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At least 1,495 records · Page 83

Propagation of quasifracture in viscoelastic media under low-cycle repeated stressing

The propagation of a craze as quasifracture under repeated cyclic stressing in polymeric systems has been under intensive investigation recently. Based upon a time-dependent crazing theory, the governing differential equation describing the propagation of a single craze as quasifracture in an infinite viscoelastic plate has been solved for sinusoidal stresses. Numerical methods have been employed to obtain the normalized craze length as a function of time. The computed results indicate that the length of a quasifracture may decelerate and decrease indicating that its velocity can reverse. This behavior may be consistent with the observed and much discussed craze healing and the enclosure model in fatigue and fracture of solids.

Liu, X. P.↗

A numerical scheme to solve unstable boundary value problems

A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.

Kalnay Derivas, E.↗

Optimal digital redesign of cascaded analogue controllers

This paper presents a new, optimal digital redesign technique for finding an optimal cascaded digital controller from the given continuous-time counterpart by minimizing a quadratic performance index. The control gains can be obtained by solving a set of Liapunov equations. The developed optimal cascaded digital controller enables the state and/or outputs of the digitally controlled closed-loop sampled-data system to optimally match those of the original continuous-time closed-loop system at any instant between sampling periods. The developed control law can be implemented using inexpensive and reliable digital electronics with a relatively long sampling period.

Shieh, L. S.↗

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique signature of visual behavior. This is true even in a restricted domain, such as piloting an aircraft, where patterns of visual signatures might represent activities like communicating, navigating, and monitoring. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these activities based on their behavioral signatures. The method is in some respects similar to recurrence analysis, but here we compare not individual fixations, but groups of fixations aggregated over a fixed time interval. The duration of this interval is a parameter that we will refer to as τ. We assume that the environment has been divided into a set of N different areas-of-interest (AOIs). For a given interval of time of duration τ, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector. These proportions can be converted to counts by multiplying by τ divided by the average fixation duration (another parameter that we fix at 280 milliseconds). We compare different intervals by computing the chi-square statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. We have investigated the method using a set of 10 synthetic "activities," that sample 4 AOIs. Four of these activities visit 3 of the 4 AOIs, with equal probability; as there are four different ways to leave-one- out, there are four such activities. Similarly, there are six different activities that leave-two-out. Sequences of simulated behavior were generated by running each activity for 40 seconds, in sequence, for a total of 6.7 minutes. The figure to the right shows the matrix of chi-square statistics, using a value of 2.8 seconds for τ, corresponding to 10 fixations. Low values (dark) indicate poor evidence for activity differences, while high values (bright) indicate strong evidence. The dark squares along the main diagonal each correspond to the forty second intervals in which the activity was held constant; the 4x4 block at the lower left corresponds to the four leave-one-out activities, while the 6x6 block in the upper right corresponds to the leave-two-out activities. (The anti-diagonal pattern of white squares indicates those activity pairs that share no AOIs.) The chi-square values can be binarized by choosing a particular significance level; we are interested in grouping bins that represent the same activity, effectively accepting the null hypothesis. Therefore, we may adopt a relatively lax criterion; for example, choosing a p-value of 0.2 means that two behaviors that have only a 1-in-5 chance of being produced by a single activity might nevertheless be clustered together. We have explored several methods to perform clustering on the data and solving for the activity probabilities. Greedy methods begin by selecting the time bin that is similar to the most (or least) other bins, and then forming a cluster from it and all other non-discriminable bins. These methods show mediocre performance, as they do not take into account temporal contiguity. Preliminary results indicate that methods that "grow" clusters in time from seed points perform better.

activity analysis↗

Thermosolutal convection during directional solidification

During solidification of a binary alloy at constant velocity vertically upward, thermosolutal convection can occur if the solute rejected at the crystal-melt interface decreases the density of the melt. We assume that the crystal-melt interface remains planar and that the flow field is periodic in the horizontal direction. The time-dependent nonlinear differential equations for fluid flow, concentration, and temperature are solved numerically in two spatial dimensions for small Prandtl numbers and moderately large Schmidt numbers. For slow solidification velocities, the thermal field has an important stabilizing influence: near the onset of instability the flow is confined to the vicinity of the crystal-melt interface. Further, for slow velocities, as the concentration increases, the horizontal wavelength of the flow decreases rapidly - a phenomenon also indicated by linear stability analysis. The lateral inhomogeneity in solute concentration due to convection is obtained from the calculations. For a narrow range of solutal Rayleigh numbers and wavelengths, the flow is periodic in time.

