135 research outputs found
Superdiffusion in a class of networks with marginal long-range connections
A class of cubic networks composed of a regular one-dimensional lattice and a
set of long-range links is introduced. Networks parametrized by a positive
integer k are constructed by starting from a one-dimensional lattice and
iteratively connecting each site of degree 2 with a th neighboring site of
degree 2. Specifying the way pairs of sites to be connected are selected,
various random and regular networks are defined, all of which have a power-law
edge-length distribution of the form with the marginal
exponent s=1. In all these networks, lengths of shortest paths grow as a power
of the distance and random walk is super-diffusive. Applying a renormalization
group method, the corresponding shortest-path dimensions and random-walk
dimensions are calculated exactly for k=1 networks and for k=2 regular
networks; in other cases, they are estimated by numerical methods. Although,
s=1 holds for all representatives of this class, the above quantities are found
to depend on the details of the structure of networks controlled by k and other
parameters.Comment: 10 pages, 9 figure
The packing of granular polymer chains
Rigid particles pack into structures, such as sand dunes on the beach, whose
overall stability is determined by the average number of contacts between
particles. However, when packing spatially extended objects with flexible
shapes, additional concepts must be invoked to understand the stability of the
resulting structure. Here we study the disordered packing of chains constructed
out of flexibly-connected hard spheres. Using X-ray tomography, we find long
chains pack into a low-density structure whose mechanical rigidity is mainly
provided by the backbone. On compaction, randomly-oriented, semi-rigid loops
form along the chain, and the packing of chains can be understood as the
jamming of these elements. Finally we uncover close similarities between the
packing of chains and the glass transition in polymers.Comment: 11 pages, 4 figure
Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations
Causal Dynamical Triangulations is a non-perturbative quantum gravity model,
defined with a lattice cut-off. The model can be viewed as defined with a
proper time but with no reference to any three-dimensional spatial background
geometry. It has four phases, depending on the parameters (the coupling
constants) of the model. The particularly interesting behavior is observed in
the so-called de Sitter phase, where the spatial three-volume distribution as a
function of proper time has a semi-classical behavior which can be obtained
from an effective mini-superspace action. In the case of the three-sphere
spatial topology, it has been difficult to extend the effective semi-classical
description in terms of proper time and spatial three-volume to include genuine
spatial coordinates, partially because of the background independence inherent
in the model. However, if the spatial topology is that of a three-torus, it is
possible to define a number of new observables that might serve as spatial
coordinates as well as new observables related to the winding numbers of the
three-dimensional torus. The present paper outlines how to define the
observables, and how they can be used in numerical simulations of the model.Comment: 26 pages, 15 figure
Locally Causal Dynamical Triangulations in Two Dimensions
We analyze the universal properties of a new two-dimensional quantum gravity
model defined in terms of Locally Causal Dynamical Triangulations (LCDT).
Measuring the Hausdorff and spectral dimensions of the dynamical geometrical
ensemble, we find numerical evidence that the continuum limit of the model lies
in a new universality class of two-dimensional quantum gravity theories,
inequivalent to both Euclidean and Causal Dynamical Triangulations
Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
This is the final fifth paper in our series of five in which we test the
Master Constraint Programme for solving the Hamiltonian constraint in Loop
Quantum Gravity. Here we consider interacting quantum field theories,
specificlly we consider the non -- Abelean Gauss constraints of Einstein --
Yang -- Mills theory and 2+1 gravity. Interestingly, while Yang -- Mills theory
in 4D is not yet rigorously defined as an ordinary (Wightman) quantum field
theory on Minkowski space, in background independent quantum field theories
such as Loop Quantum Gravity (LQG) this might become possible by working in a
new, background independent representation.Comment: 20 pages, no figure
Search for Scaling Dimensions for Random Surfaces with c=1
We study numerically the fractal structure of the intrinsic geometry of
random surfaces coupled to matter fields with . Using baby universe
surgery it was possible to simulate randomly triangulated surfaces made of
260.000 triangles. Our results are consistent with the theoretical prediction
for the intrinsic Hausdorff dimension.Comment: 10 pages, (csh will uudecode and uncompress ps-file), NBI-HE-94-3
Wilson loops in CDT quantum gravity
By explicit construction, we show that one can in a simple way introduce and
measure gravitational holonomies and Wilson loops in lattice formulations of
nonperturbative quantum gravity based on (Causal) Dynamical Triangulations. We
use this set-up to investigate a class of Wilson line observables associated
with the world line of a point particle coupled to quantum gravity, and deduce
from their expectation values that the underlying holonomies cover the group
manifold of SO(4) uniforml
Energetics of the Quantum Graphity Universe
Quantum graphity is a background independent model for emergent geometry, in
which space is represented as a complete graph. The high-energy pre-geometric
starting point of the model is usually considered to be the complete graph,
however we also consider the empty graph as a candidate pre-geometric state.
The energetics as the graph evolves from either of these high-energy states to
a low-energy geometric state is investigated as a function of the number of
edges in the graph. Analytic results for the slope of this energy curve in the
high-energy domain are derived, and the energy curve is plotted exactly for
small number of vertices . To study the whole energy curve for larger (but
still finite) , an epitaxial approximation is used. It is hoped that this
work may open the way for future work to compare predictions from quantum
graphity with observations of the early universe, making the model falsifiable.Comment: 8 pages, 3 figure
On the forces that cable webs under tension can support and how to design cable webs to channel stresses
In many applications of Structural Engineering the following question arises:
given a set of forces applied at
prescribed points , under what
constraints on the forces does there exist a truss structure (or wire web) with
all elements under tension that supports these forces? Here we provide answer
to such a question for any configuration of the terminal points
in the two- and
three-dimensional case. Specifically, the existence of a web is guaranteed by a
necessary and sufficient condition on the loading which corresponds to a finite
dimensional linear programming problem. In two-dimensions we show that any such
web can be replaced by one in which there are at most elementary loops,
where elementary means the loop cannot be subdivided into subloops, and where
is the number of forces
applied at points strictly within the convex hull of
. In three-dimensions we show
that, by slightly perturbing ,
there exists a uniloadable web supporting this loading. Uniloadable means it
supports this loading and all positive multiples of it, but not any other
loading. Uniloadable webs provide a mechanism for distributing stress in
desired ways.Comment: 18 pages, 8 figure
The geometry of the double gyroid wire network: quantum and classical
Quantum wire networks have recently become of great interest. Here we deal
with a novel nano material structure of a Double Gyroid wire network. We use
methods of commutative and non-commutative geometry to describe this wire
network. Its non--commutative geometry is closely related to non-commutative
3-tori as we discuss in detail.Comment: pdflatex 9 Figures. Minor changes, some typos and formulation
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