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A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.
The circulation functional relative to two adjacent lifting sections is studied for two cases. In the first case we consider two adjacent circles. The circulation is computed as a function of the displacement of the secondary circle along the axis joining the two centers and of the angle of attack of the secondary circle, The gradient of such functional is computed by deriving a set of elliptic functions with respect both to their argument and to their Period. In the second case studied, we considered a wing-flap configuration. The circulation is computed by some implicit mappings, whose differentials with respect to the variation of the geometrical configuration in the physical space are found by divided differences. Configurations giving rise to local maxima and minima in the circulation manifold are presented.
The gapped symmetric phase of the Affleck-Kennedy-Lieb-Tasaki model exhibits fractionalized spins at the ends of an open chain. Here, we show that breaking SU(2) symmetry and applying a global spin-lowering dissipator achieves synchronization of these fractionalized spins. Additional local dissipators ensure convergence to the ground state manifold. In order to understand which aspects of this synchronization are robust within the entire Haldane-gap phase, we reduce the biquadratic term, which eliminates the need for an external field but destabilizes synchronization. Within the ground state subspace, stability is regained using only the global lowering dissipator. These results demonstrate that fractionalized degrees of freedom can be synchronized in extended systems with a significant degree of robustness arising from topological protection. A direct consequence is that permutation symmetries are not required for the dynamics to be synchronized, representing a clear advantage of topological synchronization compared to synchronization induced by permutation symmetries.
A primary challenge of low-thrust mission design is the development of an initial guess for the state and control history of a trajectory. To address this challenge, one technique assembles dynamical structures, such as periodic orbits and their associated manifolds, into discontinuous chains that are corrected to locally optimal transfer solutions via direct transcription. In this investigation, dynamical structures that leverage low-thrust in a multi-body regime are incorporated into the orbit chain approach to expand the options available for construction of an initial guess and to guide the direct transcription algorithm toward different categories of locally optimal solutions. The properties and structures of the low-thrust model which facilitate orbit chain construction are demonstrated in representative transfer scenarios. Direct transcription is applied to converge upon locally optimal transfer trajectories in both simplified and ephemeris models. Results indicate that low-thrust dynamical structures offer a promising new catalog of options for use in the orbit chain approach to designing optimal low-thrust trajectories.
Microscopy combined with local spectroscopy is widely used to correlate nanoscale structure with functional properties in materials, but conventional measurements rely heavily on human-selected sampling locations and predefined targets, limiting data set diversity and the potential for discovery. Here, we present a framework that integrates autonomous microscopy with dual-novelty deep kernel learning (DN-DKL) for adaptive data acquisition and a dual variational autoencoder (VAE) for representation learning. DN-DKL actively guides the microscopy toward structurally and spectroscopically novel regions, enabling efficient collection of large spectral data sets. Dual-VAE embeds local structures and spectroscopic responses into a shared latent manifold that serves as a structure–property relationship map. We applied this framework for the investigation of halide perovskite films by using conductive atomic force microscopy. The results reveal distinct hysteresis behaviors that are linked to specific nanoscale structural motifs, including grain boundary junction points that show hysteresis under different bias conditions and asymmetric grain boundaries that suppress the charge transport. This framework establishes a general strategy that leverages the complementary strengths of self-driving microscopy, machine learning, and human expertise to accelerate scientific discovery in functional materials.
The current Space Shuttle Main Engine hot-gas manifold configuration contains three transfer ducts connecting the fuel bowl and the main injector torus. For the current study, a new hot-gas manifold was designed to improve on a previously tested two-duct concept. This was accomplished by eliminating separated flow regions, reducing local velocities, and providing as uniform a flowfield as possible. The two-duct hot-gas manifold tested in this study showed significant improvement over the existing three-duct design. The circumferential pressure gradient was reduced by 67 percent. The system total pressure loss from the discharge of the 180-degree turn to the transfer duct exit was 60 percent less than with the three duct hot gas manifold. Although only limited fluctuating pressure data were taken in the main injector, indications are that the environment there has been improved.
A variable time step algorithm has been implemented for solving the stochastic equations of motion for gas-surface collisions. It has been tested for a simple model of electronically inelastic collisions with an insulator surface in which the phonon manifold acts as a heat bath and electronic states are localized. In addition to reproducing the accurate nuclear dynamics of the surface atoms, numerical calculations have shown the algorithm to yield accurate ensemble averages of physical observables such as electronic transition probabilities and total energy loss of the gas atom to the surface. This new algorithm offers a gain in efficieny of up to an order of magnitude compared to fixed time step integration.
