Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “discretization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 559 records · Page 31

Discrete Open-Shell Tris(bipyridinium radical cationic) Inclusion Complexes in the Solid State

In the solid state the properties of organic radicals depend heavily on radical-radical interactions that are influenced by the superstructure of the crystalline phase. Here, we report the synthesis and characterization of a substituted tetracationic cyclophane, cyclobis(paraquat-p-1,4- dimethoxyphenylene), and outline how its bisradical dicationic redox state associates with the methyl viologen radical cation (MV •+ ) to give a trisradical tricationic inclusion complex. The (super)structures of the reduced cyclophane and this 1:1 complex in the solid-state deviate from the analogous (super)structures observed for the reduced state of cyclobis(paraquat-p-phenylene) and that of its trisradical tricationic complex. Titration experiments with a range of guests reveal that the methoxy substituents on the para-xylenyl do not influence significantly of the binding affinity of the cyclophane for small neutral guests, whereas the affinity decreases by an order of magnitude for larger radical cationic guests such as MV •+ . X-Ray diffraction reveals that the solid- state structures of the tricationic trisradical complexes to be a discrete entity with weak intermolecular orbital overlap between the neighboring complexes. Transient nutation EPR experiment and DFT calculations confirm that the complex has a doublet spin configuration in the ground state as a result of the strong orbital overlap within the complex, while the quartet-state spin configuration is higher in energy and so is inaccessible at ambient temperature. The superconducting quantum interference device (SQUID) measurement reveals that trisradical tricationic complexes interact antiferromagnetically (J/k = - 2.33 K) and form a 1D Heisenberg antiferromagnetic chain along the a-axis in the crystal. Furthermore, these results offer new insights into the design and synthesis of organic magnetic materials based on host-guest inclusion complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Alkali-Metal Interlocking of 2D V 4 O 10 Sheets Defines Discretized Interlayer Shear Relationships

Low-dimensional materials manifest structural anisotropy, quantum confinement, and tightly bound excitonic states, which make them attractive building blocks that can be assembled within three-dimensional laterally stitched heterostructures, stacked van der Waals solids, and complex moiré superlattices. Ion intercalation in the galleries between layered materials provides a means of modifying interlayer separation and coupling, but it is also known to drive the shearing of the layers. In this article, we explore the distinct ligand coordination environments afforded by vanadyl oxygens of singular [V 4 O 10 ] sheets and examine how the size, polarizability, and stoichiometry of Group I cations sandwiched between such layers determine the interlocking of the sheets in stacked structures. Based on the topochemical insertion of alkali-metal ions into the layered λ-V 2 O 5 , we identify seven types of guest ion coordination sites discretized into four distinct regimes of interlayer shear in units of half octahedral widths. The coordination preferences of intercalated cations govern how they interlock 2D [V 4 O 10 ] sheets and engender specific shear conformations. We present evidence that static and dynamic disorder in guest ion arrangement modulate the magnetic structure of the intercalated compounds based on electrostatic polarization, localization of charge and spin density, and lattice distortion. The results illustrate the use of topochemical ion insertion to modulate stacking relationships and magnetic transition characteristics.

36 MATERIALS SCIENCE↗

First Direct Observations of Propagation of Discrete Chorus Elements From the Equatorial Source to Higher Latitudes, Using the Van Allen Probes and Arase Satellites

Whistler mode chorus waves have recently been established as the most likely candidate for scattering relativistic electrons to produce the electron microbursts observed by low altitude satellites and balloons. These waves would have to propagate from the equatorial source region to significantly higher magnetic latitude in order to scatter electrons of these relativistic energies. This theoretically proposed propagation has never been directly observed. We present the first direct observations of the same discrete rising tone chorus elements propagating from a near equatorial (Van Allen Probes) to an off-equatorial (Arase) satellite. The chorus is observed first on the more equatorial satellite and is found to be more oblique and significantly attenuated at the off-equatorial satellite. Further, this is consistent with the prevailing theory of chorus propagation and with the idea that chorus must propagate from the equatorial source region to higher latitudes. Ray tracing of chorus at the observed frequencies confirms that these elements could be generated parallel to the field at the equator, and propagate through the medium unducted to Van Allen Probes A and then to Arase with the observed time delay, and have the observed obliquity and intensity at each satellite.

