Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Mixing in Transport Networks: Numerical Optimization and
  Analysis   Many foraging microorganisms rely upon cellular transport networks to deliver
nutrients, fluid and organelles between different parts of the organism.
Networked organisms ranging from filamentous fungi to slime molds demonstrate a
remarkable ability to mix or disperse molecules and organelles in their
transport media. Here we introduce mathematical tools to analyze the structure
of energy efficient transport networks that maximize mixing and sending signals
originating from and arriving at each node. We define two types of entropies on
flows to quantify mixing and develop numerical algorithms to optimize the
combination of entropy and energy on networks, given constraints on the amount
of available material. We present an in-depth exploration of optimal single
source-sink networks on finite triangular grids, a fundamental setting for
optimal transport networks in the plane. Using numerical simulations and
rigorous proofs, we show that, if the constraint on conductances is strict, the
optimal networks are paths of every possible length. If the constraint is
relaxed, our algorithm produces loopy networks that fan out at the source and
pour back into a single path that flows to the sink. Taken together, our
results expand the class of optimal transportation networks that can be
compared with real biological data, and highlight how real network morphologies
may be shaped by tradeoffs between transport efficiency and the need to mix the
transported matter.

37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org