rise of the energy density at the slip tip.Comment: 15 pages, 6 figure