898 research outputs found
Quasiuniversal connectedness percolation of polydisperse rod systems
The connectedness percolation threshold (eta_c) and critical coordination
number (Z_c) of systems of penetrable spherocylinders characterized by a length
polydispersity are studied by way of Monte Carlo simulations for several aspect
ratio distributions. We find that (i) \eta_c is a nearly universal function of
the weight-averaged aspect ratio, with an approximate inverse dependence that
extends to aspect ratios that are well below the slender rod limit and (ii)
that percolation of impenetrable spherocylinders displays a similar
quasiuniversal behavior. For systems with a sufficiently high degree of
polydispersity, we find that Z_c can become smaller than unity, in analogy with
observations reported for generalized and complex networks.Comment: 5 pages with 3 figures + 2 pages and 4 figures of supplemental
materia
Approximation of length minimization problems among compact connected sets
In this paper we provide an approximation \`a la Ambrosio-Tortorelli of some
classical minimization problems involving the length of an unknown
one-dimensional set, with an additional connectedness constraint, in dimension
two. We introduce a term of new type relying on a weighted geodesic distance
that forces the minimizers to be connected at the limit. We apply this approach
to approximate the so-called Steiner Problem, but also the average distance
problem, and finally a problem relying on the p-compliance energy. The proof of
convergence of the approximating functional, which is stated in terms of
Gamma-convergence relies on technical tools from geometric measure theory, as
for instance a uniform lower bound for a sort of average directional Minkowski
content of a family of compact connected sets
Inherently Global Nature of Topological Charge Fluctuations in QCD
We have recently presented evidence that in configurations dominating the
regularized pure-glue QCD path integral, the topological charge density
constructed from overlap Dirac operator organizes into an ordered space-time
structure. It was pointed out that, among other properties, this structure
exhibits two important features: it is low-dimensional and geometrically
global, i.e. consisting of connected sign-coherent regions with local
dimensions 1<= d < 4, and spreading over arbitrarily large space--time
distances. Here we show that the space-time structure that is responsible for
the origin of topological susceptibility indeed exhibits global behavior. In
particular, we show numerically that topological fluctuations are not saturated
by localized concentrations of most intense topological charge density. To the
contrary, the susceptibility saturates only after the space-time regions with
most intense fields are included, such that geometrically global structure is
already formed. We demonstrate this result both at the fundamental level (full
topological density) and at low energy (effective density). The drastic
mismatch between the point of fluctuation saturation (~ 50% of space-time at
low energy) and that of global structure formation (<4% of space-time at low
energy) indicates that the ordered space-time structure in topological charge
is inherently global and that topological charge fluctuations in QCD cannot be
understood in terms of individual localized pieces. Description in terms of
global brane-like objects should be sought instead.Comment: 10 pages, 3 figures; v2: typos corrected, minor modifications; v3:
misprint in Eqs. (2,3) fixe
Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties
The shape of irregular particles has significant influence on micro- and
macro-scopic behavior of granular systems. This paper presents a combined 3D
thinning and greedy set-covering algorithm to approximate realistic particles
with a clump of overlapping spheres for discrete element method (DEM)
simulations. First, the particle medial surface (or surface skeleton), from
which all candidate (maximal inscribed) spheres can be generated, is computed
by the topological 3D thinning. Then, the clump generation procedure is
converted into a greedy set-covering (SCP) problem.
To correct the mass distribution due to highly overlapped spheres inside the
clump, linear programming (LP) is used to adjust the density of each component
sphere, such that the aggregate properties mass, center of mass and inertia
tensor are identical or close enough to the prototypical particle. In order to
find the optimal approximation accuracy (volume coverage: ratio of clump's
volume to the original particle's volume), particle flow of 3 different shapes
in a rotating drum are conducted. It was observed that the dynamic angle of
repose starts to converge for all particle shapes at 85% volume coverage
(spheres per clump < 30), which implies the possible optimal resolution to
capture the mechanical behavior of the system.Comment: 34 pages, 13 figure
Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming
We propose a novel formal framework (called 3D-nCDC-ASP) to represent and
reason about cardinal directions between extended objects in 3-dimensional (3D)
space, using Answer Set Programming (ASP). 3D-nCDC-ASP extends Cardinal
Directional Calculus (CDC) with a new type of default constraints, and nCDC-ASP
to 3D. 3D-nCDC-ASP provides a flexible platform offering different types of
reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set
of constraints on 3D cardinal directions between objects, explaining
inconsistencies, and inferring missing CDC relations. We prove the soundness of
3D-nCDC-ASP, and illustrate its usefulness with applications. This paper is
under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic
Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September
2020, 29 pages, 6 figure
Just Renormalizable TGFT's on U(1)^d with Gauge Invariance
We study the polynomial Abelian or U(1)^d Tensorial Group Field Theories
equipped with a gauge invariance condition in any dimension d. From our
analysis, we prove the just renormalizability at all orders of perturbation of
the phi^4_6 and phi^6_5 random tensor models. We also deduce that the phi^4_5
tensor model is super-renormalizable.Comment: 33 pages, 22 figures. One added paragraph on the different notions of
connectedness, preciser formulation of the proof of the power counting
theorem, more general statements about traciality of tensor graph
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