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In this work, we consider assurance testing for repairable systems when supplementary information is available in addition to the data collected in the assurance test. The supplementary information is incorporated using a Bayesian inferential framework. Assurance testing is considered for both a homogeneous Poisson process and a nonhomogenous Poisson process and is illustrated with examples.
Highlights: • Non-Markovian master equation for open quantum system with power-law memory is proposed. • Non-Markovian dynamics of two-level quantum system with memory is described. • Solutions of non-Markovian quantum master equations are derived. • Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. • Exact solution of non-Markovian equations of system with memory is proposed. In this paper, non-Markovian generalization of master equation for open quantum system is proposed. Non-Markovian dynamics of two-level quantum system with memory and interaction with environment is described. To describe this system, the Gorini–Kossakowski–Sudarshan equation for open quantum states is generalized by taking into account power-law fading memory. The non-Markovian quantum processes with power-law memory are described by using integration and differentiation of non-integer orders. Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. An example of two-level quantum systems with power-law memory is suggested. Exact solution of the non-Markovian master equations of two-level open quantum systems with memory is derived.
This paper provides a physics-informed Bayesian machine learning (PIBML) description and case study. The PIBML approach applies three physics-based models to establish the initial beliefs before testing to determine the probability of milling stability (or prior). These include: receptance coupling substructure analysis (RCSA) prediction for the tool tip frequency response functions; finite element software prediction of the mechanistic force model coefficients; and a spindle speed-dependent power law model for process damping. Testing was then performed to identify optimal stable machining conditions using an expected improvement in material removal rate criterion. The prior probability of stability was updated using the test results to determine the posterior probability of stability. The test results were compared to the parameter recommendations provided by the endmill manufacturer. A demonstration integral blade rotor was machined at the optimal stable machining conditions for 304 stainless steel and 6061-T6 aluminum. Finally, the disagreement between manufacturer recommendations and milling performance in both materials tested emphasizes the need for broad implementation of PIBML approaches to increase machining productivity and efficiency.
ABSTRACT We present the results of the power spectral density (PSD) analysis for the blazars Mrk 421 and PKS 2155−304, using good-quality, densely sampled light curves at multiple frequencies, covering 17 decades of the electromagnetic spectrum, and variability time-scales from weeks up to a decade. The data were collected from publicly available archives of observatories at radio from Owens Valley Radio Observatory, optical and infrared (B, V, R, I, J, H, and Kbands), X-rays from the Swift and the Rossi X-ray Timing Explorer, high and very high energy (VHE) γ-rays from the Fermi and Very Energetic Radiation Imaging Telescope Array System as well as the High Energy Stereoscopic System. Our results are: (1) the power-law form of the variability power spectra at radio, infrared, and optical frequencies have slopes ∼1.8, indicative of random-walk-type noise processes; (2) the power-law form of the variability power spectra at higher frequencies, from X-rays to VHE γ-rays, however, have slopes ∼1.2, suggesting a flicker noise-type process; and (3) there is significantly more variability power at X-rays, high and VHE γ-rays on time-scales ≲ 100 d, as compared to lower energies. Our results do not easily fit into a simple model, in which a single compact emission zone is dominating the radiative output of the blazars across all the time-scales probed in our analysis. Instead, we argue that the frequency-dependent shape of the variability power spectra points out a more complex picture, with highly inhomogeneous outflow producing non-thermal emission over an extended, stratified volume.
This project aimed to investigate a new approach to bulk microphysics schemes. We identified the need to move beyond the fixed structural assumptions and approximation of existing schemes. For example, most schemes assume some functional form for the rain drop size distribution (e.g. a gamma or exponential distribution). Most schemes then evolve some number of statistical moments of that distribution via various processes, such as evaporation, sedimentation, collision-coalescence, and collisional breakup. These microphysical processes, in turn, are typically some fixed functional form derived from either some other (more detailed) model, or using some single-particle rates that are then integrated over the size distribution. While these process rate functions may have some free parameters to adjust, in other cases doing so is impossible (e.g. when the process rates are analytical or piecewise solutions to some target function). Our goal was to build and test a scheme that assumed no size distribution form, and used a series of power laws as the basis for the process rates. Moments of the size distribution would be predicted, but no underlying size distribution would be specified. Any number or choice of size distribution moments could be used, and any number of power laws could be employed to model the process rates. Thus, our approach is flexible, and can seamlessly scale across levels of complexity, as demanded by the data. Bayesian inference then would provide the formalism to estimate the model parameters and structure, allowing for robust uncertainty quantification. We proposed testing this framework in idealized simulations using bin microphysical schemes as a data source. We also proposed using real data to inform our microphysics scheme, and also that we would integrate our scheme into WRF.