79 ASTRONOMY AND ASTROPHYSICS↗

Anomalous Transport in Three-Dimensional Discrete Fracture Networks: Interplay Between Aperture Heterogeneity and Injection Modes

In this work, we study how the interplay between fracture aperture heterogeneity and tracer injection mode controls fluid flow and tracer transport in three-dimensional (3D) discrete fracture networks (DFNs). The direct 3-D DFN simulations show that tracer injection mode has substantial effects on tracer spreading across all levels of aperture heterogeneity. The key controlling factor for effective transport is the initial Lagrangian velocity distribution, which is determined by the interplay between injection mode and aperture heterogeneity. The fundamental difference between initial Lagrangian velocity distribution and domain-scale Eulerian velocity distribution plays a vital role in determining anomalous transport. We effectively capture the observed anomalous transport using an upscaled transport model that incorporates initial velocity distribution, stationary velocity distribution, velocity correlation length, and average advective tortuosity. With the upscaled transport model, we accurately capture the evolution of Lagrangian velocity distribution and predict longitudinal spreading in 3-D DFN.

58 GEOSCIENCES↗

A Comparison of Linear Solvers for Resolving Flow in Three-Dimensional Discrete Fracture Networks

We compare various methods for resolving steady flow within three-dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi-grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log-variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power-law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large-scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory.

58 GEOSCIENCES↗

Energy Transport and Conversion Above a Bright Discrete Auroral Arc

Magnetically connected observations of particle distributions and luminosity from the Reimei spacecraft are used to examine energy transport and conversion occurring above a discrete auroral arc. By combining imaging and in situ measurements it is shown how transverse electromagnetic and kinetic energy fluxes measured along the spacecraft trajectory converge across geomagnetic field-lines into the acceleration region. It is shown how cross-field energy transport is facilitated by the formation of vortices along the length of the arc. From an integration over the vertical extent of the acceleration region it is shown that the transverse and field-aligned flow of energy into the arc locally supports the dissipation needed to power the electron acceleration observed. Estimates of gradients in electromagnetic and kinetic energy flows show how field-aligned electron energization in the acceleration region is supported by the divergence of Poynting flux along and across the background magnetic field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Tunable discrete scale invariance in transition-metal pentatelluride flakes

Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe 5 and HfTe 5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Finally, our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials.

36 MATERIALS SCIENCE↗

Visualizing discrete Fermi surfaces and possible nodal-line to Weyl state evolution in ZrSiTe

Topological nodal line semimetals (TNLSMs) represent a quantum state of topological matter. When the crystal/time-reversal symmetry is broken, a nodal line state is expected to evolve into a Dirac semimetal, a Weyl semimetal, or other topological phases according to theoretical studies. Here, we report scanning tunneling microscopy (STM) based quasiparticle interference (QPI) measurements performed on the surface of TNLSM ZrSiTe single crystal. A discrete Fermi surface with multiple electron/hole pockets and the impurity-induced inter-/intra- pockets scatterings are directly visualized from QPI patterns. Moreover, the degenerated Dirac points at X point evolve into the pairs of Weyl nodes when Fe atoms are deposited, suggesting a possible phase transition from the nodal line to the Weyl state. The calculated band structures and the Weyl points by applying Zeeman splitting energies along x-direction, further confirm the existence of Weyl points in the Fe-doped ZrSiTe induced by the broken of time-reversal symmetry.

