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UID:4d77552e33cb239c7bcfd3089288c9d9
CATEGORIES:Mathematical Physics Seminar
CREATED:20220822T121202
SUMMARY:Order Metrics and Diffusion Spreadability to Characterize Two-Phase Microstructures Across Length Scales
LOCATION:Zoom
DESCRIPTION:<p>The capacity to devise order metrics to characterize and classify micros
 tructures of multiphase heterogeneous media across length scales is an outs
 tanding but highly challenging task, given the richness of the possible geo
 metries and topologies of the phases that can arise. I describe an initial 
 investigation to formulate order metrics to characterize the degree of orde
 r/disorder of hyperuniform and nonhyperuniform microstructures of two-phase
  media in d-dimensional Euclidean space across length scales via the local 
 volume-fraction variance [1].<br /> In the second part of my talk, I consid
 er the so-called spreadability, S(t), which is a measure of the spreadabili
 ty of diffusion information in two-phase media as a function of time t when
  a solute is contained in one of the&nbsp;phases at t=0 [2]. I derive close
 d-form general formulas for the short- and long-time behaviors of the sprea
 dability in terms of crucial small- and large-scale microstructural informa
 tion, respectively. The long-time behavior of S(t ) enables one to distingu
 ish the entire spectrum of microstructures that span from hyperuniform to n
 onhyperuniform media. For hyperuniform media, disordered or not, I show tha
 t the “excess” spreadability, S(?) ? S(t ), decays to its long-time behavio
 r exponentially faster than that of any nonhyperuniform two-phase medium, t
 he “slowest” being antihyperuniform media. The time-dependent spreadability
  is a powerful, dynamic-based figure of merit to probe and classify the spe
 ctrum of possible microstructures of two-phase media across length scales. 
 I also establish a connection between the spreadability and an outstanding 
 problem in discrete geometry, namely, microstructures with “fast” spreadabi
 lities are also those that can be derived from efficient “coverings” of spa
 ce. <br />1. S. Torquato, M. Skolnick, and J. Kim, ``Local order metrics fo
 r two-phase media across length scales,"<br />J. Phys. A: Math. &amp; Theor
 et., 55 274003 (2022).<br />2. S. Torquato, ``Diffusion spreadability as a 
 probe of the microstructure of complex media across length scales,"<br />Ph
 ys. Rev. E, 104 054102 (2021).</p>
CONTACT:Salvatore Torquato - Princeton University
DTSTAMP:20260827T173012
DTSTART;TZID=America/New_York:20220914T104500
DTEND;TZID=America/New_York:20220914T114500
SEQUENCE:0
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