96,827 research outputs found
Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams
We introduce a monotone (degenerate elliptic) discretization of the
Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is
consistent provided the solution hessian condition number is uniformly bounded.
Our approach enjoys the simplicity of the Wide Stencil method, but
significantly improves its accuracy using ideas from discretizations of optimal
transport based on power diagrams. We establish the global convergence of a
damped Newton solver for the discrete system of equations. Numerical
experiments, in three dimensions, illustrate the scheme efficiency
Do Footprint-based CAFE Standards Make Car Models Bigger?
Corporate Average Fuel Economy (CAFE) standards have historically been set equal across all manufacturer fleets of the same type. Concerns about varying costs across firms and safety implications of standards that are set homogeneously across firms and models resulted in a policy shift towards footprint-based standards. Under this type of standard, individual car models face targets based on the size of the area between the wheelbase and wheel track, so that larger models face less stringent standards, and manufacturers who make, on average, larger cars will face a lighter fleet standard. Theoretical models have shown that this type of policy creates an incentive for firms to effectively lighten the standard they face, but no purely empirical study has tested this theoretical conclusion. I use a series of difference-in-difference estimations to test whether firms respond to the policy by increasing the footprint of individual models. I find some statistically significant evidence of an increase in footprint size in response to the policy when the treatment effect is assumed to increase by market share
Dark matter variations
In this short presentation, we remind of significant unknowns regarding the
distribution of Dark Matter in our immediate neighborhood, and review the
recent improvements in the obtained limits on its abundance.Comment: 6 pages 1 figure uses \psfrag Corfu Summer Institute Proceeding
Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
We study the return probability and its imaginary () time continuation
after a quench from a domain wall initial state in the XXZ spin chain, focusing
mainly on the region with anisotropy . We establish exact Fredholm
determinant formulas for those, by exploiting a connection to the six vertex
model with domain wall boundary conditions. In imaginary time, we find the
expected scaling for a partition function of a statistical mechanical model of
area proportional to , which reflects the fact that the model exhibits
the limit shape phenomenon. In real time, we observe that in the region
the decay for large times is nowhere continuous as a function
of anisotropy: it is either gaussian at root of unity or exponential otherwise.
As an aside, we also determine that the front moves as , by analytic continuation of known arctic curves in
the six vertex model. Exactly at , we find the return probability
decays as . It is argued that this
result provides an upper bound on spin transport. In particular, it suggests
that transport should be diffusive at the isotropic point for this quench.Comment: 33 pages, 8 figures. v2: typos fixed, references added. v3: minor
change
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