633 research outputs found
Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals
We have discovered a new family of three-dimensional crystal sphere packings
that are strictly jammed (i.e., mechanically stable) and yet possess an
anomalously low density. This family constitutes an uncountably infinite number
of crystal packings that are subpackings of the densest crystal packings and
are characterized by a high concentration of self-avoiding "tunnels" (chains of
vacancies) that permeate the structures. The fundamental geometric
characteristics of these tunneled crystals command interest in their own right
and are described here in some detail. These include the lattice vectors (that
specify the packing configurations), coordination structure, Voronoi cells, and
density fluctuations. The tunneled crystals are not only candidate structures
for achieving the jamming threshold (lowest-density rigid packing), but may
have substantially broader significance for condensed matter physics and
materials science.Comment: 19 pages, 5 figure
Does the Supreme Court Follow the Economic Returns? A Response to A Macrotheory of the Court
Today, there is a widespread idea that parents need to learn how to carry out their roles as parents. Practices of parental learning operate throughout society. This article deals with one particular practice of parental learning, namely nanny TV, and the way in which ideal parents are constructed through such programmes. The point of departure is SOS family, a series broadcast on Swedish television in 2008. Proceeding from the theorising of governmentality developed in the wake of the work of Michel Foucault, we analyse the parental ideals conveyed in the series, as an example of the way parents are constituted as subjects in the ‘advanced liberal society’ of today. The ideal parent is a subject who, guided by the coach, is constantly endeavouring to achieve a makeover. The objective of this endeavour, however, is self-control, whereby the parents will in the end become their own coaches.
Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
We have formulated the problem of generating periodic dense paritcle packings
as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation
[S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the
objective function and impenetrability constraints can be exactly linearized
for sphere packings with a size distribution in -dimensional Euclidean space
, it is most suitable and natural to solve the corresponding ASC
optimization problem using sequential linear programming (SLP) techniques. We
implement an SLP solution to produce robustly a wide spectrum of jammed sphere
packings in for and with a diversity of disorder
and densities up to the maximally densities. This deterministic algorithm can
produce a broad range of inherent structures besides the usual disordered ones
with very small computational cost by tuning the radius of the {\it influence
sphere}. In three dimensions, we show that it can produce with high probability
a variety of strictly jammed packings with a packing density anywhere in the
wide range . We also apply the algorithm to generate various
disordered packings as well as the maximally dense packings for
and 6. Compared to the LS procedure, our SLP protocol is able to ensure that
the final packings are truly jammed, produces disordered jammed packings with
anomalously low densities, and is appreciably more robust and computationally
faster at generating maximally dense packings, especially as the space
dimension increases.Comment: 34 pages, 6 figure
Fluid/solid transition in a hard-core system
We prove that a system of particles in the plane, interacting only with a
certain hard-core constraint, undergoes a fluid/solid phase transition
Математична модель маршрутизації в ТКМ
In this paper, drawing on the work of Michel Foucault, I argue that academics are enmeshed in power relations in which confession operates, both on and through academics. Drawing on Foucault’s genealogy of confession, I illustrate how academics are not only invited to reflect on performance, faults, temptations and desires in their work and private life, but as teachers they mobilise the same kind of technology in relation to students. These power relations are connected to wider changes in society, where discourses on New Public Management have become all pervasive in organising and governing public institutions. The examples of the use of appraisal interviews and logbooks as governing techniques illustrate how government currently operates through the freedom of the individual. The paper ends with a discussion on how books of life could introduce a different relation of the self to the self in academia, and thus provide opportunities to live the present otherwise.
A Generalization of the Convex Kakeya Problem
Given a set of line segments in the plane, not necessarily finite, what is a
convex region of smallest area that contains a translate of each input segment?
