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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.

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DOE OSTI2024

Finite-size effects in periodic coupled cluster calculations

Here, we provide the first rigorous study of the finite-size error in the simplest and representative coupled cluster theory, namely the coupled cluster doubles (CCD) theory, for gapped periodic systems. Given exact Hartree-Fock orbitals and their corresponding orbital energies, we demonstrate that the correlation energy obtained from the approximate CCD method, after a finite number of fixed-point iterations over the amplitude equation, exhibits a finite-size error scaling as $\mathcal{O}(N^{-\frac{1}{3}}_k)$. Here $N_k$ is the number of discretization points in the Brillouin zone and characterizes the system size. Under additional assumptions ensuring the convergence of the fixed-point iterations, we demonstrate that the CCD correlation energy also exhibits a finite-size error scaling as $\mathcal{O}(N^{-\frac{1}{3}}_k)$. Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculation can be boosted to $\mathcal{O}(N^{-1}_k)$ with accurate amplitudes. This also provides the first proof of the scaling of the finite-size error in the third order Møller-Plesset perturbation theory (MP3) for periodic systems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

Digital random-number generator

For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.

Brocker, D. H.↗

DOE OSTI2022

Analysis of Vector Particle-In-Cell (VPIC) memory usage optimizations on cutting-edge computer architectures

Vector Particle-In-Cell (VPIC) is one of the fastest plasma simulation codes in the world, with particle numbers ranging from one trillion on the first petascale system, Roadrunner, to ten trillion particles on the more recent Blue Waters supercomputer. As supercomputers continue to grow rapidly in size, so too does the gap between computing capability and memory capability. Current memory systems limit VPIC simulations greatly as the maximum number of particles that can be simulated directly depends on the available memory. In this study, we present a suite of VPIC memory optimizations (i.e., particle weight, half-precision, and fixed-point optimizations) that enable a significant increase in the number of particles in VPIC simulations. Here, we assess the optimizations’ impact on memory and runtime performance for a suite of cutting-edge computer architectures such has the NVIDIA V100 GPU, the IBM Power9, and the Fujitsu A64FX architectures. Our optimizations enable a 31.25% reduction in memory usage and up to 40% increase in the number of particles. This paper extends our work on developing particle storage format optimizations Tan et al.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.

Serrallés, José Cruz [Weill Cornell Med. Coll.]↗

NASA NTRS1992

Turbulence and deterministic chaos

Deissler, Robert G.↗

NASA NTRS1980

The digital implementation of control compensators - The coefficient wordlength issue

There exist a number of mathematical procedures for designing discrete-time compensators. However, the digital implementation of these designs, with a microprocessor, for example, has not received nearly as thorough an investigation. The finite-precision nature of the digital hardware makes it necessary to choose a computational structure that will perform adequately with regard to the initial objectives of the design. This paper describes a procedure for estimating the required fixed-point coefficient wordlength for any given computational structure for the implementation of a single-input single-output LQG design. The results are compared to the actual number of bits necessary to achieve a specified performance index.

Moroney, P.↗

NASA NTRS1989

On the Nature of Navier-stokes Turbulence

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The solutions, separate exponentially with time, having a positive Liapunov exponent. Thus the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number is reduced. Several qualitatively different flows are noted. These are, fully chaotic, complex period, weakly chaotic, simple periodic, and fixed-point. Of these, only the fully chaotic flows are classified as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, is both time-dependent and aperiodic. Turbulent solutions are obtained in which energy cascades from large to small-scale motions. In general, the spectral energy transfer takes place between wavenumber bands that are considerably separated. The special transfer can occur either as a result of nonlinear turbulence self-interaction or by interaction of turbulence with mean gradients. Turbulent systems are compared with those studied in kinetic theory. The two types of systems are fundamentally different (continuous and dissipative as opposed to discrete and conservative), but there are similarities. For instance, both are nonlinear and show sensitive dependence on initial conditions. Also, the turbulent and molecular stress tensors are identical if the macroscopic velocities for the turbulent stress are replaced by molecular velocities.

