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A posteriori maximum-norm error bounds for the biquadratic spline collocation method applied to reaction-diffusion problems
Collocation with biquadratic C{sup 1}-splines for a singularly perturbed reaction-diffusion problem in two dimensions is studied. A second-order supremum norm a posteriori error bound is derived for the collocation method on an arbitrary mesh. Numerical results are presented that support our theoretical estimate.
Renormalization of states and quasiparticles in many-body downfolding
We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We show that the renormalization factor provides a unique measure of the quality of the compression as it directly represents the projection between the approximate stationary state of the many-body Hamiltonian and the full many-body wavefunction. Hence, the renormalization factor is a measure of fidelity between the effective (reduced-rank) description and the full many-body treatment for arbitrary (i.e., ground and excited) states. When the entire problem is mapped on a system of interacting quasiparticles [Romanova et al., npj Comput. Mater. 9, 126 (2023)], the effective Hamiltonians can faithfully reproduce the physics only when a clear energy scale separation exists between the subsystems and their environment. We also demonstrate that it is necessary to include quasiparticle renormalization at distinct energy scales, capturing the distinct interaction between subsystems and their surrounding environments. Numerical results from simple, exactly solvable models highlight the limitations and strengths of this approach, particularly for ground and low-lying excited states. This work lays the groundwork for applying dynamical downfolding techniques to problems concerned with (quantum) interfaces.
Real-time evolution of static electron-phonon models in time-dependent electric fields
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Reconstruction of Thermal Protection System Aeroheating using a Green’s Function Approach
Inverse heat transfer (IHT) techniques are often used to reconstruct the surface heating conditions on spacecraft thermal protection systems (TPS) during atmospheric entry. Current IHT techniques for entry spacecraft applications, however, demand substantial computational resources, and are impractical for analyses such as uncertainty quantification and real-time health monitoring. In this paper, a Green’s function sensor fusion approach is used to reconstruct the TPS surface aeroheating conditions on experimental spaceflight and ground test systems from collocated temperature and heat flux sensors embedded in the TPS. The algorithm leverages Green’s functions to model the heat conduction within the spacecraft TPS and stabilizes the recovery of the surface heating condition using the direct heat flux sensor measurement. The algorithm is validated using arc-jet ground test data and applied to the reconstruction of the Mars 2020 backshell heating during Martian atmospheric entry. The performance of the algorithm is benchmarked against a current state-of-the-art IHT framework, FIAT_Opt. The Green’s function-based reconstruction algorithm recovers the net hot-wall heat flux absorbed by the TPS and the incident heat flux from the atmospheric entry environment in close agreement with FIAT_Opt. Notably, computation of the surface heating condition is completed in three orders of magnitude less time with the Green’s function sensor fusion approach using a consumer-grade PC, versus with FIAT_Opt running on a high performance computer cluster. The efficiency of the algorithm is leveraged to compute the uncertainty contributions of input parameters to the total uncertainty in reconstructed Mars 2020 backshell heating for the full atmospheric entry heat pulse. The sensitivity analysis uncovers that, at different times throughout the entry heat pulse, uncertainties in the TPS specific heat, thermal conductivity, and emissivity are all dominant drivers of the reconstruction uncertainty. These results demonstrate Green’s functions and sensor-fusion techniques as promising IHT approaches to reconstruct atmospheric entry environments from TPS-embedded measurements, and highlight how these techniques may give access to post-flight analyses previously hindered by the prohibitive cost of current methods.
