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At least 55 records · Page 3

The time evolution of spectral discretizations of hyperbolic systems

A Chebyshev collocation spectral method, applied to hyperbolic systems is considered, particularly for those initial boundary value problems which possess only solutions tending to zero at large times. It is shown that the numerical solutions of the system will also vanish at infinity, if and only if, the numerical solution of a scalar equation of the same type does. This result is then generalized for other spectral approximations.

Lustman, L.

Mineralization through geologic time: Evolution of continental crust

In analogy to living systems, geologic entities (e.g., rocks, mineral deposits, tectonic realms and domains) are involved in the process of perpetual generation and destruction (birth/death cycles). This results in time distribution patterns akin to age structures in living populations and the systematics is amenable to treatment by the concepts of population dynamics. Utilizing this theoretical approach, the survivorship patterns for major realms of the plate tectonic system, for consitutent rocks, and for the entombed mineral resources are predicted. The present inventory encompasses global economic accumulations of metals by geologic age. The deposits of these metals were assigned to nine broad genetic categories, with an attempt to relate each category to tectonic setting within the framework of global plate tectonics.

Veizer, Jan

Nonlinear calculations of the time evolution of black hole accretion disks

Based on previous works on black hole accretion disks, I continue to explore the disk dynamics using the finite difference method to solve the highly nonlinear problem of time-dependent alpha disk equations. Here a radially zoned model is used to develop a computational scheme in order to accommodate functional dependence of the viscosity parameter alpha on the disk scale height and/or surface density. This work is based on the author's previous work on the steady disk structure and the linear analysis of disk dynamics to try to apply to x-ray emissions from black candidates (i.e., multiple-state spectra, instabilities, QPO's, etc.).

Luo, C.

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING

Time evolution of interstellar dust and far-infrared luminosity of disk galaxies

The evolution of interstellar dust in disk galaxies is modeled, assuming that dust forms predominantly in molecular clouds associated with star formation. Analytical solutions for the dust abundance in disk galaxies as a function of galaxy age are obtained for the prompt initial enrichment and accretion models of chemical evolution, consistent with observations of the heavy element abundance in the Galaxy. Star formation rates in the disks of galaxies are taken as either constant or decreasing exponentially with time. It is found that the total amount of dust in the early history of galaxies can be up to 4 times the value observed today. The total emission from dust in galaxies is calculated, using an average dust temperature derived from IRAS observations. In the strongly evolving models, the far-infrared luminosity from galaxies can be roughly two orders of magnitude larger than the current value.

Wang, Boqi

Alfven wave transport effects in the time evolution of parallel cosmic-ray modified shocks

Some of the issues associated with a more complete treatment of Alfven transport in cosmic ray shocks are explored qualitatively. The treatment is simplified in some important respects, but some new issues are examined and for the first time a nonlinear, time dependent study of plane cosmic ray mediated shocks with both the entropy producing effects of wave dissipation and effects due to the Alfven wave advection of the cosmic ray relative to the gas is included. Examination of the direct consequences of including the pressure and energy of the Alfven waves in the formalism began.

Jones, T. W.

Space-time evolution of particle emission in p–Pb collisions at $\sqrt{{s}_{\text{NN}}} = 5.02$ TeV with 3D kaon femtoscopy