Accurate modeling of mixing in the transported probability density function (PDF) method remains a great challenge, especially for turbulent premixed combustion under extreme conditions such as high Karlovitz number Ka. Recently, a power-law based mixing timescale model was developed for the large-eddy simulations (LES)/PDF modeling of high-Ka number turbulent premixed flames. It is found in this work that the power-law mixing timescale model is highly sensitive to the model parameters. It is thus critically needed to develop accurate calibration of these model parameters. The empirical specification of the model parameters developed in Zhang et. al. is found to be inadequate for accurate modeling of the mixing timescale. Here, machine learning is introduced as an attractive alternative in this work for the specification of the model parameters. A high-Ka number DNS jet flame is used as the training and validation of the machine learning models. The choices of the input parameters are discussed and compared for the machine learning models. The effect of differential molecular diffusion on mixing is examined by including the effect of the Lewis number in the training of the machine learning models. The performance of different machine learning algorithms is compared for the specification of the mixing model parameters. Overall, excellent performance of the machine learning models is observed for assisting the mixing modeling. The feasibility, interpretability, applicability, generality, and portability of using machine learning are discussed in general to provide a perspective on applying data-driven machine learning for turbulent combustion modeling studies.
This work presents a model for generating nonthermal power-law tails of particles’ energy probability density functions in turbulent collisionless plasmas, applicable to both nonrelativistic and relativistic scenarios. We propose that strong Alfvénic turbulence energizes plasma particles through curvature acceleration, particularly for particles with Larmor radii comparable to the scales of turbulence. When the energy density of the energized particles increases, the efficiency of the energy exchange process diminishes. As a result, the acceleration process saturates, leading to power-law distributions of particle momentum and energy. In the nonrelativistic case, the momentum probability density function scales as f(p)dp ∝ p −3 dp, while in the ultrarelativistic case, the energy probability density function scales as f(γ)dγ ∝ γ −3 dγ, where γ is the Lorentz factor. This model provides a unified framework for understanding particle acceleration in both energy regimes, complementing existing analytical approaches. The predicted scalings are consistent with available observations of energetic ion distributions in the heliosphere and with the findings from numerical simulations of ultrarelativistic particle acceleration in magnetically dominated plasma turbulence.
Magnetic reconnection in the relativistic and transrelativistic regimes is able to accelerate particles to hard power-law energy spectra f ∝ γ -p (approaching p = 1). The underlying acceleration mechanism that determines the spectral shape is currently a topic of intense investigation. By means of fully kinetic plasma simulations, we carry out a study of particle acceleration during magnetic reconnection in the transrelativistic regime of a proton–electron plasma. While earlier work in this parameter regime has focused on the effects of electric field parallel to the local magnetic field on the particle injection (from thermal energy to the lower-energy bound of the power-law spectrum), here we examine the roles of both parallel and perpendicular electric fields to gain a more complete understanding on the injection process and further development of a power-law spectrum. We show that the parallel electric field does contribute significantly to particle injection, and is more important in the initial phase of magnetic reconnection. However, as the simulation proceeds, the acceleration by the perpendicular electric field becomes more important for particle injection and completely dominates the acceleration responsible for the high-energy power-law spectrum. This holds robustly, in particular for longer reconnection times and larger systems, i.e., in simulations that are more indicative of the processes in astrophysical sources.
Electrochromic pseudocapacitive transition-metal oxide materials, such as tungsten oxide, which combine fast response, high energy density, and optical effects, can play a significant role as energy storage materials. Here we investigate the electrochemical kinetics of thin films of tungsten oxide, which turn transparent to sky-blue color in the lithiated state due to the reduction of W 6+ to W 5+ . In this study, we investigated the charge density, charge transfer, ion diffusion, and interfacial behavior upon Li + insertion/de-insertion in WO 3 . The electrochromic thin film's pseudocapacitive and electrical double layer mechanism was differentiated based on the power-law. Faradaic diffusion-controlled process dominates over the surface capacitive behavior at scan rates below 40 mV s –1 . These films exhibit an areal charge density of around 100 mC cm –2 and a capacitance of 80 mF cm –2 , superior to most comparable electrochromic materials and supercapacitors. This work combines electrochromics and energy storage properties and provides a fundamental understanding of pseudocapacitive and electrochromic mechanisms in WO 3 .