Deissler, Robert G.↗

NASA NTRS1979

The digital implementation of control compensators: The coefficient wordlength issue

There exists a number of mathematical procedures for designing discrete-time compensators. However, the digital implementation of these designs, with a microprocessor for example, has not received nearly as thorough an investigation. The finite-precision nature of the digital hardware makes it necessary to choose an algorithm (computational structure) that will perform 'well-enough' with regard to the initial objectives of the design. This paper describes a procedure for estimating the required fixed-point coefficient wordlength for any given computational structure for the implementation of a single-input single-output LOG design. The results are compared to the actual number of bits necessary to achieve a specified performance index.

Moroney, P.↗

DOE OSTI2024

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1978

Desirable floating-point arithmetic and elementary functions for numerical computation

The topics considered are: (1) the base of the number system, (2) precision control, (3) number representation, (4) arithmetic operations, (5) other basic operations, (6) elementary functions, and (7) exception handling. The possibility of doing without fixed-point arithmetic is also mentioned. The specifications are intended to be entirely at the level of a programming language such as FORTRAN. The emphasis is on convenience and simplicity from the user's point of view. Conforming to such specifications would have obvious beneficial implications for the portability of numerical software, and for proving programs correct, as well as attempting to provide facilities which are most suitable for the user. The specifications are not complete in every detail, but it is intended that they be complete in spirit - some further details, especially syntatic details, would have to be provided, but the proposals are otherwise relatively complete.

Hull, T. E.↗

NASA NTRS1996

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

Deissler, Robert G.↗

NASA NTRS2001

Distribution functions of probabilistic automata

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

Denotational semantics↗

DOE OSTI2024

New nonrenormalization theorem from UV/IR mixing

In this paper, we prove a new nonrenormalization theorem which arises from UV/IR mixing. This theorem and its corollaries are relevant for all four-dimensional perturbative tachyon-free closed string theories which can be realized from higher-dimensional theories via geometric compactifications. As such, our theorem therefore holds regardless of the presence or absence of spacetime supersymmetry and regardless of the gauge symmetries or matter content involved. This theorem resolves a hidden clash between modular invariance and the process of decompactification, and enables us to uncover a number of surprising phenomenological properties of these theories. Chief among these is the fact that certain physical quantities within such theories cannot exhibit logarithmic or power-law running and instead enter an effective fixed-point regime above the compactification scale. This cessation of running occurs as the result of the UV/IR mixing inherent in the theory. These effects apply not only for gauge couplings but also for the Higgs mass and other quantities of phenomenological interest, thereby eliminating the logarithmic and/or power-law running that might have otherwise appeared for such quantities. These results illustrate the power of UV/IR mixing to tame divergences—even without supersymmetry—and reinforce the notion that UV/IR mixing may play a vital role in resolving hierarchy problems without supersymmetry. Published by the American Physical Society 2024

Abel, Steven (ORCID:000000031213907X)↗

NASA NTRS2010

Optimized FPGA Implementation of Multi-Rate FIR Filters Through Thread Decomposition

Multirate (decimation/interpolation) filters are among the essential signal processing components in spaceborne instruments where Finite Impulse Response (FIR) filters are often used to minimize nonlinear group delay and finite-precision effects. Cascaded (multi-stage) designs of Multi-Rate FIR (MRFIR) filters are further used for large rate change ratio, in order to lower the required throughput while simultaneously achieving comparable or better performance than single-stage designs. Traditional representation and implementation of MRFIR employ polyphase decomposition of the original filter structure, whose main purpose is to compute only the needed output at the lowest possible sampling rate. In this paper, an alternative representation and implementation technique, called TD-MRFIR (Thread Decomposition MRFIR), is presented. The basic idea is to decompose MRFIR into output computational threads, in contrast to a structural decomposition of the original filter as done in the polyphase decomposition. Each thread represents an instance of the finite convolution required to produce a single output of the MRFIR. The filter is thus viewed as a finite collection of concurrent threads. The technical details of TD-MRFIR will be explained, first showing its applicability to the implementation of downsampling, upsampling, and resampling FIR filters, and then describing a general strategy to optimally allocate the number of filter taps. A particular FPGA design of multi-stage TD-MRFIR for the L-band radar of NASA's SMAP (Soil Moisture Active Passive) instrument is demonstrated; and its implementation results in several targeted FPGA devices are summarized in terms of the functional (bit width, fixed-point error) and performance (time closure, resource usage, and power estimation) parameters.

