The dynamics of cracks in torn thin sheets

Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke a generalization of the principle of local symmetry to provide a criterion for path selection and demonstrate qualitative agreement with the experimental findings. The nature of the singularity at the crack tip is studied with and without the interference of nonlinear terms.Comment: 7 pages, 11 figure

Exhaustion of Nucleation in a Closed System

We determine the distribution of cluster sizes that emerges from an initial phase of homogeneous aggregation with conserved total particle density. The physical ingredients behind the predictions are essentially classical: Super-critical nuclei are created at the Zeldovich rate, and before the depletion of monomers is significant, the characteristic cluster size is so large that the clusters undergo diffusion limited growth. Mathematically, the distribution of cluster sizes satisfies an advection PDE in "size-space". During this creation phase, clusters are nucleated and then grow to a size much larger than the critical size, so nucleation of super-critical clusters at the Zeldovich rate is represented by an effective boundary condition at zero size. The advection PDE subject to the effective boundary condition constitutes a "creation signaling problem" for the evolving distribution of cluster sizes during the creation era. Dominant balance arguments applied to the advection signaling problem show that the characteristic time and cluster size of the creation era are exponentially large in the initial free-energy barrier against nucleation, G_*. Specifically, the characteristic time is proportional to exp(2 G_*/ 5 k_B T) and the characteristic number of monomers in a cluster is proportional to exp(3G_*/5 k_B T). The exponentially large characteristic time and cluster size give a-posteriori validation of the mathematical signaling problem. In a short note, Marchenko obtained these exponentials and the numerical pre-factors, 2/5 and 3/5. Our work adds the actual solution of the kinetic model implied by these scalings, and the basis for connection to subsequent stages of the aggregation process after the creation era.Comment: Greatly shortened paper. Section on growth model removed. Added a section analyzing the error in the solution of the integral equation. Added reference

Accounting for Memory Bank Contention and Delay in High-Bandwidth Multiprocessors

This paper considers issues of memory performance in shared memory multiprocessors that provide a high-bandwidth network and in which the memory banks are slower than the processors. We are concerned with the effects of memory bank contention, memory bank delay, and the bank expansion factor (the ratio of number of banks to number of processors) on performance, particularly for irregular memory access patterns. This work was motivated by observed discrepancies between predicted and actual performance in a number of irregular algorithms implemented for the cray C90 when the memory contention at a particular location is high. We develop a formal framework for studying memory bank contention and delay, and show several results, both experimental and theoretical. We first show experimentally that our framework is a good predictor of performance on the cray C90 and J90, providing a good accounting of bank contention and delay. Second, we show that it often improves performance to have addi..

Systematic comparison of monoclonal versus polyclonal antibodies for mapping histone modifications by ChIP-seq.

BackgroundThe robustness of ChIP-seq datasets is highly dependent upon the antibodies used. Currently, polyclonal antibodies are the standard despite several limitations: They are non-renewable, vary in performance between lots and need to be validated with each new lot. In contrast, monoclonal antibody lots are renewable and provide consistent performance. To increase ChIP-seq standardization, we investigated whether monoclonal antibodies could replace polyclonal antibodies. We compared monoclonal antibodies that target five key histone modifications (H3K4me1, H3K4me3, H3K9me3, H3K27ac and H3K27me3) to their polyclonal counterparts in both human and mouse cells.ResultsOverall performance was highly similar for four monoclonal/polyclonal pairs, including when we used two distinct lots of the same monoclonal antibody. In contrast, the binding patterns for H3K27ac differed substantially between polyclonal and monoclonal antibodies. However, this was most likely due to the distinct immunogen used rather than the clonality of the antibody.ConclusionsAltogether, we found that monoclonal antibodies as a class perform equivalently to polyclonal antibodies for the detection of histone post-translational modifications in both human and mouse. Accordingly, we recommend the use of monoclonal antibodies in ChIP-seq experiments

OGLE-2018-BLG-0022: First Prediction of an Astrometric Microlensing Signal from a Photometric Microlensing Event

In this work, we present the analysis of the binary microlensing event OGLE-2018-BLG-0022 that is detected toward the Galactic bulge field. The dense and continuous coverage with the high-quality photometry data from ground-based observations combined with the space-based Spitzer observations of this long timescale event enables us to uniquely determine the masses M_1 = 0.40 ± 0.05 M⊙ and M_2 = 0.13 ± 0.01 M⊙ of the individual lens components. Because the lens-source relative parallax and the vector lens-source relative proper motion are unambiguously determined, we can likewise unambiguously predict the astrometric offset between the light centroid of the magnified images (as observed by the Gaia satellite) and the true position of the source. This prediction can be tested when the individual-epoch Gaia astrometric measurements are released