Mcfadden, G. B.↗

Parallel Broadband Femtosecond Reflection Spectroscopy at a Soft X-Ray Free-Electron Laser

X-ray absorption spectroscopy (XAS) and the directly linked X-ray reflectivity near absorption edges yield a wealth of specific information on the electronic structure around the resonantly addressed element. Observing the dynamic response of complex materials to optical excitations in pump–probe experiments requires high sensitivity to small changes in the spectra which in turn necessitates the brilliance of free electron laser (FEL) pulses. However, due to the fluctuating spectral content of pulses generated by self-amplified spontaneous emission (SASE), FEL experiments often struggle to reach the full sensitivity and time-resolution that FELs can in principle enable. Here, we implement a setup which solves two common challenges in this type of spectroscopy using FELs: First, we achieve a high spectral resolution by using a spectrometer downstream of the sample instead of a monochromator upstream of the sample. Thus, the full FEL bandwidth contributes to the measurement at the same time, and the FEL pulse duration is not elongated by a monochromator. Second, the FEL beam is divided into identical copies by a transmission grating beam splitter so that two spectra from separate spots on the sample (or from the sample and known reference) can be recorded in-parallel with the same spectrometer, enabling a spectrally resolved intensity normalization of pulse fluctuations in pump–probe scenarios. We analyze the capabilities of this setup around the oxygen K- and nickel L-edges recorded with third harmonic radiation of the free electron laser in Hamburg (FLASH), demonstrating the capability for pump–probe measurements with sensitivity to reflectivity changes on the per mill level.

36 MATERIALS SCIENCE↗

Energetic ionized helium in the quiet time radiation belts - Theory and comparison with observation

Theoretical calculations of helium ion distributions in the inner magnetosphere are compared to observations made by ATS-6 and Explorer-45. Coupled transport equations for equatorially mirroring singly and doubly ionized helium ions in the steady state limit with an outer boundary of L = 7 are solved. Radial profiles and energy spectra are computed at all lower L values. Theoretical quiet time predictions are compared to satellite observations of energetic helium ions in the lower MeV range. It is found that the theory adequately represents the principal characteristics of the radiation belt helium ion population.

Spjeldvik, W. N.↗

Mapping Spatiotemporal Solvent Velocity from Measured Concentration Gradients in a Polarized Electrolyte

The electric-field induced motion of neutral species impedes the efficacy of electrochemical devices. By combining operando X-ray transmission measurements with continuum mechanics, we have developed a methodology for determining the velocity of neutral solvent molecules under an applied field. The X-ray transmission experiments were used to determine ion concentration profiles as a function of space and time in a polymer electrolyte. The unsteady state solvent mass balance equation was solved numerically with experimental concentration profiles to map spatiotemporal solvent velocities. We compare our experimentally derived results with predictions made with concentrated solution theory. We use the cation transference number as the only adjustable parameter to match experimental measurements of both concentration and solvent velocity. Our approach may be used to determine solvent velocity with any operando technique used to measure time-dependent ion concentration profiles.

Abdo, Emily E↗

Evolution of Orion Mission Design for Exploration Mission 1 and 2

The evolving mission design and concepts of NASA's next steps have shaped Orion into the spacecraft that it is today. Since the initial inception of Orion, through the Constellation Program, and now in the Exploration Mission frame-work with the Space Launch System (SLS), each mission design concept and program goal have left Orion with a set of capabilities that can be utilized in many different mission types. Exploration Missions 1 and 2 (EM-1 and EM-2) have now been at the forefront of the mission design focus for the last several years. During that time, different Design Reference Missions (DRMs) were built, analyzed, and modified to solve or mitigate enterprise level design trades to ensure a viable mission from launch to landing. The resulting DRMs for EM-1 and EM-2 were then expanded into multi-year trajectory scans to characterize vehicle performance and Earth-Moon geometry trends. This provides Orion's subsystems with stressing reference trajectories to help design their system. Now that Orion has progressed through the Preliminary and Critical Design Re-views (PDR and CDR) there is a general shift in the focus of mission design from aiding the vehicle design to providing mission specific products needed for pre-flight and real time operations. Some of the mission specific products need-ed include analysis of steering law performance, inputs into navigational accura-cy assessments, abort options at any point in the mission for each valid trajecto-ry in the launch window, recontact avoidance between the upper stage and Orion post nominal separation, etc.