This question can be seen as a generalization of Kakeya's problem of finding a
convex region of smallest area such that a needle can be rotated through 360
degrees within this region. We show that there is always an optimal region that
is a triangle, and we give an optimal \Theta(n log n)-time algorithm to compute
such a triangle for a given set of n segments. We also show that, if the goal
is to minimize the perimeter of the region instead of its area, then placing
the segments with their midpoint at the origin and taking their convex hull
results in an optimal solution. Finally, we show that for any compact convex
figure G, the smallest enclosing disk of G is a smallest-perimeter region
containing a translate of every rotated copy of G.Comment: 14 pages, 9 figure
The strong thirteen spheres problem
The thirteen spheres problem is asking if 13 equal size nonoverlapping
spheres in three dimensions can touch another sphere of the same size. This
problem was the subject of the famous discussion between Isaac Newton and David
Gregory in 1694. The problem was solved by Schutte and van der Waerden only in
1953.
A natural extension of this problem is the strong thirteen spheres problem
(or the Tammes problem for 13 points) which asks to find an arrangement and the
maximum radius of 13 equal size nonoverlapping spheres touching the unit
sphere. In the paper we give a solution of this long-standing open problem in
geometry. Our computer-assisted proof is based on a enumeration of the
so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag
Images of an equatorial outflow in SS433
We have imaged the X-ray binary SS433 with unprecedented Fourier-plane
coverage at 6cm using simultaneously the VLBA, MERLIN, and the VLA, and also at
20cm with the VLBA. At both wavelengths we have securely detected smooth,
low-surface brightness emission having the appearance of a `ruff' or collar
attached perpendicularly to the well-studied knotty jets in this system,
extending over at least a few hundred AU. We interpret this smooth emission as
a wind-like outflow from the binary, and discuss its implications for the
present evolutionary stage of this system.Comment: Accepted by ApJ Letter
Optimal Packings of Superballs
Dense hard-particle packings are intimately related to the structure of
low-temperature phases of matter and are useful models of heterogeneous
materials and granular media. Most studies of the densest packings in three
dimensions have considered spherical shapes, and it is only more recently that
nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs
(whose shapes are defined by |x1|^2p + |x2|^2p + |x3|^2p <= 1) provide a
versatile family of convex particles (p >= 0.5) with both cubic- and
octahedral-like shapes as well as concave particles (0 < p < 0.5) with
octahedral-like shapes. In this paper, we provide analytical constructions for
the densest known superball packings for all convex and concave cases. The
candidate maximally dense packings are certain families of Bravais lattice
packings. The maximal packing density as a function of p is nonanalytic at the
sphere-point (p = 1) and increases dramatically as p moves away from unity. The
packing characteristics determined by the broken rotational symmetry of
superballs are similar to but richer than their two-dimensional "superdisk"
counterparts, and are distinctly different from that of ellipsoid packings. Our
candidate optimal superball packings provide a starting point to quantify the
equilibrium phase behavior of superball systems, which should deepen our
understanding of the statistical thermodynamics of nonspherical-particle
systems.Comment: 28 pages, 16 figure
On reconfiguration of disks in the plane and related problems
We revisit two natural reconfiguration models for systems of disjoint objects in the plane: translation and sliding. Consider a set of n pairwise interior-disjoint objects in the plane that need to be brought from a given start (initial) configuration S into a desired goal (target) configuration T, without causing collisions. In the translation model, in one move an object is translated along a fixed direction to another position in the plane. In the sliding model, one move is sliding an object to another location in the plane by means of an arbitrarily complex continuous motion (that could involve rotations). We obtain various combinatorial and computational results for these two models: (I) For systems of n congruent disks in the translation model, Abellanas et al. showed that 2n − 1 moves always suffice and ⌊8n/5 ⌋ moves are sometimes necessary for transforming the start configuration into the target configuration. Here we further improve the lower bound to ⌊5n/3 ⌋ − 1, and thereby give a partial answer to one of their open problems. (II) We show that the reconfiguration problem with congruent disks in the translation model is NPhard, in both the labeled and unlabeled variants. This answers another open problem of Abellanas et al. (III) We also show that the reconfiguration problem with congruent disks in the sliding model is NP-hard, in both the labeled and unlabeled variants. (IV) For the reconfiguration with translations of n arbitrary convex bodies in the plane, 2n moves are always sufficient and sometimes necessary
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