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The prolongation structure of Wahlquist and Estabrook is interpreted as a connection. In this way, some geometric insight might be provided for the description of those nonlinear partial differential equations which admit soliton solutions. A new geometric property - linked to the existence of an SL(2,R) connection - is proved for the solutions of the Korteweg-de Vries equation.
Increasing the energy storage capability of ionic liquid supercapacitors will require better understanding of ion-electrode interactions. We have probed the influence of these interactions on the structure and differential capacitance of of an ionic liquid ([EMIM][BF4]) at an ideal graphite interface as a function of model accuracy. Of note, differential capacitance is determined through newly derived and validated fluctuation formulas. In terms of model accuracy, we test electrostatic techniques, electrode charging techniques, and electrolyte interatomic potentials. For electrostatic summations, we employ high cost, high fidelity techniques as well as less expensive, approximate techniques for summation in slab geometry. For electrode charging, uniform, constant-charge and environmentally responsive, constant-potential conditions are employed. For the ionic liquid, constant charge and atomically polarizable models are employed. We comment on the role of model accuracy on the structure and energetics of the electric double layer as well as on the magnitude and shape of differential capacitance.
Whereas the conventional wisdom suggests that the force between non-magnetized homogeneous, stationary, isotropic plasma, and the dust grain is only possible for the case of relative plasma–grain velocity, it is shown that stationary non-spherical asymmetric dust grain immersed in stationary, non-magnetized, isotropic plasma can experience a force caused by the grain–plasma interactions. The component of the force due to scattering of plasma particles in the limit of infinite Debye length is considered analytically. Both the particle scattering and absorption force components are modeled numerically in the limits of infinite and finite Debye length using a newly developed 2D3V Aspherical Particle-in-Cell code. The code simulates interactions of dust grain of selected non-spherical asymmetric shape with plasmas using dust shape conforming coordinates. Here, the simulations confirm the existence of the force on non-spherical asymmetric grain in stationary non-magnetized plasma and show that the plasma screening effects can lead to reversal of the force direction.
The effect of a power law gravity field on baroclinic instability is examined, with a focus on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by a dielectric force. Growth rates are obtained of unstable normal modes as a function of parameters of the problem by solving a second order differential equation numerically. It is concluded that over the range of parameter space explored, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as parameter.
The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.
The differential equations governing the propagation of sound in a variable area duct or nozzle carrying a one-dimensional subsonic compressible fluid flow are derived and put in state variable form using acoustic pressure and particle velocity as the state variables. The duct or nozzle is divided into a number of regions. The region size is selected so that in each region the Mach number can be assumed constant and the area variation can be approximated by an exponential area variation. Consequently, the state variable equation in each region has constant coefficients. The transmission matrix for each region is obtained by solving the constant coefficient acoustic state variable differential equation. The transmission matrix for the duct or nozzle is the product of the individual transmission matrices of each region. Solutions are presented for several geometries with and without mean flow.
The high resolution and near global coverage of Magellan radar images is facilitating attempts to systematically investigate the stresses that have deformed the venusian crust. Here we continue earlier efforts to utilize approximately 170 large, radially lineated structures interpreted as dike swarms to assess the orientation of the regional maximum horizontal compressive stress (MHCS) which existed in their vicinities during emplacement. Examination of swarms near the equator reveals a link to broad scale regional structures, such as Aphrodite Terra, across distances in excess of 1000 km, suggesting the existence of first order stress fields which affect areas of more than 10(exp 6) sq km in a uniform fashion. Focusing further upon the Aphrodite Terra region, the MHCS field in the surrounding lowlands inferred from radial swarms is oriented approximately normal to the slope of the highland topography. This stress configuration appears, at a simple level, to be incompatible with that expected during either upwelling or downwelling construction of the highlands. In addition, the relatively undeformed geometry of the radial structures within the highlands implies that these dike swarm features formed more recently than their highly deformed surroundings. We conclude that the differential stresses which existed during emplacement of the dike swarms within and adjacent to the Aphrodite Terra highlands are related to the gravitational relaxation of pre-existing topography.
