Quasilocalized states of self stress in packing-derived networks

States of self stress (SSS) are assignments of forces on the edges of a network that satisfy mechanical equilibrium in the absence of external forces. In this work we show that a particular class of quasilocalized SSS in packing-derived networks, first introduced in [D. M. Sussman, C. P. Goodrich, and A. J. Liu, Soft Matter 12, 3982 (2016)], are characterized by a lengthscale $\ell_c$ that scales as $1/\sqrt{z_c-z}$ where $z$ is the mean connectivity of the network, and $z_c\!\equiv\!4$ is the Maxwell threshold in two dimensions, at odds with previous claims. Our results verify the previously proposed analogy between quasilocalized SSS and the mechanical response to a local dipolar force in random networks of relaxed Hookean springs. We show that the normalization factor that distinguishes between quasilocalized SSS and the response to a local dipole constitutes a measure of the mechanical coupling of the forced spring to the elastic network in which it is embedded. We further demonstrate that the lengthscale that characterizes quasilocalized SSS does not depend on its associated degree of mechanical coupling, but instead only on the network connectivity.Comment: 8 pages, 4 figure

Cutting the loss of derivatives for solvability under condition (psi)

For a principal type pseudodifferential operator, we prove that condition (psi) implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker's paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from 2 (Dencker's result) to 3/2 (the present paper). It is already known that condition (psi) does not imply local solvability with a loss of 1 derivative, so we have to content ourselves with a loss >1

The Puzzle of Pure Moral Motivation

People engage in pure moral inquiry whenever they inquire into the moral features of some act, agent, or state of affairs without inquiring into the non-moral features of that act, agent, or state of affairs. This chapter argues that ordinary people act rationally when they engage in pure moral inquiry, and so any adequate view in metaethics ought to be able to explain this fact. The Puzzle of Pure Moral Motivation is to provide such an explanation. This chapter argues that each of the standard views in metaethics has trouble providing such an explanation. Discussion of why reveals that a metaethical view can provide such an explanation only if it meets two constraints: it allows ordinary moral inquirers to know the essences of moral properties, and the essence of each moral property makes it rational to care for its own sake whether that property is instantiated

Let\u27s Get Moving: Labor\u27s survival depends on organizing industry-wide for justice and power

[Excerpt] Despite our almost universal lack of significant organizing victories, we continue to organize in basically the same way we have for the last 37 years. Labor\u27s model for organizing remains a site-by-site NLRB approach. We continue to fine-tune a model that most organizers know hasn\u27t worked in years. Depending on how you define success, it can be argued that our current method of organizing hasn\u27t worked in 37 years