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High order interpolation of magnetic fields with vector potential reconstruction for particle simulations
We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides C(m) continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincaré section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Lastly, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes.
Editorial: Nanotechnology for natural products
Humans around the globe have lived through an unprecedented time. The emergence and rapid spread of coronavirus disease 2019 (COVID-19) have resulted in the loss of millions of lives, and this number is still climbing every day and hour. As a consequence, there have been drastic changes over the past two years in how we live, communicate, and work, some of which may have changed forever: remote conferencing has become a new norm for businesses, schools, and academia; work-from-home and hybrid working is now more than just acceptable in many industries; most importantly, COVID-19 has raised global awareness of infectious diseases and pandemic responses to an exceptional level. Certainly, COVID-19 is not the only disease that is causing human suffering at this moment. Other highly contagious and lethal viruses, such as the human immunodeficiency virus (HIV), Ebola, and the recent addition to the list, Monkeypox, pose extraordinary challenges to modern civilizations. On the other hand, non-communicable diseases, such as heart disease, stroke, and cancer, are still claiming the majority of deaths on a global level (World Health Organization, 2020). Before the availability of synthetic drugs, civilizations worldwide relied on natural products extracted from the environment and various organisms for healthcare. Natural products and their derivatives continue to be critical components in the drug library available today. Indeed, almost a quarter of the new drugs approved by the US Food and Drug Administration (FDA) since 1981 are natural products, botanical mixtures, or their derivatives (Newman and Cragg, 2020). Recent developments in analytical characterization, genome mining, and engineering have further increased interest in drug discovery from the pool of natural products (Atanasov et al., 2021). This Research Topic celebrates a collection of studies at the intersection of natural product research and nanotechnological advances. As a successor and extension of the Research Topic in “Nanotechnology in Traditional Medicines and Natural Products” published last year (Zhang et al., 2021), the present collection focused more on recent developments in employing the synthesis and characterization of nanostructures for the delivery of functional natural products. Specifically, the use of carrier nanostructures to conjugate or encapsulate therapeutically active natural products with carrier nanostructures could enable their robust, targeted delivery tailored to either tackle a specific disease or unlock a drug administration pathway. Over the last decade, nanostructures such as liposomes (Pattni et al., 2015) and lipid nanoparticles (Hou et al., 2021) have been developed as versatile platforms for the inclusion and delivery of a wide range of therapeutical compounds; a significant advance in this aspect is the stabilization of mRNA strands for COVID-19 vaccination recently produced by Pfizer/BioNTech and Moderna (Tenchov et al., 2021). Such engineered nanomaterials are now widely used in the development of new drugs, while regulatory forces, such as the US FDA, remain cautious with the evaluation of each product on a case-by-case basis (Wang and Grainger, 2022). In this collection, Zeng et al. provided a timely review of natural products conjugated to and contained within nanomaterials for the ongoing COVID-19 pandemic. Natural products that are potentially useful in the mitigation of this disease, such as chloroquine and curcumin, supported in nanocarrier systems, have been discussed in detail. More broadly, Cheng et al. comprehensively reviewed the use of liposomes as a nanocarrier for natural products. This article provides a summary of natural product compounds and extracts used to form liposomal structures. Readers can further enjoy the practical aspects of these engineered drugs for the treatment of specific diseases as well as insights into future directions in this field.
Aerosol Vertical Turbulent Mass Flux Retrievals Through Novel Remote Sensing Algorithm
Abstract Integrated measurements of aerosol, radiation, cloud, and turbulent transport in the planetary boundary layer (PBL) are essential for understanding and modeling climate and air quality. Here, we developed a new technique for the identification of convective turbulent regions and deriving the vertical distribution of aerosol turbulent mass fluxes within PBL. The algorithm uses retrievals from coherent Doppler lidars and a high spectral resolution lidar. The technique was applied to study particle mass fluxes over 2 months (November–December 2020) during the campaign conducted at the DOE Atmospheric Radiation Measurement Southern Great Plains (SGP) site in Lamont, Oklahoma. The algorithm developed here is capable of continuously deriving vertically resolved (curtains) aerosol mass fluxes. Our data analysis shows that at the site, the 30‐min averaged fluxes at 135 m above the surface were mainly positive (upward) at ∼1 μg m −2 s −1 , suggesting that the surface is the primary source of the particle mass supplied to the boundary layer at the SGP site. Analyses of the individual case studies have revealed that not all the derived fluxes can be linked to surface emissions. Both positive and negative values in a range of ±5 μg m −2 s −1 can be caused by convective thermals interacting between the residual layer and the mixed layer and by rotation of the horizontal wind with the height. Large erroneous negative fluxes can also be caused by drizzling/precipitating clouds. We anticipate that the application of the current technique will lead to a more realistic representation of aerosol mass budgets and bidirectional mixing rates.