36 MATERIALS SCIENCE↗

Learning to Predict Crystal Plasticity at the Nanoscale: Deep Residual Networks and Size Effects in Uniaxial Compression Discrete Dislocation Simulations

The density and configurational changes of crystal dislocations during plastic deformation influence the mechanical properties of materials. These influences have become clearest in nanoscale experiments, in terms of strength, hardness and work hardening size effects in small volumes. The mechanical characterization of a model crystal may be cast as an inverse problem of deducing the defect population characteristics (density, correlations) in small volumes from the mechanical behavior. In this work, we demonstrate how a deep residual network can be used to deduce the dislocation characteristics of a sample of interest using only its surface strain profiles at small deformations, and then statistically predict the mechanical response of size-affected samples at larger deformations. As a testbed of our approach, we utilize high-throughput discrete dislocation simulations for systems of widths that range from nano- to micro- meters. We show that the proposed deep learning model significantly outperforms a traditional machine learning model, as well as accurately produces statistical predictions of the size effects in samples of various widths. By visualizing the filters in convolutional layers and saliency maps, we find that the proposed model is able to learn the significant features of sample strain profiles.

36 MATERIALS SCIENCE↗

Trade-off between processability and device performance in donor–acceptor semiconductors revealed using discrete siloxane side chains

Donor–acceptor polymeric semiconductors are crucial for state-of-the-art applications, such as electronic skin mimics. The processability, and thus solubility, of these polymers in benign solvents is critical and can be improved through side chain engineering. Nevertheless, the impact of novel side chains on backbone orientation and emerging device properties often remains to be elucidated. Here, we investigate the influence of elongated linear and branched discrete oligodimethylsiloxane (oDMS) side chains on solubility and device performance. Thereto, diketopyrrolopyrrole–thienothiophene polymers are equipped with various oDMS pendants (PDPPTT-Si n ) and subsequently phase separated into lamellar domains. The introduction of a branching point in the siloxane significantly enhanced the solubility of the polymer, as a result of increased backbone distortion. Simultaneously, the charge carrier mobility of the polymers decreased by an order of magnitude upon functionalization with long and/or branched siloxanes. This work unveils the intricate balance between processability and device performance in organic semiconductors, which is key for the development of next-generation electronic devices.

36 MATERIALS SCIENCE↗

On the convergence of an IEQ-based first-order semi-discrete scheme for the Beris-Edwards system

We present a convergence analysis of an unconditionally energy-stable first-order semi-discrete numerical scheme designed for a hydrodynamic Q-tensor model, the so-called Beris-Edwards system, based on the Invariant Energy Quadratization Method (IEQ). The model consists of the Navier–Stokes equations for the fluid flow, coupled to the Q-tensor gradient flow describing the liquid crystal molecule alignment. By using the Invariant Energy Quadratization Method, we obtain a linearly implicit scheme, accelerating the computational speed. However, this introduces an auxiliary variable to replace the bulk potential energy and it is a priori unclear whether the reformulated system is equivalent to the Beris-Edward system. In this work, we prove stability properties of the scheme and show its convergence to a weak solution of the coupled liquid crystal system. We also demonstrate the equivalence of the reformulated and original systems in the weak sense.

Weber, Franziska↗

Continuous and discrete phasor analysis of binned or time-gated periodic decays

The time-resolved analysis of periodically excited luminescence decays by the phasor method in the presence of time-gating or binning is revisited. Analytical expressions for discrete configurations of square gates are derived, and the locus of the phasors of such modified periodic single-exponential decays is compared to the canonical universal semicircle. The effects of instrument response function offset, decay truncation, and gate shape are also discussed. Finally, modified expressions for the phase and modulus lifetimes are provided for some simple cases. A discussion of a modified phasor calibration approach is presented, and an illustration of the new concepts with examples from the literature concludes this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A discretized representation for Monte Carlo simulation of deformed semiflexible chains

