More Like this

1. Scaling Exponents of Turbulent Static Pressure Structure Function in the Inertial Subrange

   https://doi.org/10.1029/2025GL116176  

   Katul, Gabriel G; Aslan, Toprak; Aurela, Mika (June 2025, Geophysical Research Letters)

   Abstract The measured variations in the turbulent static pressure structure function with scale in the roughness sublayer above a subarctic forest are empirically shown to exhibit exponents that are smaller than predicted for the inertial subrange (ISR). Three hypotheses are offered to explain these deviations. The first is based on conventional intermittency correction to the averaged turbulent kinetic energy dissipation rate, the second is based on shearing introducing deviations from locally isotropic state that must be sensed by both velocity and pressure structure functions, and the third is based on large and inertial scale pressure interactions that persist at values of within the resolvable ISR. The third hypothesis is shown to yield superior results, which allows a new formulation for to be derived that accommodates such finite interactions. 

   more » « less
2. Mobility of Condensed Counterions in Ion-Exchange Membranes: Application of Screening Length Scaling Relationship in Highly Charged Environments

   https://doi.org/10.1021/acs.est.3c06068  

   Huang, Yuxuan; Fan, Hanqing; Yip, Ngai Yin (January 2024, Environmental Science & Technology)

   Ion-exchange membranes (IEMs) are widely used in water, energy, and environmental applications, but transport models to accurately simulate ion permeation are currently lacking. This study presents a theoretical framework to predict ionic conductivity of IEMs by introducing an analytical model for condensed counterion mobility to the Donnan-Manning model. Modeling of condensed counterion mobility is enabled by the novel utilization of a scaling relationship to describe screening lengths in the densely charged IEM matrices, which overcame the obstacle of traditional electrolyte chemistry theories breaking down at very high ionic strength environments. Ionic conductivities of commercial IEMs were experimentally characterized in different electrolyte solutions containing a range of mono-, di-, and trivalent counterions. Because the current Donnan-Manning model neglects the mobility of condensed counterions, it is inadequate for modeling ion transport and significantly underestimated membrane conductivities (by up to ≈5× difference between observed and modeled values). Using the new model to account for condensed counterion mobilities substantially improved the accuracy of predicting IEM conductivities in monovalent counterions (to as small as within 7% of experimental values), without any adjustable parameters. Further adjusting the power law exponent of the screen length scaling relationship yielded reasonable precision for membrane conductivities in multivalent counterions. Analysis reveals that counterions are significantly more mobile in the condensed phase than in the uncondensed phase because electrostatic interactions accelerate condensed counterions but retard uncondensed counterions. Condensed counterions still have lower mobilities than ions in bulk solutions due to impedance from spatial effects. The transport framework presented here can model ion migration a priori with adequate accuracy. The findings provide insights into the underlying phenomena governing ion transport in IEMs to facilitate the rational development of more selective membranes. 

   more » « less
3. Heavy traffic queue length scaling in switches with reconfiguration delay

   https://doi.org/10.1007/s11134-021-09695-x  

   Wang, Chang-Heng; Maguluri, Siva Theja; Javidi, Tara (June 2021, Queueing Systems)
4. A scaling limit for the length of the longest cycle in a sparse random graph

   https://doi.org/10.1016/j.jctb.2021.01.001  

   Anastos, M.; Frieze, A. (January 2021, Journal of combinatorial theory)

   We discuss the length {\red $$L_{c,n}$$} of the longest cycle in a sparse random graph {\red $$G_{n,p},$$ $p=c/n$,} $$c$$ constant. We show that for large $$c$$ there exists a function $f(c)$ such that $$L_{c,n}/n\to f(c)$$ a.s. The function $$f(c)=1-\sum_{k=1}^\infty p_k(c)e^{-kc}$$ where $$p_k{\red (c)}$$ is a polynomial in $$c$$. We are only able to explicitly give the values $$p_1,p_2$$, although we could in principle compute any $$p_k$$. We see immediately that the length of the longest path is also asymptotic to $f(c)n$ w.h.p. 

   more » « less
5. A scaling limit for the length of the longest cycle in a sparse random digraph

   https://doi.org/10.1002/rsa.21030  

   Anastos, A.; Frieze, A. (January 2022, Random structures algorithms)

   We discuss the length $$\vL_{c,n}$$ of the longest directed cycle in the sparse random digraph $$D_{n,p},p=c/n$$, $$c$$ constant. We show that for large $$c$$ there exists a function $$\vf(c)$$ such that $$\vL_{c,n}/n\to \vf(c)$$ a.s. The function $$\vf(c)=1-\sum_{k=1}^\infty p_k(c)e^{-kc}$$ where $$p_k$$ is a polynomial in $$c$$. We are only able to explicitly give the values $$p_1,p_2$$, although we could in principle compute any $$p_k$$. 

   more » « less