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-“coupled”- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz–Kalos–Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.
Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields
In this paper, we present a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log-variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means of Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. Finally, it is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration.
Two-Sided Semi-Local Smoothing Splines
A semi-local smoothing spline of degree n and class C{sup p} is a function defined on an interval, having p continuous derivatives on that interval, and coinciding with a polynomial of degree n on the subintervals forming its partition. The domain of each polynomial is a subinterval on which m + 1 values of the approximated function are given, but in order to construct the polynomial, it is necessary to know M ≥ m + 1 values (m and M are determined by the class and the degree of the spline). The additional values can be borrowed from the adjacent subintervals. When constructing an S-spline in the periodic case, the problem of additional values is solved on the basis of periodicity, but in the nonperiodic case, one is expected to define the lacking values of a function beyond the domain. The present paper is aimed at nonperiodic two-sided S-splines whose construction does not require additional data.
Muon reconstruction in the Daya Bay water pools
Muon reconstruction in the Daya Bay water pools would serve to verify the simulated muon fluxes and offer the possibility of studying cosmic muons in general. This reconstruction is, however, complicated by many optical obstacles and the small coverage of photomultiplier tubes (PMTs) as compared to other large water Cherenkov detectors. The PMTs’ timing information is useful only in the case of direct, unreflected Cherenkov light. This requires PMTs to be added and removed as an hypothesized muon trajectory is iteratively improved, to account for the changing effects of obstacles and direction of light. Therefore, muon reconstruction in the Daya Bay water pools does not lend itself to a general fitting procedure employing smoothly varying functions with continuous derivatives. Here, we describe an algorithm which overcomes these complications. It employs the method of Least Mean Squares to determine an hypothesized trajectory from the PMTs’ charge-weighted positions. This initially hypothesized trajectory is then iteratively refined using the PMTs’ timing information. Reconstructions with simulated data reproduce the simulated trajectory to within about 5° in direction and about 45 cm in position at the pool surface, with a bias that tends to pull tracks away from the vertical by about 3°.
Gyrokinetic electromagnetic particle simulations in triangular meshes with C1 finite elements
The triangular mesh-based gyrokinetic scheme enables comprehensive axis-to-edge studies across the entire plasma volume. Our approach employs triangular finite elements with first-derivative continuity (C1), building on previous work to facilitate gyrokinetic simulations. Additionally, we have adopted the mixed variable/pullback scheme for gyrokinetic electromagnetic particle simulations. The filter-free treatment in the poloidal cross-section with triangular meshes introduces unique features and challenges compared to previous treatments using structured meshes. Our implementation has been validated through benchmarks using ITPA-toroidicity-induced Alfvén eigenmode parameters, showing its capability in moderate to small electron skin depth regimes. Additional examinations using experimental parameters confirm its applicability to realistic plasma conditions.