Proposed novel looms used to make fabric preforms for complex structural elements, both stiffening elements and skin, from continuous fiber-reinforced composite material. Components of looms include custom reed and differential fabric takeup system. Structural parts made best explained by reference to curved "I" cross-section frame. Technology not limited to these fiber orientations or geometry; fiber angles, frame radius of curvature, frame height, and flange width changed along length of structure. Weaving technology equally applicable to structural skins, such as wing of fuselage skins.
Direct air capture (DAC) systems often consist of packing material wetted by a capture fluid that reacts with CO 2 in the airstream. The efficiency of the contactor is determined by a complex relationship of fluid dynamics, heat and mass transfer, contactor geometry, and chemical properties. The efficiency of the contactor must be balanced with other factors, primarily pressure drop through the system. Triply periodic minimal surfaces (TPMS) are a class of differential surfaces that have been explored in multiple engineering applications and have been shown to exhibit excellent performance when used in heat exchangers. Their tortuous path provides a high surface-to-volume ratio and favorable trade-off between contact area and pressure drop. In this work, a gyroid-type TPMS contactor was evaluated using computational fluid dynamics for a variety of geometric parameters to explore the potential benefit of TPMS shapes for DAC applications. A thin-film model was employed to model the flow and distribution of the capture solvent, allowing efficient simulations of TPMS structures at scale by eliminating the need for a computationally intensive interface capturing method. A liquid-gas mass transfer model was implemented in the commercial software STAR-CCM+ and used to predict the CO 2 capture efficiency and study the trade-off between capture performance and pressure drop through analysis of capture rates, mass transfer coefficients, and other relevant variables. TPMS contactors with a variety of geometric parameters and two capture solvent options were investigated to determine the effect of design choices on the operational performance of DAC systems. In conclusion, results showed that while contactor geometry is the dominant factor in efficiency and pressure drop, the physiochemical properties of the solvent are an important secondary influence on the contactor performance.
This report describes an efficient and robust voxel-based methodology for computing the medial axis, local thickness, and distance-to-skeleton of arbitrary three-dimensional geometries. It is assumed that the object can be represented by an exact or approximate signed distance function on a discrete grid. The gradient of such function is used to formulate a hyperbolic partial differential equation (PDE) that models the collapse of the position vector in space. By exploiting the causality property of the PDE, the Fast Sweeping Method is able to obtain the solution in a finite number of sweeps independent of the mesh resolution. The intersection of characteristic lines leads to the formation of shocks and a discrete bisector function is used to identify the medial axis. The same PDE approach is used to compute the local thickness inside the object and obtain the distance-to-skeleton field. Multiple examples are given in two and three dimensions along with a resolution study. The methodology has optimal complexity and yields subsecond computational times for geometries with over a million zones on a single core. The methodology is also capable of parallelization across shared and distributed memory architectures.
It is shown in this work how to obtain the probabilities of photons escaping from a cold electron plasma environment after having undergone an arbitrary number of scatterings. This is done by retaining the exact differential cross section for Thomson scattering as opposed to using its polarization and angle averaged form. The results are given in the form of recursion relations. The geometry used is the semi-infinite plane-parallel geometry witlh a photon source located on a plane at an arbitrary optical depth below the surface. Analytical expressions are given for the probabilities which are accurate over a wide range of initial optical depth. These results can be used to model compact X-ray galactic sources which are surrounded by an electron-rich plasma.