DSP↗

NASA NTRS2009

Hardware Implementation of Serially Concatenated PPM Decoder

A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.

Moision, Bruce↗

NASA NTRS1998

Non-Gimbaled Antenna Pointing: Summary of Results and Analysis

There is considerable interest at this time in developing small satellites for quick-turnaround missions to investigate near-earth phenomena from space. One problem to be solved in mission planning is the means of communication between the control infrastructure in the ground segment and the satellite in the space segment. A nominal small-satellite mission design often includes an omni-directional or similar wide-pattern antenna on the satellite and a dedicated ground station for telemetry, tracking, and command support. These terminals typically provide up to 15 minutes of coverage during an orbit that is within the visibility of the ground station; however, not all orbits will pass over the ground station so that coverage gaps will exist in the data flow. To overcome this general limitation on data transmission for low-earth orbiting satellites, the Space Network (SN), operated by the National Aeronautics and Space Administration, (NASA) has been designed to transmit data to and from user satellites through the Tracking and Data Relay Satellites (TDRS) in geostationary orbit and interfacing to the White Sands Complex (WSC) in New Mexico for the data's ground entry point. The advantage of the SN over a fixed ground station is that all low-earth-satellite orbits will be within the visibility area of at least one TDRS within the SN for a large part of the orbit and the potential exists to establish a communications link if the user satellite can point an antenna in the direction of any one of the relay satellites. Within NASA, there is considerable interest in seeing that small satellite developers are aware of the advantages to the SN and that designs to include the SN are part of the satellite design. Small satellite users have not often considered using the SN because of: (1) The 26-dB link penalty differential between direct broadcast to a ground station and transmission through a TDRS to the ground; (2) The class of satellite is too small to support high-gain antennas and associated attitude control and drive electronics; (3) The class of satellites is severely weight and power limited; (4) There are perceived problems in scheduling communications for this class of user on the SN. This report addresses the potential for SN access using non-gimbaled, i.e. fixed-pointed, antennas in the design of the small satellite using modest transmission power to achieve the necessary space-to-ground transmissions. The advantage of using the SN is in the reduction of mission costs arising from using the SN infrastructure instead of a dedicated, proprietary ground station using a similar type of communications package. From the simulations and analysis presented, we will show that a modest satellite configuration can be used with the space network to achieve the data transmission goals of a number of users and thereby rival the performance achieved with proprietary ground stations. In this study, we will concentrate on the return data link (from the user satellite through a TDRS to the ground data entry point). The forward command link (from the ground data entry point through a TDRS to the user satellite) will usually be a lower data rate service and the data volume will also be considerably lower than the return link's requirement. Therefore, we assume that if the return link requirements are satisfied, then the forward link requirements can also be satisfied.

Horan, Stephen↗

DOE OSTI2022

Scaling and adiabaticity in a rapidly expanding gluon plasma

In this work we aim to gain qualitative insight on the far-from-equilibrium behavior of the gluon plasma produced in the early stages of a heavy-ion collision. It was recently discovered [1] that the distribution functions of quarks and gluons in QCD effective kinetic theory (EKT) exhibit self-similar “scaling” evolution with time-dependent scaling exponents long before those exponents reach their pre-hydrodynamic fixed-point values. In this work we shed light on the origin of this time-dependent scaling phenomenon in the small-angle approximation to the Boltzmann equation. We first solve the Boltzmann equation numerically and find that time-dependent scaling is a feature of this kinetic theory, and that it captures key qualitative features of the scaling of hard gluons in QCD EKT. We then proceed to study scaling analytically and semi-analytically in this equation. We find that an appropriate momentum rescaling allows the scaling distribution to be identified as the instantaneous ground state of the operator describing the evolution of the distribution function, and the approach to the scaling function is described by the decay of the excited states. That is to say, there is a frame in which the system evolves adiabatically. Furthermore, from the conditions for adiabaticity we can derive evolution equations for the time-dependent scaling exponents. In addition to the known free-streaming and BMSS fixed points, we identify a new “dilute” fixed point when the number density becomes small before hydrodynamization. Corrections to the fixed point exponents in the small-angle approximation agree quantitatively with those found previously in QCD EKT and arise from the evolution of the ratio between hard and soft scales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