Reconstruction of Thermal Protection System Aeroheating using a Green’s Function Approach
Inverse heat transfer (IHT) techniques are often used to reconstruct the surface heating conditions on spacecraft thermal protection systems (TPS) during atmospheric entry. Current IHT techniques for entry spacecraft applications, however, demand substantial computational resources, and are impractical for analyses such as uncertainty quantification and real-time health monitoring. In this paper, a Green’s function sensor fusion approach is used to reconstruct the TPS surface aeroheating conditions on experimental spaceflight and ground test systems from collocated temperature and heat flux sensors embedded in the TPS. The algorithm leverages Green’s functions to model the heat conduction within the spacecraft TPS and stabilizes the recovery of the surface heating condition using the direct heat flux sensor measurement. The algorithm is validated using arc-jet ground test data and applied to the reconstruction of the Mars 2020 backshell heating during Martian atmospheric entry. The performance of the algorithm is benchmarked against a current state-of-the-art IHT framework, FIAT_Opt. The Green’s function-based reconstruction algorithm recovers the net hot-wall heat flux absorbed by the TPS and the incident heat flux from the atmospheric entry environment in close agreement with FIAT_Opt. Notably, computation of the surface heating condition is completed in three orders of magnitude less time with the Green’s function sensor fusion approach using a consumer-grade PC, versus with FIAT_Opt running on a high performance computer cluster. The efficiency of the algorithm is leveraged to compute the uncertainty contributions of input parameters to the total uncertainty in reconstructed Mars 2020 backshell heating for the full atmospheric entry heat pulse. The sensitivity analysis uncovers that, at different times throughout the entry heat pulse, uncertainties in the TPS specific heat, thermal conductivity, and emissivity are all dominant drivers of the reconstruction uncertainty. These results demonstrate Green’s functions and sensor-fusion techniques as promising IHT approaches to reconstruct atmospheric entry environments from TPS-embedded measurements, and highlight how these techniques may give access to post-flight analyses previously hindered by the prohibitive cost of current methods.
Application of Contraction Mappings to the Control of Nonlinear Systems
The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.
Roadmap on methods and software for electronic structure based simulations in chemistry and materials
This Roadmap article provides a succinct, comprehensive overview of the state of electronic structure methods and software for molecular and materials simulations. Seventeen distinct sections collect insights by 51 leading scientists in the field. Each contribution addresses the status of a particular area, as well as current challenges and anticipated future advances, with a particular eye towards software related aspects and providing key references for further reading. Foundational sections cover density functional theory and its implementation in real-world simulation frameworks, Green's function based many-body perturbation theory, wave-function based and stochastic electronic structure approaches, relativistic effects and semiempirical electronic structure theory approaches. Subsequent sections cover nuclear quantum effects, real-time propagation of the electronic structure, challenges for computational spectroscopy simulations, and exploration of complex potential energy surfaces. The final sections summarize practical aspects, including computational workflows for complex simulation tasks, the impact of current and future high-performance computing architectures, software engineering practices, education and training to maintain and broaden the community, as well as the status of and needs for electronic structure based modeling from the vantage point of industry environments. Overall, the field of electronic structure software and method development continues to unlock immense opportunities for future scientific discovery, based on the growing ability of computations to reveal complex phenomena, processes and properties that are determined by the make-up of matter at the atomic scale, with high precision.
Electrochemical Electron Transfer and Proton-Coupled Electron Transfer: Effects of Double Layer and Ionic Environment on Solvent Reorganization Energies
Electron transfer and proton coupled electron transfer (PCET) reactions at electrochemical interfaces play an essential role in a broad range of energy conversion processes. The reorganization energy, which is a measure of the free energy change associated with solute and solvent rearrangements, is a key quantity for calculating rate constants for these reactions. We present a computational method for including the effects of the double layer and ionic environment of the diffuse layer in calculations of electrochemical solvent reorganization energies. This approach incorporates an accurate electronic charge distribution of the solute within a molecular-shaped cavity in conjunction with a dielectric continuum treatment of the solvent, ions, and electrode using the integral equations formalism polarizable continuum model. The molecule-solvent boundary is treated explicitly, but the effects of the electrode-double layer and double layer-diffuse layer boundaries, as well as the effects of the ionic strength of the solvent, are included through an external Green’s function. The calculated total reorganization energies agree well with experimentally measured values for a series of electrochemical systems, and the effects of including both the double layer and ionic environment are found to be very small. This general approach was also extended to electrochemical PCET and produced total reorganization energies in close agreement with experimental values for two experimentally studied PCET systems. This research was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center, funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.