Gutkowski, Jeffrey P.↗

Evolution of Orion Mission Design for Exploration Mission 1 and 2

The evolving mission design and concepts of NASA’s next steps have shaped Orion into the spacecraft that it is today. Since the initial inception of Orion, through the Constellation Program, and now in the Exploration Mission frame-work with the Space Launch System (SLS), each mission design concept and pro-gram goal have left Orion with a set of capabilities that can be utilized in many different mission types. Exploration Missions 1 and 2 (EM-1 and EM-2) have now been at the forefront of the mission design focus for the last several years. During that time, different Design Reference Missions (DRMs) were built, analyzed, and modified to solve or mitigate enterprise level design trades to ensure a viable mission from launch to landing. The resulting DRMs for EM-1 and EM-2 were then expanded into multi-year trajectory scans to characterize vehicle performance as affected by variations in Earth-Moon geometry. This provides Orion’s subsystems with stressing reference trajectories to help design their system. Now that Orion has progressed through the Preliminary and Critical Design Reviews (PDR and CDR), there is a general shift in the focus of mission design from aiding the vehicle design to providing mission specific products needed for pre-flight and real time operations. Some of the mission specific products needed include, large quantities of nominal trajectories for multiple monthly launch periods and abort options at any point in the mission for each valid trajectory in the launch window.

Gutkowski, Jeffrey P.↗

Time dependent computation of the Euler equations for designing 2-D cascades, including the case of transonic shock free design

A numerical method to solve the inverse problem for airfoil cascades is described. The case of compressible, inviscid flow is considered. The proposed method is based on the finite difference approximation of the time-dependent Euler equations. Numerical examples show the capability of the method to design subsonic or transonic shockless blades.

Zannetti, L.↗

A unified formulation of splitting-based implicit time integration schemes

Splitting-based time integration approaches such as fractional step, alternating direction implicit, operator splitting, and locally one dimensional methods partition the system of interest into components, and solve individual components implicitly in a cost-effective way. Here this work proposes a unified formulation of splitting time integration schemes in the framework of general-structure additive Runge–Kutta (GARK) methods. Specifically, we develop implicit-implicit (IMIM) GARK schemes, provide the order conditions for this class, and explain their application to partitioned systems of ordinary differential equations. We show that classical splitting methods belong to the IMIM GARK family, and therefore can be studied in this unified framework. New IMIM-GARK splitting methods are developed and tested using parabolic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamical friction in a Fuzzy Dark Matter universe

We present an in-depth exploration of the phenomenon of dynamical friction in a universe where the dark matter is composed entirely of so-called Fuzzy Dark Matter (FDM), ultralight bosons of mass m ~ O(10 -22 ) eV. We review the classical treatment of dynamical friction before presenting analytic results in the case of FDM for point masses, extended mass distributions, and FDM backgrounds with finite velocity dispersion. We then test these results against a large suite of fully non-linear simulations that allow us to assess the regime of applicability of the analytic results. We apply these results to a variety of astrophysical problems of interest, including infalling satellites in a galactic dark matter background, and determine that (1) for FDM masses m & 10 -21 eV c -2 , the timing problem of the Fornax dwarf spheroidal’s globular clusters is no longer solved and (2) the effects of FDM on the process of dynamical friction for satellites of total mass M and relative velocity vrel should require detailed numerical simulations for M/109 M m/10 -22 eV 100 km s -1 /vrel ~ 1, parameters which would lie outside the validated range of applicability of any currently developed analytic theory, due to transient wave structures in the time-dependent regi

79 ASTRONOMY AND ASTROPHYSICS↗

Mass Spectrometer Transient Analysis

This software implements a complete preprocessing pipeline for transient mass spectrometry (MS) data collected during TAP (Temporal Analysis of Products) experiments. It is designed to extract chemically meaningful fluxes from overlapping ion signals by applying a calibrated defragmentation matrix and solving the resulting linear system using non-negative least squares (NNLS) regression. The core script, preprocess_mass_spec.py, performs the following operations: Gain correction: Applies amplifier gain scalars derived from inert-packed calibration pulses to normalize signal intensities across AMUs and acquisition settings. Background subtraction: Removes experiment baselines using user-defined time windows, ensuring compatibility with slow-diffusing species and preventing negative values that would interfere with NNLS. Options to subtract before and after defragmentation. Defragmentation: Constructs a fragmentation matrix A from zeroth moments of calibration pulses (equal molar gas:inert mixtures) and solves Ax=b at each time point, where b is the raw MS signal and x is the estimated species flux. The matrix is normalized to inert signals and accounts for instrument-specific fragmentation behavior. Pulse-mode handling: Supports both averaged and individual pulse modes, enabling statistical treatment of fluxes and calculation of standard deviations. Integration and output: Computes zeroth moments (integrated fluxes) and exports time-resolved and integrated data in CSV format, suitable for downstream kinetic modeling. The software is validated using both virtual TAP simulations (VTAP) and experimental data from propane dehydrogenation (PDH) on CrOx/Al2O3 catalysts. It preserves temporal resolution by applying NNLS point-by-point across the pulse duration (typically 6,000+ time slices per pulse), leveraging the linear superposition principle to reconstruct full flux profiles. The defragmented outputs are compatible with kinetic extraction methods such as the G and Y procedures, which are used to derive rate–concentration relationships from TAP data. The details of these validations are discussed in detail in the supporting manuscript and supporting information. Example data and output files are also included. The methodology is robust to experimental noise and drift, with calibration protocols that account for pulse size effects, MS aging, and inert gas normalization. The software is modular, reproducible, and tailored for high-throughput TAP-MS workflows in catalysis research.

