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At least 253 records · Page 14

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. Previous derivations of these matrices have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The present work derives differentiating matrices on grids with arbitrarily spaced points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids through the expedient of including 'near boundary' points. Use of the differentiating matrix as an operator in the solution of problems involving ordinary differential equations is also considered.

Lakin, W. D.↗

Radiation-Hard SpaceWire/Gigabit Ethernet-Compatible Transponder

A radiation-hard transponder was developed utilizing submicron/nanotechnology from IBM. The device consumes low power and has a low fabrication cost. This device utilizes a Plug-and-Play concept, and can be integrated into intra-satellite networks, supporting SpaceWire and Gigabit Ethernet I/O. A space-qualified, 100-pin package also was developed, allowing space-qualified (class K) transponders to be delivered within a six-month time frame. The novel, optical, radiation-tolerant transponder was implemented as a standalone board, containing the transponder ASIC (application specific integrated circuit) and optical module, with an FPGA (field-programmable gate array) friendly parallel interface. It features improved radiation tolerance; high-data-rate, low-power consumption; and advanced functionality. The transponder utilizes a patented current mode logic library of radiation-hardened-by-architecture cells. The transponder was developed, fabricated, and radhard tested up to 1 MRad. It was fabricated using 90-nm CMOS (complementary metal oxide semiconductor) 9 SF process from IBM, and incorporates full BIT circuitry, allowing a loop back test. The low-speed parallel LVCMOS (lowvoltage complementary metal oxide semiconductor) bus is compatible with Actel FPGA. The output LVDS (low-voltage differential signaling) interface operates up to 1.5 Gb/s. Built-in CDR (clock-data recovery) circuitry provides robust synchronization and incorporates two alarm signals such as synch loss and signal loss. The ultra-linear peak detector scheme allows on-line control of the amplitude of the input signal. Power consumption is less than 300 mW. The developed transponder with a 1.25 Gb/s serial data rate incorporates a 10-to-1 serializer with an internal clock multiplication unit and a 10-1 deserializer with internal clock and data recovery block, which can operate with 8B10B encoded signals. Three loop-back test modes are provided to facilitate the built-in-test functionality. The design is based on a proprietary library of differential current switching logic cells implemented in the standard 90-nm CMOS 9SF technology from IBM. The proprietary low-power LVDS physical interface is fully compatible with the SpaceWire standard, and can be directly connected to the SFP MSA (small form factor pluggable Multiple Source Agreement) optical transponder. The low-speed parallel interfaces are fully compatible with the standard 1.8 V CMOS input/output devices. The utilized proprietary annular CMOS layout structures provide TID tolerance above 1.2 MRad. The complete chip consumes less than 150 mW of power from a single 1.8-V positive supply source.

Katzman, Vladimir↗

Liouville operators over the Hardy space

The role of Liouville operators in the study of dynamical systems through the use of occupation measures has been an active area of research in control theory over the past decade. This article investigates Liouville operators over the Hardy space, which encode complex ordinary differential equations in an operator over a reproducing kernel Hilbert space.

97 MATHEMATICS AND COMPUTING↗

RWPV bioreactor mass transport: earth-based and in microgravity

Mass transport and mixing of perfused scalar quantities in the NASA Rotating Wall Perfused Vessel bioreactor are studied using numerical models of the flow field and scalar concentration field. Operating conditions typical of both microgravity and ground-based cell cultures are studied to determine the expected vessel performance for both flight and ground-based control experiments. Results are presented for the transport of oxygen with cell densities and consumption rates typical of colon cancer cells cultured in the RWPV. The transport and mixing characteristics are first investigated with a step change in the perfusion inlet concentration by computing the time histories of the time to exceed 10% inlet concentration. The effects of a uniform cell utilization rate are then investigated with time histories of the outlet concentration, volume average concentration, and volume fraction starved. It is found that the operating conditions used in microgravity produce results that are quite different then those for ground-based conditions. Mixing times for microgravity conditions are significantly shorter than those for ground-based operation. Increasing the differential rotation rates (microgravity) increases the mixing and transport, while increasing the mean rotation rate (ground-based) suppresses both. Increasing perfusion rates enhances mass transport for both microgravity and ground-based cases, however, for the present range of operating conditions, above 5-10 cc/min there are diminishing returns as much of the inlet fluid is transported directly to the perfusion exit. The results show that exit concentration is not a good indicator of the concentration distributions in the vessel. In microgravity conditions, the NASA RWPV bioreactor with the viscous pump has been shown to provide an environment that is well mixed. Even when operated near the theoretical minimum perfusion rates, only a small fraction of the volume provides less than the required oxygen levels. 2002 Wiley Periodicals, Inc.