It is unclear if neutron star mergers can explain the observed r-process abundances of metal-poor stars. Collapsars, defined here as rotating massive stars whose collapse results in a rapidly accreting disk around a black hole that can launch jets, are a promising alternative. We find that we can produce a self-consistent model in which a population of collapsars with stochastic europium yields synthesizes all of the r-process material in metal-poor ([Fe/H] < - 2.5) stars. Our model reproduces the observed scatter and evolution of scatter of [Eu/Fe] abundances. We find that if collapsars are the dominant r-process site for metal-poor stars, r-process synthesis may be linked to supernovae that produce long γ-ray bursts. Our results also allow for the possibility that core-collapse supernovae beyond those that launch γ-ray bursts also produce r-process material (e.g., potentially a subset of Type Ic-BL supernovae). Furthermore, we identify collapsar jet properties (isotropic energy, engine luminosity, or engine time) that may trace r-process yield and verify that the amount of r-process yield produced per collapsar in our model ( ~ 0.07M⊙) is consistent with other independent estimates. In the future, achieving 0.05 dex precision on distribution scatter or a reliable selection function would further constrain our probe of r-process production. Our model would also hold for another prompt r-process site with a power-law yield, and work is needed to determine if, for example, fast-merging neutron stars can also explain abundance scatter.
In this work, we report a synthetic pathway by which amorphous Al(OH) 3 is converted to γ-AlOOH through hydrothermal reaction in the presence of water at temperature T = 473 K. X-ray pair distribution function measurements reveal that the initially amorphous Al(OH) 3 possesses a locally γ-Al(OH) 3 -like structure, while nanocrystalline γ-AlOOH precipitates within 1 h of continuous hydrothermal exposure. Solid state nuclear magnetic resonance measurements show that resonant features associated with four- and five-member Al clusters persist through 20 min of hydrothermal treatment, and ultraviolet (UV) spectra mark the onset of UV-induced photoluminescent features characteristic to γ-AlOOH with 10 min of exposure, indicating a coexistence region of γ-Al(OH) 3 -like and γ-AlOOH-like amorphous species. Furthermore, powder x-ray diffraction measurements of desiccated powders reveal that the conversion process takes place in distinct, power law-defined stages with initial γ-AlOOH nucleation occurring within the first 20 min, followed by a ~ 1 h period of rapid grain coarsening and the subsequent onset of Lifshitz-Slyozov-Wagner-like coalescence.
Magnetic reconnection is a primary driver of particle acceleration processes in space and astrophysical plasmas. Understanding how particles are accelerated and the resulting particle energy spectra is among the central topics in reconnection studies. We review recent advances in addressing this problem in nonrelativistic reconnection that is relevant to space and solar plasmas and beyond. We focus on particle acceleration mechanisms, particle transport due to 3D reconnection physics, and their roles in forming power-law particle energy spectra. We conclude by pointing out the challenges in studying particle acceleration and transport in a large-scale reconnection layer and the relevant issues to be addressed in the future.
Recent observations have shown that in many large solar energetic particle (SEP) events the event-integrated differential spectra resemble double power laws. We perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation, including protons and heavier ions. We find that for all ion species the energy spectra integrated over the simulation domain can be described by a double power law, and the break energy depends on the ion charge-to-mass ratio as E B ~ (Q/A) α , with α varying from 0.16 to 1.2 by considering different turbulence spectral indices. We suggest that the double-power-law distribution may emerge as a result of the superposition of energetic particles from different source regions where the acceleration rates differ significantly due to particle diffusion. The diffusion and mixing of energetic particles could also provide an explanation for the increase of Fe/O at high energies as observed in some SEP events. Although further mixing processes may occur, our simulations indicate that either a power-law break or rollover can occur near the Sun and predict that the spectral forms vary significantly along the shock front, which may be examined by upcoming near-Sun SEP measurements from the Parker Solar Probe and Solar Orbiter.
