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This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying mathematical model is governed by the three-dimensional Helmholtz equation, and the available data consist solely of the magnitude of the scattered wave field. To address the nonlinearity and servere ill-posedness of this phaseless inverse scattering problem, we introduce a robust, globally convergent numerical framework combining several key regularization strategies. Our method first employs a phase retrieval step based on the Wentzel--Kramers--Brillouin (WKB) ansatz, where the lost phase information is reconstructed by solving a nonlinear optimization problem. Subsequently, we implement a Fourier-based dimension reduction technique, transforming the original problem into a more stable system of elliptic equations with Cauchy boundary conditions. To solve this resulting system reliably, we apply the Carleman convexification approach, constructing a strictly convex weighted cost functional whose global minimizer provides an accurate approximation of the true solution. Numerical simulations using synthetic data with high noise levels demonstrate the effectiveness and robustness of the proposed method, confirming its capability to accurately recover both the geometric location and contrast of hidden scatterers. 

X-ray spectroscopy has long been a powerful diagnostic tool for hot, dilute plasmas, providing insights into plasma conditions by measuring line shifts and broadenings of atomic transitions. The technique critically depends on the accuracy of atomic physics models used to interpret spectroscopic measurements for inferring plasma properties such as free-electron density and temperature. Over the past decades, the atomic and plasma physics communities have developed robust atomic physics models to account for various processes in hot, dilute classical plasmas. While these models have been successful in that regime, their applicability becomes uncertain when interpreting x-ray spectroscopy experiments of above-solid-density plasmas. Given that finite-temperature density-functional theory (DFT) offers a more accurate description of dense plasma environments, we present the development of a DFT-based multi-band kinetic model, VERITAS, designed to improve the interpretation of x-ray spectroscopic measurements in high-density plasmas produced by laser-driven spherical implosions. This work details the VERITAS model and its application to both time-integrated and time-resolved x-ray spectra from implosion experiments on OMEGA. The advantages and limitations of the VERITAS model will also be discussed, along with potential directions for advancing x-ray spectroscopy of dense and superdense plasmas. 

Abstract The current change in battery technology followed by the almost immediate adoption of lithium as a key resource powering our energy needs in various applications is undeniable. Lithium-ion batteries (LIBs) are at the forefront of the industry and offer excellent performance. The application of LIBs is expected to continue to increase. The adoption of renewable energies has spurred this LIB proliferation and resulted in a dramatic increase in LIB waste. In this review, we address waste LIB collection and segregation approaches, waste LIB treatment approaches, and related economics. We have coined a “green score” concept based on a review of several quantitative analyses from the literature to compare the three mainstream recycling processes: pyrometallurgical, hydrometallurgical, and direct recycling. In addition, we analyze the current trends in policymaking and in government incentive development directed toward promoting LIB waste recycling. Future LIB recycling perspectives are analyzed, and opportunities and threats to LIB recycling are presented. 

Experimental efforts supplemented by modeling gauged whether common additives found in soaps and laundry detergents interfered with polyacrylate adhesive-based capture of microplastics. On the experimental front, poly(2-ethylhexyl acrylate) (PEHA) samples were evaluated using gravimetric analysis, probe tack, and functional assessments of adhesive-coated glass slides immersed into DI water solutions containing both microparticles and additives (solvents, softeners, and non-ionic surfactants). Nylon-6 spheres and polyethylene terephthalate microplastics were chosen for adsorption using a count-based method by ImageJ imaging analysis. Molecular dynamics computations simulated 2-ethyl-hexylacrylate (2-EHA) adhesive and microplastic interactions in the presence of water, citrate, glycerol and tergitol detergent additives. The experimental work showed that fewer microplastics were collected when tergitol was added and was in line with lower experimental Work of Adhesion (WoAaq) results for nylon and PETE (94.5% and 54.5% reductions respectively). Computational results also confirmed lower adhesion in the presence of tergitol. The experiments also showed that the adhesive swelled while equilibrating in additive solutions. Models suggested that tergitol most negatively impacted particle binding through a competitive “blocking” of the adhesive substrate while the other additives were less conclusive about potential interferences based on competitive binding. 

This paper addresses the inverse scattering problem in a domain $$\Omega$$. The input data, measured outside $$\Omega$$, involve the waves generated by the interaction of plane waves with various directions and unknown scatterers that are fully occluded inside $$\Omega$$. The output of this problem is the spatial dielectric constant of these scatterers. Our approach to solving this problem consists of two primary stages. Initially, we eliminate the unknown dielectric constant from the governing equation, resulting in a system of partial differential equations. Subsequently, we develop the Carleman contraction mapping method to effectively tackle this system. It is noteworthy to highlight the robustness of this method. It does not require a precise initial guess of the true solution, and its computational cost is relatively inexpensive. Some numerical examples are presented.