Topics include: Coherent Frequency Reference System for the NASA Deep Space Network; Diamond Heat-Spreader for Submillimeter-Wave Frequency Multipliers; 180-GHz I-Q Second Harmonic Resistive Mixer MMIC; Ultra-Low-Noise W-Band MMIC Detector Modules; 338-GHz Semiconductor Amplifier Module; Power Amplifier Module with 734-mW Continuous Wave Output Power; Multiple Differential-Amplifier MMICs Embedded in Waveguides; Rapid Corner Detection Using FPGAs; Special Component Designs for Differential-Amplifier MMICs; Multi-Stage System for Automatic Target Recognition; Single-Receiver GPS Phase Bias Resolution; Ultra-Wideband Angle-of-Arrival Tracking Systems; Update on Waveguide-Embedded Differential MMIC Amplifiers; Automation Framework for Flight Dynamics Products Generation; Product Operations Status Summary Metrics; Mars Terrain Generation; Application-Controlled Parallel Asynchronous Input/Output Utility; Planetary Image Geometry Library; Propulsion Design With Freeform Fabrication (PDFF); Economical Fabrication of Thick-Section Ceramic Matrix Composites; Process for Making a Noble Metal on Tin Oxide Catalyst; Stacked Corrugated Horn Rings; Refinements in an Mg/MgH2/H2O-Based Hydrogen Generator; Continuous/Batch Mg/MgH2/H2O-Based Hydrogen Generator; Strain System for the Motion Base Shuttle Mission Simulator; Ko Displacement Theory for Structural Shape Predictions; Pyrotechnic Actuator for Retracting Tubes Between MSL Subsystems; Surface-Enhanced X-Ray Fluorescence; Infrared Sensor on Unmanned Aircraft Transmits Time-Critical Wildfire Data; and Slopes To Prevent Trapping of Bubbles in Microfluidic Channels.
An experimental investigation of boundary-layer transition and convective surface heating on wind tunnel models that simulated aeroshells comprised of multiple blocks of thermal protection system (TPS) material has been performed. Two representative entry vehicle geometries, a sphere-cone aeroshell and a sphere-cone aeroshell, were considered. Multiple cast ceramic models of each geometry were fabricated with varying fence heights or gap depths to represent gap fillers that either protrude above, or are recessed below, the TPS blocks due to differential ablation during reentry. Wind tunnel testing was performed at Mach 6 over a range of Reynolds numbers sufficient to produce laminar, transitional, and turbulent flow. Convective surface heating and boundary-layer transition onset data were obtained using global phosphor thermography. The experimental heating data are presented herein, as are comparisons to laminar and turbulent smooth-wall heat transfer distributions from computational flow field simulations.
This Phase I report presents a comprehensive study on photophoretic flyers—innovative, ultralight, solar-powered vehicles that harness photophoretic forces generated via Knudsen pumping to achieve sustained flight in the mesosphere (50–80 km altitude). By integrating advanced materials such as nanocardboard— characterized by its extremely low areal density (~1 g/m²) and high bending stiffness—with ultrathin light-absorbing coatings, the project converts incident solar radiation directly into a directed thrust. Extensive experimental investigations, coupled with high-fidelity computational fluid dynamics (CFD) simulations using ANSYS Fluent, validate the concept across various three-dimensional geometries, including spherical, conical, and rocket-shaped configurations. These simulations bridge the gap between free-molecular and continuum flow regimes, demonstrating that optimized designs can generate lift forces sufficient to support kilogram-scale payloads even in low-pressure environments. At the heart of this innovation is the use of Knudsen pumping, where temperature gradients across porous surfaces induce directional gas flow, creating a modest overpressure that provides lift. The report introduces an analytical framework that interpolates between the well-known low-Reynolds number drag regime and the high-Reynolds number momentum theory. This model accurately predicts lift based on design parameters such as microchannel dimensions, porous wall geometry, areal density, and nozzle exit area. For instance, simulations indicate that 10-meter-scale structures with carefully engineered porous walls can achieve the necessary pressure differential to support scientifically significant payloads (~1 kg). The study also explores a hybrid propulsion approach that combines solar buoyancy with photophoretic lift. Initially, solar heating creates a buoyant force that elevates the flyer to mesospheric altitudes. Once in the optimal pressure range, the photophoretic mechanism—powered by Knudsen pumping—takes over as the primary source of lift, ensuring stable, long-duration flight. This dual-mode operation not only facilitates the deployment of photophoretic flyers but also broadens the potential applications for mesospheric exploration. In addition to propulsion, the report investigates the integration of photophoretic thrusters for trajectory control of existing research balloons in the upper stratosphere. By dynamically adjusting the nozzle orientation and controlling the flow-through velocity, these thrusters provide precise maneuverability, enabling the flyers to counteract atmospheric disturbances and adjust their flight paths in real time. For example, a photophoretic thruster approximately 7.5 by 7.5 meters in size could be unfolded below a payload gondola of a 60 million-cubic-foot zero-pressure balloon. Such a thruster can provide horizontal speed control of approximately 1 m/s using only sunlight and no moving parts (except those needed to track the Sun and control the jet direction). Importantly, photophoretic thrusters operate more efficiently at higher altitudes, which is complementary to known trajectory control techniques, such as propellers and tethered wings, which are more effective at lower altitudes. Finally, the report identifies three scientific research thrusts where mesospheric aircraft technology can have a profound impact: atmospheric tides, characterization of gravity waves, and investigation of mesospheric instabilities. Overall, the findings of this Phase I project represent a significant advancement in photophoretic propulsion technology. By demonstrating that large-scale, ultralight structures can be powered solely by solar radiation—via carefully engineered Knudsen pumping—this work lays a robust foundation for scalable, near-space flight architectures. Future refinements in material fabrication, structural optimization, and integrated trajectory control are expected to further enhance performance, paving the way for operational demonstrations that could revolutionize atmospheric science, remote sensing, and communication networks.
