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Results for “asymptotic thresholds”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators

Abstract In this paper, we show that the common hard kernel of double-log-type or threshold-type factorization for certain space-like parton correlators that arise in the context of lattice parton distributions, theheavy-light Sudakov hard kernel, has linear infrared (IR) renormalon. We explicitly demonstrate how this IR renormalon correlates with ultraviolet (UV) renormalons of next-to-leading power operators in two explicit examples: threshold asymptotics of space-like quark-bilinear coefficient functions and transverse momentum dependent (TMD) factorization of quasi wave function amplitude. Theoretically, the pattern of renormalon cancellation complies with general expectations to marginal asymptotics in the UV limit. Practically, this linear renormalon explains the slow convergence of imaginary parts observed in lattice extraction of the Collins-Soper kernel and signals the relevance of next-to-leading power contributions. Fully factorized, fully controlled threshold asymptotic expansion for space-like quark-bilinear coefficient functions in coordinate and moment space has also been proposed.

Physics↗
NASA NTRS2006

Protograph LDPC Codes for the Erasure Channel

This viewgraph presentation reviews the use of protograph Low Density Parity Check (LDPC) codes for erasure channels. A protograph is a Tanner graph with a relatively small number of nodes. A "copy-and-permute" operation can be applied to the protograph to obtain larger derived graphs of various sizes. For very high code rates and short block sizes, a low asymptotic threshold criterion is not the best approach to designing LDPC codes. Simple protographs with much regularity and low maximum node degrees appear to be the best choices Quantized-rateless protograph LDPC codes can be built by careful design of the protograph such that multiple puncturing patterns will still permit message passing decoding to proceed

long erasure codes↗
DOE OSTI2025

Rare events and Griffiths phases in topological quantum error correction

The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

classical statistical mechanics↗
NASA NTRS2004

Maximum likelihood decoding analysis of Accumulate-Repeat-Accumulate Codes

Repeat-Accumulate (RA) codes are the simplest turbo-like codes that achieve good performance. However, they cannot compete with Turbo codes or low-density parity check codes (LDPC) as far as performance is concerned. The Accumulate Repeat Accumulate (ARA) codes, as a subclass of LDPC codes, are obtained by adding a pre-coder in front of RA codes with puncturing where an accumulator is chosen as a precoder. These codes not only are very simple, but also achieve excellent performance with iterative decoding. In this paper, the performance of these codes with (ML) decoding are analyzed and compared to random codes by very tight bounds. The weight distribution of some simple ARA codes is obtained, and through existing tightest bounds we have shown the ML SNR threshold of ARA codes approaches very closely to the performance of random codes. We have shown that the use of precoder improves the SNR threshold but interleaving gain remains unchanged with respect to RA code with puncturing.

low density parity codes (LDPC)↗
DOE OSTI2022

Driven responses of periodically patterned superconducting films

Here, we simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density J c , the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field E (t) with a defect "hopping" frequency f 0 , which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

The asymptotic behaviour of the scattering matrix in a neighbourhood of the endpoints of a spectral gap

The behaviour of the scattering matrix is investigated as the spectral parameter approaches an endpoint of a spectral gap of a quantum waveguide from the inside or the outside. The waveguide has two sleeves, one is cylindrical and the other periodic. When the spectral parameter traverses the spectral gap, the scattering matrix is reshaped because the number of waves inside and outside the gap is different. Notwithstanding, the smaller scattering matrix (in size) is transformed continuously into an identical block in the bigger scattering matrix and, in addition, the latter takes block diagonal form in the limit at the endpoint of the gap, that is, at the spectral threshold. The unexpected phenomena are related to the other block. It is shown that in the limit this block can only take certain values at the threshold, and taking one or other of these values depends on the structure of the continuous spectrum and also on the structure of the subspace of 'almost standing' waves at the threshold, which are solutions of the homogeneous problem that transfer no energy to infinity. A criterion for the existence of such solutions links the dimension of this subspace to the multiplicity of the eigenvalue −1 of the threshold scattering matrix. Asymptotic formulae are obtained, which show, in particular, that the phenomenon of anomalous scattering of high-amplitude waves at near-threshold frequencies, discovered by Weinstein in a special acoustic problem, also occurs in periodic waveguides. Bibliography: 38 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Experience, lessons learned and methodology in the design of space systems to accommodate total dose and SEU effects

