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..

Synthesizing Short-Circuiting Validation of Data Structure Invariants

This paper presents incremental verification-validation, a novel approach for checking rich data structure invariants expressed as separation logic assertions. Incremental verification-validation combines static verification of separation properties with efficient, short-circuiting dynamic validation of arbitrarily rich data constraints. A data structure invariant checker is an inductive predicate in separation logic with an executable interpretation; a short-circuiting checker is an invariant checker that stops checking whenever it detects at run time that an assertion for some sub-structure has been fully proven statically. At a high level, our approach does two things: it statically proves the separation properties of data structure invariants using a static shape analysis in a standard way but then leverages this proof in a novel manner to synthesize short-circuiting dynamic validation of the data properties. As a consequence, we enable dynamic validation to make up for imprecision in sound static analysis while simultaneously leveraging the static verification to make the remaining dynamic validation efficient. We show empirically that short-circuiting can yield asymptotic improvements in dynamic validation, with low overhead over no validation, even in cases where static verification is incomplete

Priority Queues with Multiple Time Fingers

A priority queue is presented that supports the operations insert and find-min in worst-case constant time, and delete and delete-min on element x in worst-case O(lg(min{w_x, q_x}+2)) time, where w_x (respectively q_x) is the number of elements inserted after x (respectively before x) and are still present at the time of the deletion of x. Our priority queue then has both the working-set and the queueish properties, and more strongly it satisfies these properties in the worst-case sense. We also define a new distribution-sensitive property---the time-finger property, which encapsulates and generalizes both the working-set and queueish properties, and present a priority queue that satisfies this property. In addition, we prove a strong implication that the working-set property is equivalent to the unified bound (which is the minimum per operation among the static finger, static optimality, and the working-set bounds). This latter result is of tremendous interest by itself as it had gone unnoticed since the introduction of such bounds by Sleater and Tarjan [JACM 1985]. Accordingly, our priority queue satisfies other distribution-sensitive properties as the static finger, static optimality, and the unified bound.Comment: 14 pages, 4 figure

Observation of String Breaking in QCD

We numerically investigate the transition of the static quark-antiquark string into a static-light meson-antimeson system. Improving noise reduction techniques, we are able to resolve the signature of string breaking dynamics for n_f=2 lattice QCD at zero temperature. This result can be related to properties of quarkonium systems. We also study short-distance interactions between two static-light mesons.Comment: 27 pages, 22 figures, changed decimal place of errors in 3 entries of Table, corrected reference

Stability of the solutions of the Gross-Pitaevskii equation

We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static properties. We find, for example, the obvious result that static stability always implies dynamic stability and present a simple explanation of the fact that dynamic stability can exist even in the presence of static instability.Comment: 7 pages, 1 figur

The unified Skyrmion profiles and Static Properties of Nucleons

An unified approximated solution for symmetric Skyrmions was proposed for the SU(2) Skyrme model for baryon numbers up to 8,which take the hybrid form of a kink-like solution and that given by the instanton method. The Skyrmion profiles are examined by computing lowest soliton energy as well as the static properties of nucleons within the framework of collective quantization, with a good agreement with the exact numeric results. The comparisons with the previous computations as well as the experimental data are also given.Comment: 6 pages, 3 figures, 3 tables, Created by LaTex Syste

Static and dynamic properties of shell-shaped condensates

Static, dynamic, and topological properties of hollow systems differ from those that are fully filled as a result of the presence of a boundary associated with an inner surface. Hollow Bose-Einstein condensates (BECs) naturally occur in various ultracold atomic systems and possibly within neutron stars but have hitherto not been experimentally realized in isolation on Earth because of gravitational sag. Motivated by the expected first realization of fully closed BEC shells in the microgravity conditions of the Cold Atomic Laboratory aboard the International Space Station, we present a comprehensive study of spherically symmetric hollow BECs as well as the hollowing transition from a filled sphere BEC into a thin shell through central density depletion. We employ complementary analytic and numerical techniques in order to study equilibrium density profiles and the collective mode structures of condensate shells hosted by a range of trapping potentials. We identify concrete and robust signatures of the evolution from filled to hollow structures and the effects of the emergence of an inner boundary, inclusive of a dip in breathing-mode-type collective mode frequencies and a restructuring of surface mode structure across the transition. By extending our analysis to a two-dimensional transition of a disk to a ring, we show that the collective mode signatures are an essential feature of hollowing, independent of the specific geometry. Finally, we relate our work to past and ongoing experimental efforts and consider the influence of gravity on thin condensate shells. We identify the conditions under which gravitational sag is highly destructive and study the mode-mixing effects of microgravity on the collective modes of these shells.Comment: 26 pages, 13 figure