The structural analysis of the Advanced Main Combustion Chamber (AMCC) is presented. The AMCC is an advanced fabrication concept of the Space Shuttle Main Engine main combustion chamber (MCC). Reduced cost and fabrication time of up to 75 percent were the goals of the AMCC with cast jacket with vacuum plasma sprayed or platelet liner. Since the cast material for the AMCC is much weaker than the wrought material for the MCC, the AMCC is heavier and strength margins much lower in some areas. Proven hand solutions were used to size the manifolds cutout tee areas for combined pressure and applied loads. Detailed finite element strength analyses were used to size the manifolds, longitudinal ribs, and jacket for combined pressure and applied local loads. The design of the gimbal actuator strut attachment lugs were determined by finite element analyses and hand solutions.
In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.
The Geostationary Synthetic Thinned Aperture Radiometer (GeoSTAR) team recently concluded its second Earth Science Technology Office (ESTO) IIP-07, "GeoSTAR technology development and risk reduction for PATH". The major accomplishments during this project at JPL were:1) Demonstrate performance and scalability of the 183 GHz receivers 2) Local oscillator phasing architecture and technology 3) Subarray design validation including feedhorns, manifolds and alignment 4) System demonstration of signal distribution topology and measurements. Significant progress has been made to retiring risk of the various subsystems.
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.
The α-vacua are a 1-parameter family of quantum field vacua in de Sitter space which are invariant under the isometry group SO(1, d). In this work give a path integral construction of the de Sitter α-vacua. We explain that these states can be prepared by acting on the Bunch-Davies vacuum with a certain non-local charge operator. While most conserved charges live on a single codimension-1 manifold, we show that this particular charge lives on a pair of two codimension-1 manifolds which are antipodal mirrors of each other. The rules for the manipulation of this charge as an insertion in the path integral are explained. We further explain how this charge can be used to solve for the wavefunctionals of the α-vacua at $\mathcal{I}$ | (in the regime that α is small) by deforming the equator of de Sitter space to $\mathcal{I}$ + /$\mathcal{I}$ – .
In this work, we propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial state, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. We prove that fast mixing at low temperature for the two-dimensional toric code can be achieved by augmenting local jump operators with simple global jump operators, which enable efficient transitions between logical sectors. To establish tight lower bounds on the spectral gap, we introduce a new reduction method that eventually maps the problem to estimating the spectral gap of a perturbed graph Laplacian on a stair graph. Our proof also shows that the Lindblad dynamics with a digitally implemented low-temperature local Davies generator is able to efficiently drive the quantum state toward the ground state manifold.
A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using both canonical and non-canonical Hamiltonian formulations. Our schemes apply to both formulations, but the canonical formulation results in a particularly efficient scheme that also conserves particle density and energy exactly. The collisionless update is coupled to a Bhatnagar-Gross-Krook (BGK) collision operator that provides a simplified model for relaxation to local thermodynamic equilibrium. An iterative scheme is constructed to ensure collisional invariants (density, momentum and energy) are preserved numerically. Rotation of the manifold is incorporated by modifying the Hamiltonian while ensuring a canonical formulation. Several test problems, including a kinetic version of the classical Sod shock problem, Kelvin-Helmholtz instability on the surfaces of a sphere and a hyperboloid, with and without rotations, are presented. A prospectus for further development of this approach to simulation of kinetic theory in general relativity is presented.
High-resolution SEM images of uranium-oxide powders encode micro- and nanoscale clues to their synthesis route and calcination temperature. We trained a ResNet-50 model on 11 commercial-scale U₃O₈ classes, ammonium diuranate (ADU) or uranyl peroxide (H₂O₂) precursors calcined at temperatures ranging from 400 to 750 °C and added a 256-D projection head before the classifier to analyze the learned representation. The best of eight seeds reached 92.4 % accuracy on reserved testing data, but our focus is the structure of the embedding space rather than the accuracy and labels. We quantify class relatedness in the original 256-D space using centroid similarity and distributional distances, and we use Uniform Manifold Approximation Projection (UMAP) for visualization. ‘Unknown’ images from different preparation methods, SEM operators, and from the literature localized near the expected classes under a nearest-centroid analysis without retraining, as well as clustered in similar UMAP space. In conclusion, this embedding-centered workflow complements black-box classification by providing quantitative, similarity-based comparisons of U₃O₈ morphologies and reduces storage space by up to 98 % for image data used in millisecond vector search comparisons.
Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parametrize a manifold of zero modes and more broadly provide judicious coordinates on the space of fields. However, changing from local coordinates around a saddle point to more global collective coordinates is remarkably subtle. The main complication is that the mapping from local coordinates to collective coordinates is generically multivalued. Consequently one is forced to either restrict the domain of path integral in a delicate way, or otherwise correct for the multivaluedness by dividing the path integral by certain intersection numbers. We provide a careful treatment of how to fix collective coordinates while accounting for these intersection numbers, and then demonstrate the importance of the fix for free theories. We also provide a detailed study of the fix for interacting theories and show that the contributions of higher intersections to the path integral can be nonperturbatively suppressed. Using a variety of examples ranging from single-particle quantum mechanics to quantum field theory, we explain and resolve various pitfalls in the implementation of collective coordinates. Published by the American Physical Society 2024
The Space Shuttle Main Engine (SSME) consists of 1080 conical tubes, which are furnace brazed themselves, manifolds, and surrounding structural jacket making almost four miles of braze joints. Subsequent furnace braze cycles are performed due to localized braze voids between the coolant tubes. SSME nozzle experiences extremely high heat flux (180 mW/sq m) during hot fire. Braze voids between coolant tubes may result in hot combustion gas escape causing jacket bulges. The nozzle can be disqualified for flight or result in mission failure if the braze voids exceed the limits. Localized braze processes were considered to eliminate braze voids, however, damage to the parent materials often prohibited use of such process. Being the only manned flight reusable rocket engine, it has stringent requirement on the braze process. Poor braze quality or damage to the parent materials limits the nozzle service life. The objective of this study was to develop a laser brazing process to provide quality, localized braze joints without adverse affect on the parent materials. Gold (Au-Cu-Ni-Pd-Mn) based high temperature braze alloys were used in both powder and wire form. Thin section iron base superalloy A286 tube was used as substrate materials. Different Laser Systems including CO2 (10.6 micrometers, 1kW), ND:YAG (1.06 micrometers, 4kW). and direct diode laser (808nm. 150W) were investigated for brazing process. The laser process variables including wavelength. laser power, travel speed and angle of inclination were optimized according to bead geometry and braze alloy wetting at minimum heat input level, The properties of laser brazing were compared to that of furnace brazing. Microhardness profiles were used for braze joint property comparison between laser and furnace brazing. The cooling rate of laser brazing was compared to furnace brazing based on secondary dendritic arm spacing, Both optical and Scanning Electron Microscope (SEM) were used to evaluate the microstructures of the braze materials and tube substrate. Metallography of the laser braze joint was compared to the furnace braze. SEM Energy Disperse X-Ray Spectra (EDX) and back scattered imaging were used to analyze braze alloy segregation. Although all of the laser systems, CO2, ND:YAG, and direct diode laser produced good braze joint, the direct diode laser was selected for its system simplicity, compactness and portability. Excellent laser and braze alloy coupling is observed with powder alloy compared to braze alloy wire. Good wetting is found with different gold based braze alloys. The laser brazing process can be optimized so that the adverse affect on the parent materials can be eliminated. Metallography of the laser braze joint has shown that quality braze joint was produced with laser brazing process. Penetration of the laser braze to the substrate is at neglectable level. Zero penetration is observed. Microstructure examinations shown that no observable changes of the microstructure (grain structure and precipitation) in the HAZ area between laser braze and furnace braze. Wide gaps can be laser brazed with single pass for up to 0.024 inches. Finer dendritic structure is observed in laser brazing compared with equiaxial and coarser grain of the furnace brazing microstructure. Greater segregation is also found in the furnace braze. Higher hardness of the laser braze joint comparing to furnace braze is observed due to the fast cooling rate and Finer microstructure in the laser brazing. Laser braze joint properties meet or exceed the furnace joint properties. Direct diode laser for thin section tube brazing with high temperature braze alloys have been successfully demonstrated. The laser's high energy density and precise control has shown significant advantages in reducing process heat input to the substrates and provide high quality braze joints comparing to other localized braze process such as torch, TIG, and MPTA processes. Significant cost savings can be realized particularly with localized braze comparing to a full furnace braze cycle.
We examine domain wall formulation in late time phase transitions. We find that in the invisible axion domain wall phenomenon, thermal effects alone are insufficient to drive different parts of the disconnected vacuum manifold. This suggests that domain walls do not form unless either there is some supplemental (but perhaps not unreasonable) dynamics to localize the scalar field responsible for the phase transition to the low temperature maximum (to an extraordinary precision) before the onset of the phase transition, or there is some non-thermal mechanism to produce large fluctuations in the scalar field. The fact that domain wall production is not a robust prediction of late time transitions may suggest future directions in model building.