Development of a reverse genetics system to generate a recombinant Ebola virus Makona expressing a green fluorescent protein
Previous studies have demonstrated the potential application of reverse genetics technology in studying a broad range of aspects of viral biology, including gene regulation, protein function, cell entry, and pathogenesis. Here, we describe a highly efficient reverse genetics system used to generate recombinant Ebola virus (EBOV) based on a recent isolate from a human patient infected during the 2014–2015 outbreak in Western Africa. We also rescued a recombinant EBOV expressing a fluorescent reporter protein from a cleaved VP40 protein fusion. Using this virus and an inexpensive method to quantitate the expression of the foreign gene, we demonstrate its potential usefulness as a tool for screening antiviral compounds and measuring neutralizing antibodies. - Highlights: • Recombinant Ebola virus (EBOV) derived from Makona variant was rescued. • New protocol for viral rescue allows 100% efficiency. • Modified EBOV expresses a green fluorescent protein from a VP40-fused protein. • Modified EBOV was tested as tool to screen antiviral compounds and measure neutralizing antibodies.
Designing field-controllable graphene-dot-graphene single molecule switches: A quantum-theoretical proof-of-concept under realistic operating conditions
A theoretical proof of the concept that a particularly designed graphene-based moletronics device, constituted by two semi-infinite graphene subunits, acting as source and drain electrodes, and a central benzenoid ring rotator (a “quantum dot”), could act as a field-controllable molecular switch is outlined and analyzed with the density functional theory approach. Besides the ideal (0 K) case, we also consider the operation of such a device under realistic operating (i.e., finite-temperature) conditions. An in-depth insight into the physics behind device controllability by an external field was gained by thorough analyses of the torsional potential of the dot under various conditions (absence or presence of an external gating field with varying strength), computing the torsional correlation time and transition probabilities within the Bloembergen-Purcell-Pound formalism. Both classical and quantum mechanical tunneling contributions to the intramolecular rotation were considered in the model. The main idea that we put forward in the present study is that intramolecular rotors can be controlled by the gating field even in cases when these groups do not possess a permanent dipole moment (as in cases considered previously by us [I. Petreska et al., J. Chem. Phys. 134, 014708-1–014708-12 (2011)] and also by other groups [P. E. Kornilovitch et al., Phys. Rev. B 66, 245413-1–245413-7 (2002)]). Consequently, one can control the molecular switching properties by an external electrostatic field utilizing even nonpolar intramolecular rotors (i.e., in a more general case than those considered so far). Molecular admittance of the currently considered graphene-based molecular switch under various conditions is analyzed employing non-equilibrium Green’s function formalism, as well as by analysis of frontier molecular orbitals’ behavior.
Inkless, dry printing nanographene via in-Situ Coordinated laser ablation and sintering processes
Printing carbon, such as graphene and other carbon structures, for flexible and printed electronics currently relies on either ink-based printing, laser-induced forward transfer (LIFT), or laser-induced graphitization (LIG) to convert carbon-rich precursor materials, such as polymers, to graphene-like carbon structures. Liquid inks contain toxic solvents, surfactants, and stabilizing additives that degrade electrical conductivity and require high-temperature post-processing. On the other hand, LIG is limited by the substrate. Here, this study introduces an additive manufacturing method for dry-printing carbon nanomaterials, ranging from amorphous carbon to crystalline graphene-like structures, on various substrates. The system utilizes laser ablation of a solid graphite target to create pure carbon nanoparticles in situ and on demand. An inert gas carries the nanoparticles onto the substrate, where they can be deposited either as amorphous structures or laser-sintered in real time to form various graphitic structures. The study of laser processing parameters, specifically fluence and pulse repetition frequency, revealed three unique regimes of nanostructure evolution that influence the morphological and electrical properties of these printed structures. Raman spectroscopy confirmed graphitization with a resistivity slightly higher than that of the bulk graphite target. The conductivity/resistivity could be tuned as a function of sintering laser power. Scanning transmission electron microscopy (STEM) revealed that turbostratic nanographene formed with an interlayer spacing of 0.40 nm. Despite ink-based printing methods, such as screen printing, inkjet printing (IJP), and aerosol jet printing (AJP), this eco-friendly and green manufacturing technique could eliminate toxic chemicals, reduce environmental impact, and enable single-step fabrication of carbon-based devices for applications in wearable sensors, energy storage, flexible electronics, and Internet of Things (IoT) devices.
