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1. Functionalized electrospun polymer nanofibers for treatment of water contaminated with uranium

   https://doi.org/10.1039/C9EW00834A  

   Johns, Adam; Qian, Jiajie; Carolan, Margaret E.; Shaikh, Nabil; Peroutka, Allison; Seeger, Anna; Cerrato, José M.; Forbes, Tori Z.; Cwiertny, David M. (March 2020, Environmental Science: Water Research & Technology)

   Uranium (U) contamination of drinking water often affects communities with limited resources, presenting unique technology challenges for U 6+ treatment. Here, we develop a suite of chemically functionalized polymer (polyacrylonitrile; PAN) nanofibers for low pressure reactive filtration applications for U 6+ removal. Binding agents with either nitrogen-containing or phosphorous-based ( e.g. , phosphonic acid) functionalities were blended (at 1–3 wt%) into PAN sol gels used for electrospinning, yielding functionalized nanofiber mats. For comparison, we also functionalized PAN nanofibers with amidoxime (AO) moieties, a group well-recognized for its specificity in U 6+ uptake. For optimal N-based (Aliquat® 336 or Aq) and P-containing [hexadecylphosphonic acid (HPDA) and bis(2-ethylhexyl)phosphate (HDEHP)] binding agents, we then explored their use for U 6+ removal across a range of pH values (pH 2–7), U 6+ concentrations (up to 10 μM), and in flow through systems simulating point of use (POU) water treatment. As expected from the use of quaternary ammonium groups in ion exchange, Aq-containing materials appear to sequester U 6+ by electrostatic interactions; while uptake by these materials is limited, it is greatest at circumneutral pH where positively charged N groups bind negatively charged U 6+ complexes. In contrast, HDPA and HDEHP perform best at acidic pH representative of mine drainage, where surface complexation of the uranyl cation likely drives uptake. Complexation by AO exhibited the best performance across all pH values, although U 6+ uptake via surface precipitation may also occur near circumneutral pH values and at high (10 μM) dissolved U 6+ concentrations. In simulated POU treatment studies using a dead-end filtration system, we observed U removal in AO-PAN systems that is insensitive to common co-solutes in groundwater ( e.g. , hardness and alkalinity). While more research is needed, our results suggest that only 80 g (about 0.2 lbs.) of AO-PAN filter material would be needed to treat an individual's water supply (contaminated at ten-times the U.S. EPA maximum contaminant level for U) for one year. 

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2. Accumulation on and extraction of lead from point-of-use filters for evaluating lead exposure from drinking water

   https://doi.org/10.1039/d0ew00496k  

   Pan, Weiyi; Johnson, Elizabeth R.; Giammar, Daniel E. (October 2020, Environmental Science: Water Research & Technology)

   null (Ed.)

   The precise quantification of Pb exposure from tap water can help water utilities and public health organizations assess and mitigate elevated Pb concentrations. Several sampling protocols have been developed for this purpose; however, each existing protocol has limitations associated with sampling time, sample sizes, and ease of application. This study confirmed the ability of point-of-use faucet filters to accumulate Pb and then developed an extraction method that can enable quantification of Pb exposure from tap water. Nearly all Pb from both real and synthetic tap water was accumulated on POU filters, and four different methods for extracting the accumulated Pb were evaluated. Approximately 100% Pb recovery was achieved with a single pass flow-through method using a nitric acid solution. This Pb exposure quantification method could potentially be applied to real drinking water systems to provide an effective indication of Pb exposure from tap water. 

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3. Exceptional Point of Degeneracy as a Desirable Point of Operation for Oscillator With Discrete Nonlinear Gain and Radiating Elements

   https://doi.org/10.23919/USNC-URSINRSM57467.2022.9881400  

   Mealy, Tarek; Nikzamir, Alireza; Abdelshafy, Ahmed F.; Capolino, Filippo (January 2022, 2022 United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM))

   An oscillator made of a periodic waveguide comprising of uniform lossless segments with discrete nonlinear gain and radiating resistive elements prefers to operate at exceptional point of degeneracy (EPD). The steady-state regime is an EPD with π phase shift between unit cells, for various choices of small signal gain of the nonlinear elements and number of unit cells. We demonstrated this fact by monitoring both current and voltage across each nonlinear gain element and finding its effective admittance at the oscillating frequency and checking the degeneracy of the eigenmodes at such point. The EPD studied here is very promising for many applications that incorporate discrete distributed coherent sources and radiation-loss elements. Operating in the vicinity of such special degeneracy conditions may lead to potential performance enhancement in the various microwave, THz and optical systems with distributed gain and radiation, paving the way for a new class of active integrated antenna arrays and radiating laser arrays. 

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4. Acceleration methods for fixed-point iterations

   https://doi.org/10.1017/S0962492924000096  

   Saad, Yousef (July 2025, Acta Numerica)

   A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative procedures, and this led practitioners to seek faster alternatives to reach the limit. ‘Acceleration techniques’ comprise a broad array of methods specifically designed with this goal in mind. They started as a means of improving the convergence of general scalar sequences by various forms of ‘extrapolation to the limit’, i.e. by extrapolating the most recent iterates to the limit via linear combinations. Extrapolation methods of this type, the best-known of which is Aitken’s delta-squared process, require only the sequence of vectors as input. However, limiting methods to use only the iterates is too restrictive. Accelerating sequences generated by fixed-point iterations by utilizing both the iterates and the fixed-point mapping itself has proved highly successful across various areas of physics. A notable example of these fixed-point accelerators (FP-accelerators) is a method developed by Donald Anderson in 1965 and now widely known as Anderson acceleration (AA). Furthermore, quasi-Newton and inexact Newton methods can also be placed in this category since they can be invoked to find limits of fixed-point iteration sequences by employing exactly the same ingredients as those of the FP-accelerators. This paper presents an overview of these methods – with an emphasis on those, such as AA, that are geared toward accelerating fixed-point iterations. We will navigate through existing variants of accelerators, their implementations and their applications, to unravel the close connections between them. These connections were often not recognized by the originators of certain methods, who sometimes stumbled on slight variations of already established ideas. Furthermore, even though new accelerators were invented in different corners of science, the underlying principles behind them are strikingly similar or identical. The plan of this article will approximately follow the historical trajectory of extrapolation and acceleration methods, beginning with a brief description of extrapolation ideas, followed by the special case of linear systems, the application to self-consistent field (SCF) iterations, and a detailed view of Anderson acceleration. The last part of the paper is concerned with more recent developments, including theoretical aspects, and a few thoughts on accelerating machine learning algorithms. 

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5. A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

   https://doi.org/10.1007/s42967-021-00179-6  

   Li, Liang; Zhu, Jun; Shu, Chi-Wang; Zhang, Yong-Tao (March 2022, Communications on Applied Mathematics and Computation)

   Abstract Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations (PDEs). The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions. A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems. Hence, they are easy to be applied to a general hyperbolic system. To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains, inverse Lax-Wendroff (ILW) procedures were developed as a very effective approach in the literature. In this paper, we combine a fifth-order fixed-point fast sweeping WENO method with an ILW procedure to solve steady-state solution of hyperbolic conservation laws on complex computing regions. Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids. Numerical results show high-order accuracy and good performance of the method. Furthermore, the method is compared with the popular third-order total variation diminishing Runge-Kutta (TVD-RK3) time-marching method for steady-state computations. Numerical examples show that for most of examples, the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions. 

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