We now have considerable experience with successfully designing science systems to function properly, even during and after exposure to ionizing radiation approaching one Megarad, and during large solar particle events with substantial high Z fluxes such as the events that happened in August, 1972 and in the fall of 1989. Nevertheless, with changing device dimensions and properties, newer technologies and new applications, new problems arise. Some recent basic research has shed light on these problems and pointed the way to better diagnostic tests. In the case of single event upsets, clearly one cannot always accurately predict upset probabilities simply by knowing the quiescent Linear Energy Transfer (LET) threshold and the asymptotic cross-section of the device.

Trainor, James H.↗
NASA NTRS2018

Convergence Analysis of Turbulent Flow Solutions

Data from the "Turbulence Modeling Resource" website for turbulent flow over an NACA-0012 airfoil is analyzed to determine the convergence behavior of three second-order CFD (Computational Fluid Dynamics) codes: CFL3D (Computational Fluids Lab 3 Dimensional flow solver), FUN3D (Fully Unstructured Navier-stokes flow solver), and TAU (German Aerospace Center (DLR) 2 dimensional code for unstructured hybrid grids solving the Reynolds-Averaged Navier-Stokes equations or the Euler equations). The convergence of both integrated properties and pointwise data are examined. Several different methods for estimating errors and computing convergence rates are compared. A high-order extension to the Richardson extrapolation is developed that improves the accuracy of the mesh limit values and provides a quantitative estimate of the threshold of the asymptotic regime. The coefficient of total drag exhibits second-order convergence for all three codes, and convergence is monotone over a sequence of 7 grids. Other force coefficients are not so well behaved. The convergence rates of the viscous component of drag on the three nest grids ranges from 3:0 for CFL3D to 1:0 for FUN3D. The three codes are converging to similar but not identical solutions. The largest differences between the codes are in the coefficient of lift for which the difference between CFL3D and FUN3D is greater than 10 (sup minus 4). The best agreement occurs in the viscous component of drag, which is the only force component for which all three codes are converging towards each other at a rate of second-order. The agreement between the two unstructured grid codes is good with all properties except lift converging towards common values at a rate of second-order. No one code was universally better than the other. The TAU code has the lowest error in total drag, FUN3D has the lowest error in lift, and CFL3D has the lowest error in the viscous component of drag.

Atkins, Harold L.↗
DOE OSTI2018

Transverse Mode Coupling Instability of the Bunch with Oscillating Wake Field and Space Charge

Transverse mode coupling instability of a single bunch caused by oscillating wake field is considered in the paper. The instability threshold is found at different frequencies of the wake with space charge tune shift taken into account. The wake phase advance in the bunch length from 0 up to $4\pi$ is investigated. It is shown that the space charge can push the instability threshold up or down dependent on the phase advance. Transition region is investigated thoroughly, and simple asymptotic formulas for the threshold are represented.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel -statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. It is shown that the proposed test is more powerful than the existing tests in detecting sparse and weak signals in covariances. Multiple testing procedures are constructed to discover different covariances and the sub-groups of variables with different covariance structures between the two populations. The proposed procedures are based on the multi-level thresholding test, which are able to control the false discovery proportion () with high power. Simulation experiments and a case study on the returns of the S&P 500 stocks before and after the COVID-19 pandemic are conducted to demonstrate and compare the utilities of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Prediction of error rates in dose-imprinted memories on board CRRES by two different methods

An analysis of the expected space radiation effects on the single event upset (SEU) properties of CMOS/bulk memories onboard the Combined Release and Radiation Effects Satellite (CRRES) is presented. Dose-imprint data from ground test irradiations of identical devices are applied to the predictions of cosmic-ray-induced space upset rates in the memories onboard the spacecraft. The calculations take into account the effect of total dose on the SEU sensitivity of the devices as the dose accumulates in orbit. Estimates of error rates, which involved an arbitrary selection of a single pair of threshold linear energy transfer (LET) and asymptotic cross-section values, were compared to the results of an integration over the cross-section curves versus LET. The integration gave lower upset rates than the use of the selected values of the SEU parameters. Since the integration approach is more accurate and eliminates the need for an arbitrary definition of threshold LET and asymptotic cross section, it is recommended for all error rate predictions where experimental sigma-versus-LET curves are available.

