## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS

Cellular networks are ubiquitous in nature. They exhibit behavior on many different length and time scales and are generally metastable. Most technologically useful materials are
polycrystalline microstructures composed of a myriad of small
monocrystalline grains separated by grain boundaries. The
energetics and connectivity of the grain boundary network plays a
crucial role in determining the properties of a material across a wide
range of scales. A central problem in materials science is to
develop technologies capable of producing an arrangement of
grains—a texture—appropriate for a desired set of material
properties. Here we discuss the role of energy in texture development, measured by a character distribution. We derive an entropy based theory based on mass transport and a Kantorovich-Rubinstein-Wasserstein metric to suggest that, to first approximation, this distribution behaves like the solution to a Fokker-Planck Equation.

DCDS

Recently, several numerical invariants have been introduced to characterize
the distortion induced by automorphisms of a free group.
We unify these by interpreting them in terms of an entropy function
of a kind familiar in thermodynamic ergodic theory. We draw an analogy
between this approach and the Manhattan curve associated to a
pair of hyperbolic surfaces.

keywords:
entropy.
,
subshifts of finite typ
,
automorphisms
,
distortion spectrum
,
thermodynamic
formalism
,
Free groups

DCDS

For conformal graph directed Markov systems, we construct a spectral triple
from which one can recover the associated conformal measure via
a Dixmier trace. As a particular case, we can recover the Patterson-Sullivan
measure for a class of Kleinian groups.

## Year of publication

## Related Authors

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