The measurement of three-dimensional femtoscopic correlations between identical charged kaons (K ± K ± ) produced in p–Pb collisions at center-of-mass energy per nucleon pair $\sqrt{{s}_{\text{NN}}}=5.02$ TeV with ALICE at the LHC is presented for the first time. This measurement, supplementary to those in pp and Pb–Pb collisions, allows understanding the particle-production mechanisms at different charged-particle multiplicities and provides information on the dynamics of the source of particles created in p–Pb collisions, for which a general consensus does not yet exist. It is shown that the measured source sizes increase with charged-particle multiplicity and decrease with increasing pair transverse momentum. These trends for K ± K ± are similar to the ones observed earlier in identical charged-pion and ${\text{K}}_{\text{s}}^{0}{\text{K}}_{\text{s}}^{0}$ correlations in Pb–Pb collisions at various energies and in π ± π ± correlations in p–Pb collisions at $\sqrt{{s}_{\text{NN}}}=5.02$ TeV. At comparable multiplicity, the source sizes measured in p–Pb collisions agree within uncertainties with those observed in pp collisions, and there is an indication that they are smaller than those observed in Pb–Pb collisions. The obtained results are also compared with predictions from the hadronic interaction model EPOS 3, which tends to underestimate the source size for the most central collisions and agrees with the data for semicentral and peripheral events. Furthermore, the time of maximal emission for kaons is extracted. It turns out to be comparable with the value obtained in highly peripheral Pb–Pb collisions at the same energy, indicating that the kaon emission evolution is similar to that in p–Pb collisions.

Heavy Ion Experiments

The time evolution of magnetic fields on solar-like stars

Magnetic fields play a crucial role in governing the rotational evolution of solarlike stars. Techniques for measuring stellar magnetic fields are reviewed, and the most recent determinations of magnetic-field strengths and surface-area coverages on cool stars are analyzed for correlations with age. Tentative evidence for a decrease in magnetic flux with age is found, primarily caused by a reduction in the magnetic area filling factor with time.

Saar, Steven H.

In-depth Analysis of LISA Pathfinder Performance Results: Time Evolution, Noise Projection, Physical Models, and Implications for LISA

We present an in-depth analysis of the LISA Pathfinder differential acceleration performance over the entire course of its science operations, spanning approximately 500 days. We find: (1) The evolution of the Brownian noise that dominates the acceleration amplitude spectral density (ASD), for frequencies f≳1 mHz, is consistent with the decaying pressure due to the outgassing of a single gaseous species. (2) Between f=36 μHz and 1 mHz, the acceleration ASD shows a 1/f tail in excess of the Brownian noise of almost constant amplitude, with ≃20% fluctuations over a period of a few days, with no particular time pattern over the course of the mission. (3) At the lowest considered frequency of f=18 μHz, the ASD significantly deviates from the 1/f behavior, because of temperature fluctuations that appear to modulate a quasistatic pressure gradient, sustained by the asymmetries of the outgassing pattern. We also present the results of a projection of the observed acceleration noise on the potential sources for which we had either a direct correlation measurement or a quantitative estimate from dedicated experiments. These sources account for approximately 40% of the noise power in the 1/f tail. Finally, we analyze the possible sources of the remaining unexplained fraction and identify the possible measures that may be taken to keep those under control in LISA.

M Armano

The spatial distribution and time evolution of impact-generated magnetic fields

The production of magnetic fields was revealed by laboratory hypervelocity impacts in easily vaporized targets. As quantified by pressure measurements, high frame-rate photography, and electrostatic probes, these impacts tend to produce large quantities of slightly ionized vapor, which is referred to as impact-generated plasma. Nonaligned electron density and temperature gradients within this plasma may lead to production of the observed magnetic fields. Past experiments were limited to measuring a single component of the impact-generated magnetic fields at only a few locations about the developing impact crater and consequently gave little information about the field production mechanism. To understand this mechanism, the techniques were extended to map the three components of the magnetic field both in space and time. By conducting many otherwise identical experiments with arrayed magnetic detectors, a preliminary 3-D picture was produced of impact-generated magnetic fields as they develop through time.

Crawford, D. A.

Impacts into a Strength‐Layered Target: The Time Evolution of the Excavation‐Stage Flow

Impact cratering has dominated the evolution and modification of planetary surfaces throughout the history of the solar system. Impact craters can serve as probes to understanding the details of a planetary subsurface; for example, Oberbeck and Quaide suggested that crater morphology can be used to estimate the thickness of a regolith layer on top of a more competent unit. Lunar craters show a morphological progression from a simple bowl shape to flat‐floored and concentric craters as diameter increases for a given regolith thickness. The final shape of the impact crater is a result of the subsurface flow‐field initiated as the projectile transfers its energy and momentum to the target surface at the moment of impact. Therefore, when a regolith layer is present over a stronger substrate, such as is the case on the lunar mare, the substrate modifies the flow‐field resulting in the distinctive final crater morphology. Here we report on a series of experimental impacts into targets composed of a thin (2 cm) layer of loose sand on top of a stronger substrate. We use the Ejection‐Velocity Measurement System (EVMS, Fig.1) developed by [3] to examine the ejecta kinematics at specific times during the formation of these craters in strength‐layered targets.

