1,237 research outputs found
On growth and fluctuation of k-abelian complexity
An extension of abelian complexity, so called k-abelian complexity, has been considered recently in a number of articles. This paper considers two particular aspects of this extension: First, how much the complexity can increase when moving from a level k to the next one. Second, how much the complexity of a given word can fluctuate. For both questions we give optimal solutions. (C) 2017 Elsevier Ltd. All rights reserved
Fast simulation of large-scale growth models
We give an algorithm that computes the final state of certain growth models
without computing all intermediate states. Our technique is based on a "least
action principle" which characterizes the odometer function of the growth
process. Starting from an approximation for the odometer, we successively
correct under- and overestimates and provably arrive at the correct final
state.
Internal diffusion-limited aggregation (IDLA) is one of the models amenable
to our technique. The boundary fluctuations in IDLA were recently proved to be
at most logarithmic in the size of the growth cluster, but the constant in
front of the logarithm is still not known. As an application of our method, we
calculate the size of fluctuations over two orders of magnitude beyond previous
simulations, and use the results to estimate this constant.Comment: 27 pages, 9 figures. To appear in Random Structures & Algorithm
Cellular automata and self-organized criticality
Cellular automata provide a fascinating class of dynamical systems capable of
diverse complex behavior. These include simplified models for many phenomena
seen in nature. Among other things, they provide insight into self-organized
criticality, wherein dissipative systems naturally drive themselves to a
critical state with important phenomena occurring over a wide range of length
and time scales.Comment: 23 pages, 12 figures (most in color); uses sprocl.tex; chapter
submitted for "Some new directions in science on computers," G. Bhanot, S.
Chen, and P. Seiden, ed
Resolving the Structure of Black Holes: Philosophizing with a Hammer
We give a broad conceptual review of what we have learned about black holes
and their microstate structure from the study of microstate geometries and
their string theory limits. We draw upon general relativity, supergravity,
string theory and holographic field theory to extract universal ideas and
structural features that we expect to be important in resolving the information
problem and understanding the microstate structure of Schwarzschild and Kerr
black holes. In particular, we emphasize two conceptually and physically
distinct ideas, with different underlying energy scales: a) the transition that
supports the microstate structure and prevents the formation of a horizon and
b) the representation of the detailed microstate structure itself in terms of
fluctuations around the transitioned state. We also show that the supergravity
mechanism that supports microstate geometries becomes, in the string theory
limit, either brane polarization or the excitation of non-Abelian degrees of
freedom. We thus argue that if any mechanism for supporting structure at the
horizon scale is to be given substance within string theory then it must be
some manifestation of microstate geometries.Comment: 32 pages + reference
The Role of Temperature in a Dimensional Approach to QCD_3
We analyze the role played by temperature in QCD_3 by means of a dimensional
interpolating approach. Pure gauge QCD_3 is defined on a strip of finite width
L, which acts as an interpolating parameter between two and three dimensions. A
two-dimensional effective theory can be constructed for small enough widths
giving the same longitudinal physics as QCD_3. Explicit calculations of
T-dependent QCD_3 observables can thus be performed. The generation of a
deconfinig phase transition, absent in QCD_2, is proven through an exact
calculation of the electric or Debye mass at high T. Low and high T behaviors
of relevant thermodynamic functions are also worked out. An accurate estimate
of the critical temperature is given and its evolution with L is studied in
detail.Comment: 27 pages, 3 postscript figures. Changes in section
- …