In this study, we present a novel orientation discretization approach based on the rhombic triacontahedron for Monte Carlo simulations of semiflexible polymer chains, aiming at enhancing structural analysis through rheo-small-angle scattering (rheo-SAS). Our approach provides a more accurate representation of the geometric features of semiflexible chains under deformation, surpassing the capabilities of traditional lattice structures. Validation against the Kratky–Porod chain system demonstrated superior consistency, underscoring its potential to significantly improve the precision of uncovering geometric details from rheo-SAS data. Further, this approach opens new avenues for investigating the conformations of semiflexible polymers and mechanically induced phase transitions in more complex polymer structures, offering deeper insights into their behavior under various conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Control simulations of many-body quantum systems by a synergism of discrete real-time learning and optimal control theory

We present a self-consistent algorithm for optimal control simulations of many-body quantum systems. The algorithm features a two-step synergism that combines discrete real-time machine learning (DRTL) with Quantum Optimal Control Theory (QOCT) using the time-dependent Schrödinger equation. Specifically, in step (1), DRTL is employed to identify a compact working space (i.e., the important portion of the Hilbert space) for the time evolution of the many-body quantum system in the presence of a control field (i.e., the initial or previously updated field), and in step (2), QOCT utilizes the DRTL-determined working space to find a newly updated control field for a chosen objective. Steps 1 and 2 are iterated until a self-consistent control objective value is reached such that the resulting optimal control field yields the same targeted objective value when the corresponding working space is systematically enlarged. Furthermore, to demonstrate this two-step self-consistent DRTL-QOCT synergistic algorithm, we perform optimal control simulations of strongly interacting 1D as well as 2D Heisenberg spin systems. In both scenarios, only a single spin (at the left end site for 1D and the upper left corner site for 2D) is driven by the time-dependent control fields to create an excitation at the opposite site as the target. It is found that, starting from all spin-down zero excitation states, the synergistic method is able to identify working spaces and convergence of the desired controlled dynamics with just a few iterations of the overall algorithm. In the cases studied, the dimensionality of the working space scales only quasi-linearly with the number of spins.

Artificial neural networks↗

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Physics↗

Cas9 interrogates DNA in discrete steps modulated by mismatches and supercoiling

The CRISPR-Cas9 nuclease has been widely repurposed as a molecular and cell biology tool for its ability to programmably target and cleave DNA. Cas9 recognizes its target site by unwinding the DNA double helix and hybridizing a 20-nucleotide section of its associated guide RNA to one DNA strand, forming an R-loop structure. A dynamic and mechanical description of R-loop formation is needed to understand the biophysics of target searching and develop rational approaches for mitigating off-target activity while accounting for the influence of torsional strain in the genome. Here we investigate the dynamics of Cas9 R-loop formation and collapse using rotor bead tracking (RBT), a single-molecule technique that can simultaneously monitor DNA unwinding with base-pair resolution and binding of fluorescently labeled macromolecules in real time. By measuring changes in torque upon unwinding of the double helix, we find that R-loop formation and collapse proceed via a transient discrete intermediate, consistent with DNA:RNA hybridization within an initial seed region. Using systematic measurements of target and off-target sequences under controlled mechanical perturbations, we characterize position-dependent effects of sequence mismatches and show how DNA supercoiling modulates the energy landscape of R-loop formation and dictates access to states competent for stable binding and cleavage. Consistent with this energy landscape model, in bulk experiments we observe promiscuous cleavage under physiological negative supercoiling. The detailed description of DNA interrogation presented here suggests strategies for improving the specificity and kinetics of Cas9 as a genome engineering tool and may inspire expanded applications that exploit sensitivity to DNA supercoiling.

59 BASIC BIOLOGICAL SCIENCES↗

Discontinuous Galerkin discretization for quantum simulation of chemistry

All-electron electronic structure methods based on the linear combination of atomic orbitals method with Gaussian basis set discretization offer a well established, compact representation that forms much of the foundation of modern correlated quantum chemistry calculations—on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block-diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from O(N 4.5 ) in molecular orbital representations to O(N 2.6 ) in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1–2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