Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session T43: Disordered Hyperuniform Materials: Discovery and Design
11:30 AM–2:30 PM,
Thursday, March 17, 2022
Room: McCormick Place W-375B
Sponsoring Units: DCOMP DSOFT DCMP
Chair: Houlong Zhuang, Arizona State University
Abstract: T43.00001 : Diffusion spreadability as a dynamic-based probe of hyperuniform and nonhyperuniform media across length scales*
11:30 AM–12:06 PM
chemistry, materials science, petroleum engineering and biology. The focus of this investigation
is the ``spreadability", S(t ), which is a measure of the spreadability of diffusion information
as a function of time . Exact formulas for the spreadability in any Euclidean space dimension are derived
in terms of two-point statistics that characterize the microstructure.
These are singular results since they are rare examples of
mass transport problems where exact solutions are possible. Further, closed-form general formulas are derived
for the short- and long-time behaviors of S(t ) in terms of crucial small- and large-scale structural information, respectively. The long-time behavior of S(t ) enables one to distinguish the entire spectrum of translationally invariant microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the “excess” spreadability,
S(∞) − S(t ), decays to its long-time behavior exponentially faster than that of any nonhyperuniform
medium, the slowest being "antihyperuniform media". The stealthy hyperuniform class is described by an
excess spreadability with the fastest decay rate among all translationally invariant structures.
Moreover, we establish a remarkable connection between the spreadability and an outstanding problem in discrete geometry, namely,
microstructures with ``fast" spreadabilities are also those that can be derived from efficient ``coverings" of space.
We also identify heretofore unnoticed remarkable links between the spreadability and
NMR pulsed field gradient spin-echo amplitude as well as diffusion MRI measurements. The
spreadability is a powerful, dynamic-based means to probe the spectrum of
microstructures across length scales.
1. S. Torquato, Phys. Rev. E, 104, 054102 (2021).
*American Chemical SocietyPetroleum Research Fund under Grant No. 61199-ND9
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