Search NASA⌕ Search

SEARCH · Search NASA

Results for “three space dimension”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Spatial BCS-BEC crossover in superconducting $\textit{p–n}$ junctions

Here, we present a theory of superconducting $\textit{p–n}$ junctions. To this end, we consider a two band model of doped bulk semiconductors with attractive interactions between the charge carriers and derive the superconducting order parameter, the quasiparticle density of states, and the chemical potential as a function of the semiconductor gap $Δ_0$ and the doping level ε. We verify previous results for the quantum phase diagram for a system with constant density of states in the conduction and valence band, which show BCS-superconductor to Bose-Einstein-condensation (BEC) and BEC-to-insulator transitions as a function of doping level and the size of the band gap. Then, we extend this formalism to a density of states which is more realistic for 3D systems and derive the corresponding quantum phase diagram, where we find that a BEC phase can only exist for small band gaps $Δ_0 < Δ ^{\ast}_0$. For larger band gaps, we find rather a direct transition from an insulator to a BCS phase. Next, we apply this theory to study the properties of superconducting $\textit{p–n}$ junctions. We derive the spatial variation of the superconducting order parameter along the $\textit{p–n}$ junction. As the potential difference across the junction leads to energy band bending, we find a spatial crossover between a BCS and BEC condensate, as the density of charge carriers changes across the $\textit{p–n}$ junction. For the two-dimensional system, we find two possible regimes, when the bulk is in a BCS phase, a BCS-BEC-BCS junction with a single BEC layer in the space charge region, and a BCS-BEC-I-BEC-BCS junction with two layers of BEC condensates separated by an insulating layer. In three dimensions we find that there can also be a conventional BCS-I-BCS junction for semiconductors with band gaps exceeding $Δ^{\ast}_0$. Thus, we find that there can be BEC layers in the well controlled setting of doped semiconductors, where the doping level can be varied to change and control the thickness of BEC and insulator layers, making Bose-Einstein condensates thereby possibly accessible to experimental transport and optical studies in solid-state materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Designing a Nanoscale Three-phase Electrochemical Pathway to Promote Pt-catalyzed Formaldehyde Oxidation

Gas-phase heterogeneous catalysis is a process spatially constrained on the two-dimensional surface of a solid catalyst. Here, we introduce a new toolkit to open up the third dimension. We discovered that the activity of a solid catalyst can be dramatically promoted by covering its surface with a nanoscale-thin layer of liquid electrolyte while maintaining efficient delivery of gas reactants, a strategy we call three-phase catalysis. Introducing the liquid electrolyte converts the original surface catalytic reaction into an electrochemical pathway with mass transfer facilitated by free ions in a three-dimensional space. Furthermore, we chose the oxidation of formaldehyde as a model reaction and observed a 25000-times enhancement in the turnover frequency of Pt in three-phase catalysis as compared to conventional heterogeneous catalysis. We envision three-phase catalysis as a new dimension for catalyst design and anticipate its applications in more chemical reactions from pollution control to the petrochemical industry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

$\mathrm{A}$ $\mathrm{CFT}$ distance conjecture

We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data

This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.

42 ENGINEERING↗
DOE OSTI2021

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Accurate computational design of three-dimensional protein crystals

Protein crystallization plays a central role in structural biology. Despite this, the process of crystallization remains poorly understood and highly empirical, with crystal contacts, lattice packing arrangements and space group preferences being largely unpredictable. Programming protein crystallization through precisely engineered side-chain-side-chain interactions across protein-protein interfaces is an outstanding challenge. Here, in this study, we develop a general computational approach for designing three-dimensional protein crystals with prespecified lattice architectures at atomic accuracy that hierarchically constrains the overall number of degrees of freedom of the system. We design three pairs of oligomers that can be individually purified, and upon mixing, spontaneously self-assemble into >100 µm three-dimensional crystals. The structures of these crystals are nearly identical to the computational design models, closely corresponding in both overall architecture and the specific protein-protein interactions. The dimensions of the crystal unit cell can be systematically redesigned while retaining the space group symmetry and overall architecture, and the crystals are extremely porous and highly stable. Our approach enables the computational design of protein crystals with high accuracy, and the designed protein crystals, which have both structural and assembly information encoded in their primary sequences, provide a powerful platform for biological materials engineering.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Archeological wood conservation with selected organosilicon compounds studied by XFM and nanoindentation

Waterlogged wood conservation is a complex and challenging task. Detailed knowledge about the interactions between the applied chemicals and wood is necessary to ensure the effective and safe conservation of wooden artifacts. The present research aims to determine the mechanism of dimensional stabilization of archeological wood by organosilicon compounds using the combination of synchrotron-based X-ray fluorescence microscopy (XFM) and nanoindentation. Archeological oak wood was treated with methyltrimethoxysilane, (3-mercaptopropyl)trimethoxysilane, or 1,3-bis-[(diethylamino)-3-(propoxy)propan-2-ol]-1,1,3,3-tetramethyldisiloxane, which in previous studies were found to be more effective than other organosilicons in stabilizing wood dimensions. The XFM and nanoindentation results showed that all three organosilicons infiltrated wood cell walls and enhanced their mechanical properties. The XFM also showed that part of the chemicals filled some void spaces like cell lumina. Based on the results obtained here and in our previous research, it is determined that the mechanism of archeological wood dimensional stabilization by organosilicon treatment is complex and likely involves both filling cell lumina and infiltration into cell walls where organosilicons interact with wood polymers.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Global plant trait relationships extend to the climatic extremes of the tundra biome

