76,666 research outputs found
Retail Bottle Pricing at the Border: Evidence of Cross-Border Shopping, Fraudulent Redemptions, and Use Tax Evasion
This paper examines the pattern of retail prices for deposit eligible goods near Michigan’s borders. Michigan’s unique bottle redemption system and lower sales tax generate incentives for various potentially illegal household responses. Such incentives and behavior should be capitalized in the prices of affected goods. I empirically quantify the spatial price effects and find patterns consistent with theoretical predictions. Michigan’s border prices are higher (lower) for goods with higher (lower) per unit costs by up to 38%. Price-distance trends reflect the waning of these effects away from the border
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
We formulate hydrodynamic equations and spectrally accurate numerical methods
for investigating the role of geometry in flows within two-dimensional fluid
interfaces. To achieve numerical approximations having high precision and level
of symmetry for radial manifold shapes, we develop spectral Galerkin methods
based on hyperinterpolation with Lebedev quadratures for -projection to
spherical harmonics. We demonstrate our methods by investigating hydrodynamic
responses as the surface geometry is varied. Relative to the case of a sphere,
we find significant changes can occur in the observed hydrodynamic flow
responses as exhibited by quantitative and topological transitions in the
structure of the flow. We present numerical results based on the
Rayleigh-Dissipation principle to gain further insights into these flow
responses. We investigate the roles played by the geometry especially
concerning the positive and negative Gaussian curvature of the interface. We
provide general approaches for taking geometric effects into account for
investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure
Spectral Numerical Exterior Calculus Methods for Differential Equations on Radial Manifolds
We develop exterior calculus approaches for partial differential equations on
radial manifolds. We introduce numerical methods that approximate with spectral
accuracy the exterior derivative , Hodge star , and their
compositions. To achieve discretizations with high precision and symmetry, we
develop hyperinterpolation methods based on spherical harmonics and Lebedev
quadrature. We perform convergence studies of our numerical exterior derivative
operator and Hodge star operator
showing each converge spectrally to and . We show how the
numerical operators can be naturally composed to formulate general numerical
approximations for solving differential equations on manifolds. We present
results for the Laplace-Beltrami equations demonstrating our approach.Comment: 22 pages, 13 figure
Stationary states and energy cascades in inelastic gases
We find a general class of nontrivial stationary states in inelastic gases
where, due to dissipation, energy is transfered from large velocity scales to
small velocity scales. These steady-states exist for arbitrary collision rules
and arbitrary dimension. Their signature is a stationary velocity distribution
f(v) with an algebraic high-energy tail, f(v) ~ v^{-sigma}. The exponent sigma
is obtained analytically and it varies continuously with the spatial dimension,
the homogeneity index characterizing the collision rate, and the restitution
coefficient. We observe these stationary states in numerical simulations in
which energy is injected into the system by infrequently boosting particles to
high velocities. We propose that these states may be realized experimentally in
driven granular systems.Comment: 4 pages, 4 figure
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