Fractionation of Organosolv Lignin Using Acetone:Water and Properties of the Obtained Fractions
In this study, lignin fractions with different molecular weight were prepared using a simple and almost green method from switchgrass and pine organosolv lignin. Different proportions of acetone in water, ranging from 30 to 60%, were used for lignin fractionation. A higher concentration of acetone dissolved higher molecular weight fractions of the lignin. Fractionated organosolv lignin showed different molecular weight and functional groups. Higher molecular weight fractions exhibited more aliphatic and less phenolic OH than lower molecular weight fractions. Lower molecular weight fractions lead to more homogeneous structure compared to samples with a higher molecular weight. In conclusion, all fractions showed strong antioxidant activity.
Spin injection and filtering in halfmetal/semiconductor (CrAs/GaAs) heterostructures
Theoretical investigations of spin-dependent transport in GaAS/CrAs/GaAs halfmetal-semiconductor heterostructures indicate that this system is a candidate for an efficient room temperature spin injector and filter. The spin dependent electronic structure of zincblende CrAs and the band offset between GaAs and CrAs are determined by ab-initio calculations within the method of linear muffin tin orbitals (LMTO). This band structure is mapped onto an effective sp{sup 3}d{sup 5}s* nearest neighbor tight-binding (TB) Hamiltonian and the steady-state transport characteristic is calculated within a non-equilibrium Green’s function approach. Even at room temperature we find current spin polarizations up to 97%.
Multiscale Approach to Fast ModSim for Laser Processing of Metals for Future Nuclear Deterrence Environments
Predicting performance of parts produced using laser-metal processing remains an out- standing challenge. While many computational models exist, they are generally too computationally expensive to simulate the build of an engineering-scale part. This work develops a reduced order thermal model of a laser-metal system using analytical Green's function solutions to the linear heat equation, representing a step towards achieving a full part performance prediction in an "overnight" time frame. The developed model is able to calculate a thermal history for an example problem 72 times faster than a traditional FEM method. The model parameters are calibrated using a non-linear solution and microstructures and residual stresses calculated and compared to a non-linear case. The calibrated model shows promising agreement with a non-linear solution.
Versatile recognition of graphene layers from optical images under controlled illumination through green channel correlation method
In this study, a simple yet versatile method is proposed for identifying the number of exfoliated graphene layers transferred on an oxide substrate from optical images, utilizing a limited number of input images for training, paired with a more traditional number of a few thousand well-published Github images for testing and predicting. Two thresholding approaches, namely the standard deviation-based approach and the linear regression-based approach, were employed in this study. The method specifically leverages the red, green, and blue color channels of image pixels and creates a correlation between the green channel of the background and the green channel of the various layers of graphene. This method proves to be a feasible alternative to deep learning-based graphene recognition and traditional microscopic analysis. The proposed methodology performs well under conditions where the effect of surrounding light on the graphene-on-oxide sample is minimum and allows rapid identification of the various graphene layers. Here, the study additionally addresses the functionality of the proposed methodology with nonhomogeneous lighting conditions, showcasing successful prediction of graphene layers from images that are lower in quality compared to typically published in literature. In all, the proposed methodology opens up the possibility for the non-destructive identification of graphene layers from optical images by utilizing a new and versatile method that is quick, inexpensive, and works well with fewer images that are not necessarily of high quality.
Code verification for practically singular equations
We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.
A Kinematic Rupture Model Generator Using Irikura's Recipe
In this project we developed GEN_SRF4 a computer program for generating kinematic rupture models, compatible with the SRF format, using Irikura and Miyake (2011) asperity-based earthquake rupture model (IM2011, hereafter). IM2011, also known as Irkura’s recipe, has been widely used to model and simulate ground motion from earthquakes in Japan. An essential part of the method is its kinematic rupture generation technique, which is based on a deterministic rupture asperity modeling approach. The source model simplicity and efficiency of IM2011 at reproducing ground motion from earthquakes recorded in Japan makes it attractive to developers and users of the Southern California Earthquake Center Broadband Platform (SCEC BB platform). Besides writing the code the objective of our study was to test the transportability of IM2011 to broadband simulation methods used by the SCEC BB platform. Here we test it using the Graves and Pitarka (2010) method, implemented in the platform. We performed broadband (0.1- -10 Hz) ground motion simulations for a M6.7 scenario earthquake using rupture models produced with both GEN_SRF4 and rupture generator of Graves and Pitarka (2016), (GP2016 hereafter). In the simulations we used the same Green’s functions, and same high frequency approach for calculating the low-frequency and high-frequency parts of ground motion, respectively.