J. L. B. Anderson

Dependence of ion-cyclotron range of frequencies instabilities on species mix and fast-ion distribution: II. Time evolution

Dedicated DIII-D experiments studied instabilities below the ion cyclotron frequency f ci and at cyclotron harmonics by injecting thirteen different neutral beam populations into plasmas with different thermal compositions of H and D at five different values of toroidal field. The resulting database of 2529 conditions is described in Part 1: Stability. This paper focuses on the temporal evolution. For some beam geometries, the ion cyclotron emission (ICE) is much stronger at the beginning of injection, suggesting the importance of ‘bump-on-tail’ energy drive. Sawtooth crashes cause the emission to cease for some beam types and emission bands, but the opposite effect occurs for others. When unstable, for virtually all conditions and frequency bands, the emission bursts in a cycle reminiscent of predator-prey oscillations. Evidence for nonlinear interaction between ICE harmonics is observed. Strongly unstable modes typically appear within 1 ms from the start of beam injection and often decay within 0.1 ms when the beam turns off, but both the initial rise and final decay of the mode power exhibit a wide variety of behavior.

electromagnetic ion cyclotron instabilities

Study of the time evolution of the lithosphere

A three dimensional geoid of all oceanic regions was obtained using a data set derived from the GEOS-3 radar altimeter. The editing and organization of the complete SEASAT geophysical data set are described. The geographical area located between 25 and 35 degrees south, and between 320 and 335 degrees east, around the Rio Grande Rise in the south Atlantic, was selected for continued study.

Roufosse, M. C.

Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities

The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation-theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave-wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the prturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave-wave resonance condition which, in turn, causes the wave amplitude to cease its growth.

Hoshino, M.

Space-time evolution of whistler mode wavegrowth in the magnetosphere

The modeling and simulation of the growth of ducted single-frequency whistler-mode waves through cyclotron resonance with radiation belt electrons are considered. The Siple transmitter and a geomagnetically conjugate receiving station are used for the present study. The results can be applied to slowly varying frequency signals and to broadband 'noiselike' signals.

Carlson, C. R.

Time evolution of a miniflare as seen in H-alpha, UV lines, and X-rays

A miniflare that occurred in active region Hale 16896 on 1980 June 15 was observed in H-alpha, UV lines, and soft X-rays. These data allow us to analyze the flare emission and derive the energetics and dynamics of the chromospheric plasma involved. Our results indicate that the energy released by the miniflare was about 10(exp 28) ergs, about four orders of magnitude smaller than that of a large flare. However, hard X-rays (5.5-8.0 keV) were observed which indicated a plasma with temperature as high as 27 x 10(exp 6) K. The H-alpha wings, C IV, and X-rays all showed a short-lived and compact (3 sec x 3 sec) brightening in a location near the leading sunspot. At this location, small-scale changes in the magnetic field were observed from about 2 hr before to about 6 hr after the miniflare. Only very small velocities seem to have been associated with most of the event in H-alpha. The data are consistent with short and dense loops at temperatures above 10(exp 7) K which lost a large fraction of their energy via downward conduction through regions at the footpoints. Several secondary events appear to have been triggered by the miniflare along an arch filament which itself was not greatly affected. A number of much less energetic (10(exp 25)-10(exp 26) erg) events preceded and followed the mini-flare. One of these occurred 11 minutes after the mini-flare and displayed a highly Doppler-shifted signature from the foot-point of a C IV arch. This arch delineates the connection that existed between the location of the mini-flare and the location of secondary events triggered by the flare.

Fontenla, J.