Brucker, G. J.↗
DOE OSTI2021

Risk-Adaptive Experimental Design for High-Consequence Systems: LDRD Final Report

Constructing accurate statistical models of critical system responses typically requires an enormous amount of data from physical experiments or numerical simulations. Unfortunately, data generation is often expensive and time consuming. To streamline the data generation process, optimal experimental design determines the 'best' allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this project, we tailored and extended traditional design paradigms to target distribution tails. Our approach included (i) the development of new optimality criteria to shape the distribution of prediction variances, (ii) the development of novel risk-adapted surrogate models that provably overestimate certain statistics including the probability of exceeding a threshold, and (iii) the asymptotic analysis of regression approaches that target tail statistics such as superquantile regression. To accompany our theoretical contributions, we released implementations of our methods for surrogate modeling and design of experiments in two complementary open source software packages, the ROL/OED Toolkit and PyApprox.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Pair production in superstrong magnetic fields

The production of electron-positron pairs by single photons in magnetic fields 10 to the twelth power G was investigated in detail for photon energies near threshold as well as for the asymptotic limit of high photon energy. The exact attenuation coefficient, which is derived and then evaluated numerically, is strongly influenced by the discrete energy states of the electron and positron. Near threshold, it exhibits a sawtooth pattern as a function of photon energy, and its value is significantly below that predicted by the asymptotic expression for the attenuation coefficient. The energy distributions of the created pair are computed numerically near threshold and analytic expressions are derived in the asymptotic limit. These results indicate that as field strength and photon energy increase, it becomes increasingly probable for the pair to divide the photon energy unequally. This effect, as well as the threshold behavior of the attenuation coefficient, could have important consequences for pulsar models.

Daugherty, J. K.↗
DOE OSTI2023

Analytical population dynamics underlying harmful algal blooms triggered by prey avoidance

A modified version of the NPZD ecosystem model is used to analytically examine the effects of predation avoidance, a possible mechanism for triggering harmful algal blooms (HAB). To resolve HAB development caused by predation avoidance, an additional phytoplankton functional group is considered, one that has slower nutrient uptake and better predation avoidance characteristics than the non-harmful phytoplankton group used in traditional NPZD models. Because the two phytoplankton groups (one non-harmful and one HAB) compete for only one resource within the same system, steady state (equilibrium) conditions cannot occur without the presence of zooplankton; only the non-harmful phytoplankton group, which defeats the HAB group in the resource competition, can survive in the equilibrium. The presence of sufficient zooplankton effectively acts to replenish the nutrient pool by consuming the non-harmful phytoplankton. When this occurs, two equilibrium states are found: one with both phytoplankton groups coexisting, and one that only includes the HAB group. Further, the condition required for equilibrium is that the total nitrogen within the system should be larger than a threshold determined by model coefficients. The threshold and feasibility of the equilibrium are sensitive to the relative HAB predation avoidance coefficient. If the coefficient is larger than the ratio of net growth rates between the HAB and non-harmful phytoplankton group, the threshold becomes infinite, and an equilibrium is not feasible. The time scale for the system to reach an equilibrium state that includes a HAB group is determined asymptotically. The dependence of a threshold condition as a controlling factor may explain the regime shift of dominant species causing HABs. The ecosystem model is fully implemented into the Regional Ocean Modeling System and applied to an idealized coastal embayment (with depths and geometry taken from San Francisco Bay) to show numerically the dominance of prey avoidance dynamics in a natural shallow water environment that includes advection and diffusion. The analytical results improve strategies for HAB modeling and provide guidance for setting model coefficients necessary to resolve a HAB event.

54 ENVIRONMENTAL SCIENCES↗