Effects of He Ion Irradiation in Simple Borosilicate Glasses for HLW Immobilisation - 20324
High-level radioactive waste (HLW) consists of fission products and minor actinides. Borosilicate glass is the host material of choice in most countries to safely immobilize HLW, followed by eventual geological disposal. HLW glasses will experience both self-heating and self-irradiation effects due to the decay of fission products and minor actinides present therein. During the first 500 years of geological disposal, beta-gamma decay will be the main source of radiation due to short half-lives of fission products, as compared to very long-lived actinides which will be responsible for irradiation over much longer timescales. High-energy alpha particles and alpha recoil nuclei can potentially have significant impact (stored energy, volume change, accumulated dose, chemical durability) on the performance of the wasteform over longer timescales. Thus, to ensure safe and economic disposal over geological periods (10{sup 4} - 10{sup 6} years), the assessment of performance and properties in terms of radiation effects becomes indispensable. This work aims to simulate the effects of alpha decay in radioactive waste glasses. Two international glasses, namely UK 'MW' lithium-sodium borosilicate and Indian sodium-barium borosilicate, which are being used as HLW immobilization matrices by the UK and India respectively, were prepared by a melt-quench method and annealed below their glass transition temperatures. Both glasses were irradiated with 650 KeV He{sup 2+} ions with doses ranging from 10{sup 15} to 10{sup 17} ions/cm{sup 2}. Structural analysis was carried out using electron paramagnetic resonance (EPR) and Raman spectroscopies. First derivative continuous wave EPR spectra were recorded for all pristine and irradiated glass monoliths at room temperature using an X-band (frequency 9.6 GHz) EPR Bruker spectrometer. Results from EPR analyses showed the formation of irradiation induced paramagnetic centers at g ∼ 2.00 in all irradiated glasses. Raman spectra of pristine and irradiated samples were acquired, and showed notable changes in glass structure post-irradiation, with the emergence of a broad Raman band at 1560 cm{sup -1} upon irradiation with high fluences. (authors)
Gauge invariance of the helicity continuity equation
The derivation of the helicity continuity equation in electromagnetic theory is performed without specifying a gauge. In contrast with previous proposals, the form of this equation is shown to be gauge invariant without invoking a Helmholtz decomposition. The helicity and its flow, the latter associated with the spin in quantized fields, involve two sets of a vector and a scalar potential, where each set can independently undergo a gauge transformation. There are alternative definitions of the helicity and flow densities that arise from different grouping of terms in the continuity differential equation. The various definitions acquire an unambiguous meaning, depending on the gauge and the physical context. The helicity density, defined as ϱ{sub A{sub C}{sup (2)}} : =με(A·B-C·E) and flow density J{sub AC}{sup (2)} : =με(E-∇ϕ{sub A})×A+(B-∇ϕ{sub C})×C, include all the rotational content of the free fields regardless of the gauge. In free space, these quantities satisfy a gauge invariant conservation equation without gauge-fixing source terms. A further asset of the present formulation is that charge and current source terms can be readily incorporated. The helicity source terms are of the form μB·∫Jdt-μ∫Bdt·J. A helicity continuity equation in terms solely of transverse fields is derived in the Coulomb gauge.
Computer-controlled finishing via dynamically constraint position-velocity-time scheduler
In a Computer Numerical Controlled (CNC) finishing process, the target material removal from an optical surface is guided by the convolution between the influence function of a machine tool and its dwell time at certain points over the surface. To reduce dynamics stressing and increase machining efficiency, the dwell time must be converted to varying velocities, which are the actual inputs to the machine tool controller. Conventionally, the conversion assumed constant acceleration and relied on linear motion interpolation, which caused discontinuities in velocities. This unsmooth motion affects the material removal distribution, and, thus, the accuracy of the finished surface shape. Many modern CNC machines support the smoother, cubic-polynomial interpolated Position-Velocity-Time (PVT) motion mode; however, the conventional scheduler may fail to provide suitable velocities for the PVT. Here in this study answers this challenge by proposing a novel PVT-based velocity scheduler that achieves smooth motion while considering CNC dynamic limits. Firstly, the principle of the PVT is explained, and the PVT-based velocity scheduler is formulated. Secondly, a quadratic programming is used to optimize the velocities by imposing the CNC dynamic constraints and the C 1 continuities (zeroth and first derivatives are continuous) simultaneously. Thirdly, the smoothness and accuracy of the scheduled velocities are studied on different kinds of tool paths via simulation. Finally, a sub-0.3 nm level surface finishing experiment using ion beam figuring is demonstrated to verify the feasibility of the proposed method. The PVT-based scheduler and simulator code is open-sourced.