Kristy, Stephen [Idaho National Laboratory (INL), ↗

Numerical methods for fractional Fokker–Planck equation with multiplicative Marcus Lévy noises

The Fokker–Planck equation (FPE) is an important deterministic tool for investigating stochastic dynamical systems. In this paper, we consider the space-time fractional FPE driven by multiplicative Marcus Lévy noises. Efficient numerical schemes are presented to solve the equations. Stability and convergence of the methods are also discussed. We give some numerical experiments to validate our schemes, and examine the effects of parameters on solutions. Additionally, we analyze the maximal likely trajectories and the critical time for the change of the most probability location.

Mathematics↗

Scattering of impact wave by a crack in composite plate

The surface responses due to impact load on an infinite uniaxial graphite/epoxy plate with and without delamination cracks are investigated both in time and frequency domain by using a hybrid method combining the finite element discretization of the near-field with boundary integral representation of the field outside a contour enclosing completely the crack. This combined method leads to a set of linear unsymmetric complex matrix equations which are solved to obtain the response in the frequency domain by biconjugate gradient method. The time domain response is then obtained by using an FFT. In order to capture the time-domain characteristics accurately, high order finite elements have been used. Also, both the six node singular elements and eight node transition elements are used around the crack tips to model the crack-tip singularity. It is shown that from the numerical results for surface responses both depth and length of this crack can be identified.

Ju, T. H.↗

Optimal K/S impulsive transfer

The necessary equations in K/S variables (E-formulation) are developed for an optimal N-impulse solution of the time-open and rendezvous problems. The equations are particularly simple when only two impulses are assumed. The developed algorithm is extremely fast and reliable because the equations that must be solved are smooth, well-behaved (almost sinusoidal) functions. Numerical results for a two-impulse time-open and rendezvous problem are presented.

Jezewski, D. J.↗

Measuring Greenland Ice Mass Variation With Gravity Recovery and the Climate Experiment Gravity and GPS

The response of the Greenland ice sheet to climate change could significantly alter sea level. The ice sheet was much thicker at the last glacial maximum. To gain insight into the global change process and the future trend, it is important to evaluate the ice mass variation as a function of time and space. The Gravity Recovery and Climate Experiment (GRACE) mission to fly in 2001 for 5 years will measure gravity changes associated with the current ice variation and the solid earth's response to past variations. Our objective is to assess the separability of different change sources, accuracy and resolution in the mass variation determination by the new gravity data and possible Global Positioning System (GPS) bedrock uplift measurements. We use a reference parameter state that follows a dynamic ice model for current mass variation and a variant of the Tushingham and Peltier ICE-3G deglaciation model for historical deglaciation. The current linear trend is also assumed to have started 5 kyr ago. The Earth model is fixed as preliminary reference Earth model (PREM) with four viscoelastic layers. A discrete Bayesian inverse algorithm is developed employing an isotropic Gaussian a priori covariance function over the ice sheet and time. We use data noise predicted by the University of Texas and JPL for major GRACE error sources. A 2 mm/yr uplift uncertainty is assumed for GPS occupation time of 5 years. We then carry out covariance analysis and inverse simulation using GRACE geoid coefficients up to degree 180 in conjunction with a number of GPS uplift rates. Present-day ice mass variation and historical deglaciation are solved simultaneously over 146 grids of roughly 110 km x 110 km and with 6 time increments of 3 kyr each, along with a common starting epoch of the current trend. For present-day ice thickness change, the covariance analysis using GRACE geoid data alone results in a root mean square (RMS) posterior root variance of 2.6 cm/yr, with fairly large a priori uncertainties in the parameters and a Gaussian correlation length of 350 km. Simulated inverse can successfully recover most features in the reference present-day change. The RMS difference between them over the grids is 2.8 cm/yr. The RMS difference becomes 1.1 cm/yr when both are averaged with a half Gaussian wavelength of 150 km. With a fixed Earth model, GRACE alone can separate the geoid signals due to past and current load fairly well. Shown are the reference geoid signatures of direct and elastic effects of the current trend, the viscoelastic effect of the same trend starting from 5 kyr ago, the Post Glacial Rebound (PGR), and the predicted GRACE geoid error. The difference between the reference and inverse modeled total viscoelastic signatures is also shown. Although past and current ice mass variations are allowed the same spatial scale, their geoid signals have different spatial patterns. GPS data can contribute to the ice mass determination as well. Additional information is contained in the original.

Wu, Xiao-Ping↗