The majority of variation in six traits critical to the growth, survival and reproduction of plant species is thought to be organised along just two dimensions, corresponding to strategies of plant size and resource acquisition. However, it is unknown whether global plant trait relationships extend to climatic extremes, and if these interspecific relationships are confounded by trait variation within species. We test whether trait relationships extend to the cold extremes of life on Earth using the largest database of tundra plant traits yet compiled. We show that tundra plants demonstrate remarkably similar resource economic traits, but not size traits, compared to global distributions, and exhibit the same two dimensions of trait variation. Three quarters of trait variation occurs among species, mirroring global estimates of interspecific trait variation. Plant trait relationships are thus generalizable to the edge of global trait-space, informing prediction of plant community change in a warming world.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Massively parallel quantum chemical density matrix renormalization group method

Here, we present, to the best of our knowledge, the first attempt to exploit the supercomputer platform for quantum chemical density matrix renormalization group (QCDMRG) calculations. We have developed the parallel scheme based on the in-house MPI global memory library, which combines operator and symmetry sector parallelisms, and tested its performance on three different molecules, all typical candidates for QC-DMRG calculations. In case of the largest calculation, which is the nitrogenase FeMo cofactor cluster with the active space comprising 113 electrons in 76 orbitals and bond dimension equal to 6000, our parallel approach scales up to approximately 2000 CPU cores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Geometric Delocalization in Two Dimensions

We demonstrate the existence of transient two-dimensional surfaces where a random-walking particle escapes to infinity in contrast to localization in standard flat two-dimensional space. We first prove that any rotationally symmetric two-dimensional membrane embedded in flat three-dimensional space cannot be transient. Then we formulate a criterion for the transience of a general asymmetric two-dimensional membrane. We use it to explicitly construct a class of transient two-dimensional manifolds with a nontrivial metric and height function but “zero average curvature,” which we dub “tablecloth manifolds.” The absence of the logarithmic infrared divergence of the Laplace-Beltrami operator in turn implies the absence of weak localization, nonexistence of bound states in shallow potentials, and breakdown of the Mermin-Wagner theorem and Kosterlitz-Thouless transition on the tablecloth manifolds, which may be realizable in both quantum simulators and corrugated two-dimensional materials.

Anderson localization↗
DOE OSTI2022

Geometrically stabilized skyrmionic vortex in FeGe tetrahedral nanoparticles

The concept of topology has dramatically expanded the research landscape of magnetism, leading to the discovery of numerous magnetic textures with intriguing topological properties. A magnetic skyrmion is an emergent topological magnetic texture with a string-like structure in three dimensions and a disk-like structure in one and two dimensions. Skyrmions in zero dimensions have remained elusive due to challenges from many competing orders. Here, by combining electron holography and micromagnetic simulations, we uncover the real-space magnetic configurations of a skyrmionic vortex structure confined in a B20-type FeGe tetrahedral nanoparticle. An isolated skyrmionic vortex forms at the ground state and this texture shows excellent robustness against temperature without applying a magnetic field. Furthermore, our findings shed light on zero-dimensional geometrical confinement as a route to engineer and manipulate individual skyrmionic metastructures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Filamentation and focusing of electron beams due to interactions with plasma waves

Results of numerical modeling of the interaction of an electron beam propagating across relativistic plasma waves indicate that electron beam filamentation and focusing may occur under certain conditions. The model is based on solving the relativistic equation of motion in three dimensions for the individual electrons in a tenuous Gaussian beam, as they pass through a relativistic plasma wave. Several electron beam and plasma wave parameters were varied, and the results are summarized. One of the results is that the spacing of the electron beam filaments correlates with the wavelength of the plasma wave. The electron beam filaments appear as vertical slabs after the beam exits the plasma waves. The electron beam also compresses to a focus after it exits the plasma, and the focal distance depends on several parameters including the electron beam energy and phase velocity of the relativistic plasma wave. It is suggested that these focusing and filamentation phenomena may be the basis for diagnostics schemes for laser plasma interactions. The parameters used in the model were electron beam energies in the 5–50 keV range and plasma wave properties typical for the beat-wave produced by CO2 lasers, which correspond to the facilities available in our laboratory. The limitations of these results to lower energy density beam and plasma regimes and to higher energy density regimes will be discussed.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Causality and dimensionality in geometric scattering

We report the scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly. In the case of zero-range forces, causality leads to constraints on scattering trajectories in the geometric picture. The effect of spatial dimensionality is also investigated by considering scattering in two and three dimensions. In the geometric formulation it is found that dimensionality is encoded in the phase of the harmonic potential that appears in the geometric action.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Electrochemical reactivity of atomic and molecular species under solid-state confinement