Models, Biological↗

Differential current driver

Three operational amplifiers in closed-loop configuration, form stable current driver for variable non-ground-reference loads. Circuit uses lower-voltage power supplies than other circuits of this type, and provides constant voltage-to-current gain in low noise configuration. Additional reactive elements could offer frequency compensation for complex loads.

Kopp, G. F.↗

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗

Detailed study of the eikonal reaction theory for the breakup of one-neutron halo nuclei

Background: One-neutron removal reactions are used to study the single-particle structure of unstable nuclei, and in particular the exotic halo nuclei. The eikonal reaction theory (ERT) has been developed by Yahiro, Ogata, and Minomo [Prog. Theor. Phys. 126, 167 (2011)] to include dynamical effects, which are missing in the usual eikonal description of these reactions. Encouraging results have been obtained for total breakup cross sections in comparison to more elaborate reaction models. Purpose: Here, we extend these comparisons to more differential breakup cross sections expressed as functions of the relative energy or parallel momentum between the core and halo neutron. Method: ERT predictions of these cross sections are compared to state-of-the-art calculations. Results: The hypotheses upon which the ERT is based are confirmed and their range of validity is made clearer. The actual ordering of the evolution operators affects ERT differential cross sections and a specific choice leads to excellent agreement with the reference calculation. Dynamical effects in the treatment of the neutron-target interaction can be significant in the parallel-momentum observable. Conclusions: The role of the different interactions in the dynamics of breakup reactions of one-neutron halo nuclei are better understood and improvements to the ERT are suggested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Fast Multigrid Techniques in Total Variation-Based Image Reconstruction

Existing multigrid techniques are used to effect an efficient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-differential equation which, when discretized using cell-centered finite differences, yields a full matrix equation. A fixed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the differential operator. With effective preconditioning, the method presented seems to require Omicron(n) operations. Numerical results are given for a two-dimensional example.

Oman, Mary Ellen↗

Operability thresholds for thermally damaged EBW detonators

Operability thresholds that differentiate between functional RP-87 exploding bridge wire (EBW) detonators and nonfunctional RP-87 EBW detonators (duds) were determined by measuring the time delay between initiation and early wall movement (function time). The detonators were inserted into an externally heated hollow cylinder of aluminum and fired with current flow from a charged capacitor using an exploding bridge wire (EBW initiated). Functioning detonators responded like unheated pristine detonators when the function time was 4 μs or less. The operability thresholds of the detonators were characterized with a simple decomposition cookoff model calibrated using a modified version of the Sandia Instrumented Thermal Ignition (SITI) experiment. These thresholds are based on the calculated state of the PETN when the detonators fire. The operability threshold is proportional to the positive temperature difference (ΔT) between the maximum temperature within the PETN and the onset of decomposition (~406 K). Furthermore, the temperature difference alone was not sufficient to define the operability threshold. The operability threshold was also proportional to the time that the PETN had been at elevated temperatures. That is, failure was proportional to both temperature and reaction rate. The reacted gas fraction is used in the current work for the reaction correlation. Melting of PETN also had a significant effect on the operability threshold. Detonator failure occurred when the maximum temperature exceeded the nominal melting point of PETN (414 K) for 45±5 s or more.

42 ENGINEERING↗

On the differential representation and color-kinematics duality of AdS boundary correlators

The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory. We show that tree-level AdS boundary correlators for generic states can be expressed as nonlocal differential operators of a certain structure acting on contact Witten diagrams. We further write the boundary correlators in a form that is very similar to flat space amplitudes, with Mandelstam variables replaced by certain combinations of single-state conformal generators, prove that all tree-level AdS boundary correlators have a differential representation, and detail the conversion of such differential expressions to position space. We illustrate the construction through the computation of the boundary correlators of scalars coupled to gluons and gravitons; when converted to position space, they reproduce known results. Color-kinematics duality and BCJ relations can be defined in analogy with their flat space counterparts, and are respected by the scalar correlators with a gluon exchange. We also discuss potential approaches to the double copy and find that its direct generalization may require nontrivial extensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Visualization of Two-phase Flow Maldistribution in Brazed Plate Heat Exchangers

