55,685 research outputs found
Thermal breakage of a semiflexible polymer: Breakage profile and rate
Understanding fluctuation-induced breakages in polymers has important
implications for basic and applied sciences. Here I present for the first time
an analytical treatment of the thermal breakage problem of a semi-flexible
polymer model that is asymptotically exact in the low temperature and high
friction limits. Specifically, I provide analytical expressions for the
breakage propensity and rate, and discuss the generalities of the results and
their relevance to biopolymers
Equilibrium kinetics of self-assembling, semi-flexible polymers
Self-assembling, semi-flexible polymers are ubiquitous in biology and
technology. However, there remain conflicting accounts of the equilibrium
kinetics for such an important system. Here, by focusing on a dynamical
description of a minimal model in an overdamped environment, I identify the
correct kinetic scheme that describes the system at equilibrium in the limits
of high bonding energy and dilute concentration.Comment: 12 pages, 4 figure
Interface stability, interface fluctuations, and the Gibbs-Thomson relation in motility-induced phase separations
Minimal models of self-propelled particles with short-range volume exclusion
interactions have been shown to exhibit signatures of phase separation. Here I
show that the observed interfacial stability and fluctuations in
motility-induced phase separations (MIPS) can be explained by modeling the
microscopic dynamics of the active particles in the interfacial region. In
addition, I demonstrate the validity of the Gibbs-Thomson relation in MIPS,
which provides a functional relationship between the size of a condensed drop
and its surrounding vapor concentration. As a result, the coarsening dynamics
of MIPS at vanishing supersaturation follows the classic Lifshitz-Slyozov
scaling law at the late stage.Comment: 11 pages, 6 figure
Fluctuation-induced collective motion: A single-particle density analysis
In a system of noisy self-propelled particles with interactions that favor
directional alignment, collective motion will appear if the density of
particles increases beyond a certain threshold. In this paper, we argue that
such a threshold may depend also on the profiles of the perturbation in the
particle directions. Specifically, we perform mean-field, linear stability,
perturbative and numerical analyses on an approximated form of the
Fokker-Planck equation describing the system. We find that if an angular
perturbation to an initially homogeneous system is large in magnitude and
highly localized in space, it will be amplified and thus serves as an
indication of the onset of collective motion. Our results also demonstrate that
high particle speed promotes collective motion.Comment: To appear in Physical Review E
Wasserstein Introspective Neural Networks
We present Wasserstein introspective neural networks (WINN) that are both a
generator and a discriminator within a single model. WINN provides a
significant improvement over the recent introspective neural networks (INN)
method by enhancing INN's generative modeling capability. WINN has three
interesting properties: (1) A mathematical connection between the formulation
of the INN algorithm and that of Wasserstein generative adversarial networks
(WGAN) is made. (2) The explicit adoption of the Wasserstein distance into INN
results in a large enhancement to INN, achieving compelling results even with a
single classifier --- e.g., providing nearly a 20 times reduction in model size
over INN for unsupervised generative modeling. (3) When applied to supervised
classification, WINN also gives rise to improved robustness against adversarial
examples in terms of the error reduction. In the experiments, we report
encouraging results on unsupervised learning problems including texture, face,
and object modeling, as well as a supervised classification task against
adversarial attacks.Comment: Accepted to CVPR 2018 (Oral
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