Advantage of multi-band solar-induced chlorophyll fluorescence to derive canopy photosynthesis in a temperate forest
When solar-induced chlorophyll fluorescence (SIF) is developed as a novel approach to quantify gross primary production (GPP), narrow SIF emission spectrum around the atmospheric oxygen absorption windows (˜ 761 nm and ˜687 nm) has been widely used to represent SIF and to derive GPP. As SIF is a continuous spectrum, deriving the full broadband SIF emission spectrum over 640–850 nm provides an opportunity to fully explore the potential of SIF in estimating GPP. Using high-frequency measurements of canopy carbon flux and SIF emissions at the atmospheric absorption bands, here we reconstruct the full SIF spectrum from SIF signals at the absorption bands, and then analyze correlations between the GPP and the selected single SIF bands and their combinations using both linear regression (LR) and Gaussian processes regression (GPR). Our results indicate that (1) the red SIF bands (640–700 nm) shows low correlation with GPP due to the strong (re)absorption of red SIF emissions by leaf chlorophyll; (2) the individual bands in near-infrared area (at 720 nm, 740 nm, and 761 nm) can determine about 60% and 62% of the variance in GPP with hourly scale by LR and GPR, respectively, and the combination of those SIF bands provide increased predictive power, explaining 66% and 76% variance in GPP with hourly scale by LR and GPR, respectively; (3) the solar radiation saturation, fraction of direct solar radiation, air temperature and leaf area index may have negative impacts on the SIF-GPP correlations when they are beyond optimal thresholds; and (4) the temporal aggregation of SIF-GPP (daily scale) enhances the correlations as compared with the hourly scale: the daily combination of SIF bands (at 687 nm, 720 nm, and 761 nm) can account for 80% and 93% of variance in daily daytime GPP by LR and GPR, respectively, suggesting that the combination of these three bands of SIF on the daily scale is the best proxy for GPP. Our results provide a new approach to analyze the SIF-GPP correlations using the ground-based full broadband SIF emission, suggesting that multi-bands SIF has a stronger capacity in predicting plant GPP than traditionally used signal band SIF data.
Extending Discrete Exterior Calculus to a Fractional Derivative
Fractional partial differential equations (FDEs) are used to describe phenomena that involve a “non-local” or “long-range” interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the dense matrices arising from standard discretization procedures. In this paper, we begin to extend the well-established computational toolkit of Discrete Exterior Calculus (DEC) to the fractional setting, focusing on proper discretization of the fractional derivative. We define a Caputo-like fractional discrete derivative, in terms of the standard discrete exterior derivative operator from DEC, weighted by a measure of distance between $p$-simplices in a simplicial complex. We discuss key theoretical properties of the fractional discrete derivative and compare it to the continuous fractional derivative via a series of numerical experiments.
Continuously differentiable PIC shape functions for triangular meshes
In this study, a new class of continuously-differentiable shape functions is developed and applied to two-dimensional electrostatic PIC simulation on an unstructured simplex (triangle) mesh. It is shown that troublesome aliasing instabilities are avoided for cold plasma simulation in which the Debye length is as small as 0.01 cell sizes. These new shape functions satisfy all requirements for PIC particle shape. They are non-negative, have compact support, and partition unity. They are given explicitly by cubic expressions in the usual triangle logical (areal) coordinates. The shape functions are not finite elements because their structure depends on the topology of the mesh, in particular, the number of triangles neighboring each mesh vertex. Nevertheless, they may be useful as approximations to solution of other problems in which continuity of derivatives is required or desired.
Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties
In a continuum setting, the energy–momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy–momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derive electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy–momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the Abraham–Minkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy–momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.
Stabilization of Softwood-Derived Pyrolysis Oils for Continuous Bio-oil Hydroprocessing
The use of fast pyrolysis as a potential renewable liquid transportation fuel alternative to crude oil depends on successful catalytic upgrading to produce a refinery-ready product with oxygen content and qualities (i.e. specific functional group or compound content) that is compatible with the product’s proposed insertion point. Catalytic upgrading of bio-oil requires high temperature and pressure, while similar to crude oil hydrotreating, is not as straightforward for the thermally unstable pyrolysis oil. For years, a two-temperature zone, downflow trickle bed reactor was the state-of-the art for continuous operation. However, pressure excursion due to plug formation still occurred, typically at the high temperature transition zone, leading to a process shutdown within 140 h. Recently, a bio-oil pre-treatment process, together with a robust commercial catalyst, was found to be enabling the continuous operation of the two-zone hydroprocessing system. Here, we report the results on pre-treating bio-oil at 413 K and 8.4 MPa of flowing H2 (500 L H2/L bio-oil, 0.5 L bio-oil/L catalyst bed) and the attempts to characterize this oil product to understand the chemistry which enabled the long-term processing of bio-oil.