It is shown that the space of sequences of length n which have an extrapolation of McMillan degree k, and no extrapolations of lower McMillan degree can be given the structure of a differentiable manifold. This approach makes the proof of certain known results on the partial realization problem quite straightforward and makes it possible to establish some important new results as well. A key tool is the fact, proven here, that the set of n by a real Hankel matrices of rank r is a manifold with r+1 connected components.
With recent computed tomography (CT) efforts using Artificial Intelligence (AI) and Deep Learning (DL)techniques, there is a strong need for differentiable forward projection models that can be integrated into existing DL frameworks. We developed a pytorch-based package library providing differentiable forward and back projection functions and classes to facilitate forward and back propagation of CT operations in the training procedure. This forward projectors support three CT projection geometries: cone, parallel and modular beams. This package can be used with both CPU and GPU with CUDA.
Computational results of shock waves impinging on targets and the ensuing diffraction flowfield are presented. A number of two-dimensional cases are computed with finite difference techniques. The classical case of a shock wave/cylinder interaction is compared with shock tube data and shows the quality of the computations on a pressure-time plot. Similar results are obtained for a shock wave/rectangular body interaction. Here resolution becomes important and the use of grid clustering techniques tend to show good agreement with experimental data. Computational results are also compared with pressure data resulting from shock impingement experiments for a complicated truck-like geometry. Here of significance are the grid generation and clustering techniques used. For these very complicated bodies, grids are generated by numerically solving a set of elliptic partial differential equations.
A particularly favorable radial lineup between spacecraft in Earth orbit and Pioneers 10 and 11 (near the ecliptic plane at approximately 5.5 AU and approximately 4.5 AU, respectively) occurred in mid-1974, when the solar corona was in a stable and well-defined warped-dipole configuration. The radial alignment study reported here differs from previous applications of the technique in two respects: (1) It is the first time a two-dimensional (2-D) MHD model has been tested over such a lengthy propagation interval; the 2-D capability is crucial for treatment of the nonradial shearing motions occurring across the stream interface. (2) The three-dimensional (3-D) structure observed in the white light corona at that time is related to the systematic patterns of nonradial flow deflections appearing at the Pioneer corotating interaction region (CIR) fronts. Comparison of predicted and observed flows for pairs of streams in two successive rotations reveals that when the parent coronal hole projects far across the solar equator in a predominantly north-south orientation (i.e., nearest the 2-D idealization), the mapping is accurate down to details of the flow structures. But where the spacecraft tracks along a latitudinal boundary of a hole or the associated stream front is inclined at a shallow angle to the equator, the numerical projections deviate systematically from the observations. Among the sources of error are 3-D dynamical interactions neglected in the model, differential rotation effects, and slow temporal evolution of the coronal structures. A characteristic pattern of north-south and east-west deflections indicative of the 3-D geometry appears across the CIRs, but these patterns evidently reflect primarily the local, as opposed to global, orientation of the 3-D stream fronts. Such patterns appear common in CIRs observed by Pioneer during this period. These findings thus hold special relevance for the analysis of Ulysses observations, since the present coronal configuration is similar to that of 1974.