The nanoconfinement of electrochemically-active guest species in host solid state electrode materials provides opportunities to tune mass transport between the bulk electrolyte and inner surface of the electrode, enhance electron-transfer rates, and/or improve the stability and dispersion of active material. Here, this review summarizes recent experimental and theoretical electrochemical studies of three types of nanoconfined guest species: (1) ion adsorption of electrolyte ions, (2) confined redox-active molecules, and (3) electrocatalytic reactions of confined ions/solvents and catalytic particles. The examples discussed in this review illustrate how the confinement of guest species within enclosed spaces with nanoscale dimensions – such as pores, pockets, channels, and interlayers – can lead to improved electrochemical performance.

25 ENERGY STORAGE↗
DOE OSTI2022

Conformal bootstrap deformations

We explore the space of extremal functionals in the conformal bootstrap. By recasting the bootstrap problem as a set of non-linear equations parameterized by the CFT data, we find an efficient algorithm for converging to the extremal solution corresponding to the boundary of allowed regions in the parameter space of CFTs. Furthermore, by deforming these solutions, we demonstrate that certain solutions corresponding to known theories are continuously connected. Employing these methods, we will explore the space of non-unitary CFTs in the context of modular as well as correlation function bootstrap. In two dimensions, we show that the extremal solution corresponding to the Ising model is connected to that of the Yang-Lee minimal model. By deforming this solution to three dimensions, we provide evidence that the CFT data obtained in this way is compatible with the E-expansion for a non-unitary theory

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Interaction of extended dislocations with nanovoid clusters

Voids of nanoscale dimensions in irradiated metals can act as obstacles to dislocation motion and cause strengthening. In this work, nanovoid strengthening and the influences of void size, void spacing and material properties, such as stacking fault energies, on dislocation bypass mechanisms are investigated using Phase Field Dislocation Dynamics, a three-dimensional mesoscale model that predicts the minimum energy pathway taken by discrete dislocations. A broad range of face centered cubic metals (copper, nickel, silver, rhodium, and platinum) and nanovoid sizes and spacings are treated, altogether spanning void size–to–dislocation stacking fault width ratios from less than unity to ten. Material γ-surfaces, calculated from ab initio methods, are input directly into the formulation. The analysis reveals that the critical bypass stress scales linearly with the linear void fraction, effective isotropic shear modulus, and ratio of the intrinsic to unstable stacking fault energies. With only a few exceptions, the critical stress is controlled by the stress required for the leading partial to impinge the voids (to move within range of the attractive image stress field of the void). When the void diameter is nearly an order of magnitude greater than the stacking fault width, the mechanism determining critical strength shifts to the stress for the dislocation to breakaway after partially cutting the void. Furthermore, this situation corresponds to that treated by line tension models and is realized here for Pt, with a sub-nanometer stacking fault width.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Model-predictive optimal control of ferrofluidic microrobots in three-dimensional space

Ferrofluid microrobots have emerged as promising tools for minimally invasive medical procedures. Their unique properties to navigate complex fluids and reach otherwise inaccessible regions of the human body have enabled new applications in targeted drug delivery, tissue engineering, and diagnostics. Here, this paper proposes a model-predictive controller for the external magnetic manipulation of ferrofluid microrobots in three dimensions (3D). The internal optimization routine of the controller determines appropriate changes in the applied electromagnetic field to minimize the deviation between the actual and desired trajectories of the microrobot. A linear system governing locomotion is derived and used as the equality constraints of the optimization problems associated with the feedback index. In addition to ferrofluid droplets, the controller presented in this work may be applied to other magnetically-pulled microrobots. Several experiments are performed to validate the controller and showcase its ability to adapt to changes in system parameters such as the desired tracking trajectory and the size, orientation, deformation, and velocity of the microrobot. The accuracy of the controller is analyzed for each experiment, and the average error is found to be within 0.25 mm for small velocities. An additional experiment is performed to demonstrate significant improvement over a PID controller that is optimally tuned using Bayesian optimization. The results presented in this paper suggest that the proposed control algorithm could enable new microrobotic capabilities in minimally invasive medical procedures, lab-on-a-chip applications, and microfluidics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

On the new universality class in structurally disordered n -vector model with long-range interactions

We study a stability boundary of a region where nontrivial critical behavior of an n-vector model with long-range power-law decaying interactions is induced by the presence of a structural disorder (e.g., weak quenched dilution). This boundary is given by the marginal dimension of the order parameter nc dependent on space dimension, d, and a control parameter of the interaction decay, σ, below which the model belongs to the new dilution-induced universality class. Exploiting the Harris criterion and recent field theoretical renormalization group results for the pure model with long-range interactions, we get nc as a three loop ɛ = 2σ – d-expansion. We provide numerical values for nc applying series resummation methods. Our results show that not only the Ising systems (n = 1) can belong to the new disorder-induced long-range universality class at d = 2 and 3.

Physics↗