Brazed plate heat exchangers (BPHEs) are widely used in refrigeration and HVAC applications, but are susceptible to two-phase flow maldistribution especially when operated as evaporators. Existing visualization approaches are either limited to idealized conditions or suffer from poor optical transparency. This paper presents a novel visualization method in which one edge of a BPHE, parallel to the refrigerant inlet or outlet port, is removed by wire electrical discharge machining and replaced with a flat, transparent plate. The planar geometry allows the use of optically and infrared (IR)-transparent materials, enabling both high-speed videography and IR thermography of the two-phase flow at the channel entrances and exits. Preliminary tests with R134a and R1234ze(Z) at saturation temperatures between 5 °C and 15 °C demonstrate that distinct two-phase flow patterns in the inlet header can be clearly identified and differentiated under realistic operating conditions. Potentials of optical flow analysis of high-speed videos are shown to provide objective, quantitative indicators for flow regime characterization and comparison. IR imaging of the outlet port reveals non-uniform temperature distributions at the channel exits, providing independent evidence of maldistribution across the channel stack. Limitations of IR temperature accuracy due to the spectral properties of the sapphire window are discussed, and directions for improvement are identified.

Hausherr, Carsten [Technical University of Berlin ↗

Model-parallel Fourier neural operators as learned surrogates for large-scale parametric PDEs

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. Here, we demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up to 512 A100 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO 2 dynamics in the Earth’s subsurface.

58 GEOSCIENCES↗

A Prototype Real-Time Area Differential GPS System

In this paper we describe the system architecture, algorithms, and preliminary results from an operating prototype Wide Area Differential GPS (WADGPS) system spanning the continetal US (CONUS).

Prototype Wide Area↗

Evaluation of 2-μm Pulsed Integrated Path Differential Absorption Lidar for Carbon Dioxide Measurement—Technology Developments, Measurements, and Path to Space

The societal benefits of understanding climate change through the identification of global carbon dioxide sources and sinks led to the recommendation for NASA's Active Sensing of Carbon Dioxide Emissions over Nights, Days, and Seasons space-based mission for global carbon dioxide measurements. For more than 15 years, the NASA Langley Research Center has developed several carbon dioxide active remote sensors using the differential absorption lidar technique operating at 2-μm wavelength. Recently, an airborne double-pulsed integrated path differential absorption lidar was developed, tested, and validated for atmospheric carbon dioxide measurement. Results indicated 1.02% column carbon dioxide measurement uncertainty and 0.28% bias over the ocean. Currently, this technology is progressing toward triple-pulse operation targeting both atmospheric carbon dioxide and water vapor-the dominant interfering molecule on carbon dioxide remote sensing. Measurements from the double-pulse lidar and the advancement of the triple-pulse lidar development are presented. In addition, measurement simulations with a space-based IPDA lidar, incorporating new technologies, are also presented to assess feasibility of carbon dioxide measurements from space.

Singh, Upendra N.↗

Characterization of high thermal conductivity fuel surrogates before and after ion irradiation

High thermal conductivity nuclear fuels offer important potential advantages over traditional oxide-based fuels such as higher burnup, reduction in fission gas release, and better overall safety of the system. One proposed approach to high thermal conductivity fuels utilizes high thermal conductivity nonfissile additives with UO 2 fuel to lower the fuel operating temperature and thereby take advantage of the highly favorable radiation resistance of UO 2 at lower operating temperatures. However, differential swelling in the matrix and high conductivity additive phases during high dose irradiation could lead to internal cracking and poor performance. In the current study, ceria (CeO 2 ) and zirconia (ZrO 2 ) surrogate matrices were used to model UO2 behavior. Additives of 10 vol. % Al 2 O 3 or SiC in the form of short fibers or platelets were used for the high conductivity second phase. The nuclear fuel surrogates were sintered to achieve densities greater than 93% of the ideal values. Scanning electron microscopy (SEM) imaging and X-ray diffraction confirmed the uniform distribution of the second phase and that no intermetallic second phase was formed during sintering. The thermal conductivity of the sintered samples was measured from 50 °C to 900 °C and confirmed the desirable increase compared to pure CeO 2 /ZrO 2 pellets. Samples were irradiated with 20 MeV Ni 6+ ions at midrange doses ranging from 1 to 15 displacements per atom (dpa) and temperatures from 300 °C to 700 °C. Post irradiation characterization revealed a good stability of the samples at low to medium doses with matrix lattice parameter swelling of < 0.14 % but showed a significant microstructural deterioration and decrease of the mechanical properties at 15 dpa.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks

We employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.

97 MATHEMATICS AND COMPUTING↗