In this work, we employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant–matrix pair correlation function and the penetrant–matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.
Abstract Hyporheic zones regulate biogeochemical processes in streams and rivers, but high spatiotemporal heterogeneity makes it difficult to predict how these processes scale from individual reaches to river basins. Recent work applying allometric scaling (i.e., power‐law relationships between size and function) to river networks provides a new paradigm for understanding cumulative hyporheic biogeochemical processes. We used previously published model predictions of reach‐scale hyporheic aerobic respiration to explore patterns in allometric scaling across two climatically divergent basins with differing characteristics in the Pacific Northwest, United States. In the model, hydrologic exchange fluxes (HEFs) regulate hyporheic respiration, so we examined how HEFs might influence allometric scaling of respiration. We found consistent scaling behaviors where HEFs were either very low or very high, but differences between basins when HEFs were moderate. Our findings provide initial model‐generated hypotheses for factors influencing allometric scaling of hyporheic respiration. These hypotheses can be used to optimize new data generation efforts aimed at developing predictive understanding of allometries that can, in turn, be used to scale biogeochemical dynamics across watersheds.
Energetic GeV photons expected from the closest and the most energetic Gamma-ray bursts (GRBs) provide a unique opportunity to study the very-high-energy emission as well as the possible correlations with lower energy bands in realistic GRB afterglow models. In the standard GRB afterglow model, the relativistic homogeneous shock is usually considered to be fully adiabatic, however, it could be partially radiative. Based on the external forward-shock scenario in both stellar wind and constant-density medium, we present a radiative-adiabatic analytical model of the synchrotron self-Compton (SSC) and synchrotron processes considering an electron energy distribution with a power-law index of $1\lt p\lt 2$ and $2\le p$. We show that the SSC scenario plays a relevant role in the radiative parameter $\epsilon$, leading to a prolonged evolution during the slow cooling regime. In a particular case, we derive the Fermi/LAT light curves together with the photons with energies $\ge 100$ MeV in a sample of nine bursts from the second Fermi/LAT GRB catalogue that exhibited temporal and spectral indices with $\gtrsim 1.5$ and $\approx 2$, respectively. These events can hardly be described with closure relations of the standard synchrotron afterglow model, and also exhibit energetic photons above the synchrotron limit. We have modelled the multiwavelength observations of our sample to constrain the microphysical parameters, the circumburst density, the bulk Lorentz factor, and the mechanism responsible for explaining the energetic GeV photons.
The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-emission approximations. Previous work has computed overlap effects for double splitting g → gg → ggg. To make use of those results, one also needs calculations of related virtual loop corrections to single splitting g → gg in order to cancel severe (power-law) infrared (IR) divergences. This paper provides calculations of nearly all such processes involving gluons and discusses how to organize the results to demonstrate the cancellation. In the soft emission limit, our results reproduce the known double-log behavior of earlier authors who worked in leading-log approximation. We also present a first (albeit numerical and not yet analytic) investigation of sub-leading, single IR logarithms. Ultraviolet divergences appearing in our calculations correctly renormalize the coupling αs in the usual LPM result for leading-order g → gg.
Mo 2 C is one of the few compounds that possess good electronic conductivity. Meanwhile, it possesses a natural 1D zigzag tunnel structure that is ideally suited for fast ion diffusion. Here, an effective approach is demonstrated for fabrication of structurally stable N-doped Mo 2 C/C nanobelts. They demonstrate high and fast energy storage ability with initial capacitances of 1139 C g -1 at 1 mV s-1, 151 C g -1 at an extremely high scan rate of 2000 mV s -1 and 208 C g -1 at a discharge current density of 200 A g -1 . After electrochemical activation of cycling, the capacity is continuously enhanced and much higher capacitances of 2523 C g -1 at 1 mV s -1 and 1403 C g -1 at 50 A g -1 are achieved after 15,000 cycles at 50 mV s -1 . Using the power law, it is evaluated that a surface-controlled capacitive process makes the main contribution to the capacity, which is over 90% when the scan rates are higher than 10 mV s -1 and still high as 73% at 1 mV s -1 . From in situ synchrotron XRD, it is found that there is a negligible change in the crystal structure and volume during charging/discharging, reflecting an insertion-type charge storage mechanism.