5,848 research outputs found
Geometric realizations of Tamari interval lattices via cubic coordinates
We introduce cubic coordinates, which are integer words encoding intervals in
the Tamari lattices. Cubic coordinates are in bijection with interval-posets,
themselves known to be in bijection with Tamari intervals. We show that in each
degree the set of cubic coordinates forms a lattice, isomorphic to the lattice
of Tamari intervals. Geometric realizations are naturally obtained by placing
cubic coordinates in space, highlighting some of their properties. We consider
the cellular structure of these realizations. Finally, we show that the poset
of cubic coordinates is shellable
The Environmental Implications of Redistributive Land Reform
Acknowledgements Thank you to the two anonymous referees who commented on this piece. Conflict of interest The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) received no financial support for the research, authorship, and/or publication of this article.Peer reviewedPostprin
The Indycamp : Demonstrating Access to Land and Access to Justice
Peer reviewedPostprin
Acoustic modes in metallic nanoparticles: atomistic versus elasticity modeling
The validity of the linear elasticity theory is examined at the nanometer
scale by investigating the vibrational properties of silver and gold
nanoparticles whose diameters range from about 1.5 to 4 nm. Comparing the
vibration modes calculated by elasticity theory and atomistic simulation based
on the Embedded Atom Method, we first show that the anisotropy of the stiffness
tensor in elastic calculation is essential to ensure a good agreement between
elastic and atomistic models. Second, we illustrate the reduction of the number
of vibration modes due to the diminution of the number of atoms when reducing
the nanoparticles size. Finally, we exhibit a breakdown of the
frequency-spectra scaling of the vibration modes and attribute it to surface
effects. Some critical sizes under which such effects are expected, depending
on the material and the considered vibration modes are given.Comment: Accepted to Phys. Rev.
Abandonment of land and the Scottish Coal case : was it Unprecedented?
The support of the Carnegie Trust for the Universities of Scotland in the provision of a research incentive grant that contributed to this note is gratefully acknowledged.Peer reviewedPostprin
How granular materials deform in quasistatic conditions
Based on numerical simulations of quasistatic deformation of model granular
materials, two rheological regimes are distinguished, according to whether
macroscopic strains merely reflect microscopic material strains within the
grains in their contact regions (type I strains), or result from instabilities
and contact network rearrangements at the microscopic level (type II strains).
We discuss the occurrence of regimes I and II in simulations of model materials
made of disks (2D) or spheres (3D). The transition from regime I to regime II
in monotonic tests such as triaxial compression is different from both the
elastic limit and from the yield threshold. The distinction between both types
of response is shown to be crucial for the sensitivity to contact-level
mechanics, the relevant variables and scales to be considered in
micromechanical approaches, the energy balance and the possible occurrence of
macroscopic instabilitie
- …