Initial Distribution Research Articles

Topology optimization of a thermal cloak in the frequency domain

Designing wideband thermal cloaks remains a challenge, especially at high frequencies. We propose an optimization approach for the design of a thermal cloak for an arbitrary object with large thermal conductivity (copper), in a given frequency band and for a specific diffusion direction. Cloaking performance is assessed as a function of frequency (in the optimal direction) and as a function of angle (at the optimal frequency). Near-perfect cloaking is achieved over a finite frequency band, and, moreover, the thermal cloak performs well in the time domain, including in the transient regime, irrespective of the initial temperature distribution. Interestingly, this specially optimized cloak also works fairly well for other objects with large thermal conductivity but breaks down for those of low thermal conductivity.

Cryogenic deformation tailors the dislocation accumulation mode to modify grain boundary character distribution of Incoloy 925

Cryogenic deformation was introduced in thermomechanical processing to restrict dislocation mobility and tailor the initial dislocation distribution at the deformation stage, subsequently followed by annealing treatment to alter the grain boundary characteristic distribution with a view to the feasibility of grain boundary engineering in Incoloy 925. The microstructural evolution deformed at cryogenic (77 K) and room temperature (298 K) under various rolling reductions and annealing conditions was systematically studied to optimize the grain boundary network, which is evaluated using multi-source quantitative statistics of the twin related domains. The results showed that cryogenic deformation can adjust the dislocation accumulation mode and plastic deformation mechanism. Geometrically dislocation distributions, reconstructed by HR-EBSD device, with fishbone-like, ribbon-like or lamellar characteristics can be observed for the deformed specimens. During the subsequent annealing, the samples with 5% and 15% pre-strain are incapable of producing the ideal twin related domains, while the sample annealed at 1075°C with 10% pre-strain show the optimization of GBCD with the highest Σ3n (n = 1, 2, and 3) boundary fraction being 69.67%. Compared with the room temperature pre-deformation, cryogenic deformation can effectively reduce the critical temperature of GBE, and also leads to the Σ3n grain boundaries proportion increasing from 31.47% to 67.46% in 10%/1050°C sample. Meanwhile, with the appropriate strain, cryogenic deformation is more conducive to optimizing the GBCD than room-temperature deformation.

Detailed analysis of banded chorus gap formation by an electron shell distribution

In a recent paper [K. Min, Phys. Plasmas 30, 012904 (2023)], the formation of the banded chorus with a gap in intensity at half the electron cyclotron frequency (Ωe/2) is demonstrated by particle-in-cell simulations including an isotropic shell distribution at an intermediate energy. This follow-up study focuses on the phase space density (PSD) hill formation process and its role in the chorus wave damping at the gap. We first show that phase-trapped particles closely follow single wave characteristics in momentum space. This means that the formation of either PSD hole or hill is primarily determined by the temperature anisotropy, T⊥/T‖, of an initial distribution function. The critical value of T⊥/T‖ increases (decreases) for a higher (lower) resonant frequency. We then revisit the recent banded chorus simulations to investigate how the presence of an isotropic shell distribution self-consistently affects chorus wave evolution at the gap. Initially, with an increasing wave frequency, more and more shell electrons get trapped and a PSD hill is formed. The enhanced PSD hill counteracts wave growth driven by phase-trapped anisotropic electrons and subsequently reduces wave amplitude. The weakened wave self-consistently feeds back to the particle trapping, ultimately suppressing both the PSD hole and hill. By the time the wave frequency reaches about 0.45Ωe, the gyro-phase structure of the electron distribution becomes much less organized. In some cases, however, the wave growth at the upstream source region can be strong enough that waves still manage to go through the gap frequency, suggesting that additional process(es) should likely be accompanied.

What long-period comets tell us about the Oort Cloud

Context. The Oort Cloud is located in the farthest outskirts of the Solar System, extending to a heliocentric distance of several tens of thousands of au, and remains the last region of the Solar System where no object has been detected. Thus, all our knowledge of the Oort Cloud has been deduced from the observed long-period comets that are thought to originate from it. Aims. We aimed to retrieve valuable information that might be hidden in the orbital distributions of the observed long-period comets. Such information will allow us to impose constraints not only on the present shape of the Oort Cloud but also on its initial shape 4.5 Gyr ago. This has direct implications for the scenario proposed for its formation. Methods. We used two different databases of long-period comets. First, we calculated the distribution of orbital elements that might carry valuable information about the shape of the Oort Cloud. Then, we compared the distribution with that obtained from two synthetic samples of observable comets. These samples correspond to two considerably different initial configurations: one is a disk model, where we consider a swarm of comets with orbits aligned to the ecliptic plane and with a cometary perihelion close to the giant planets. The other is an isotropic model, where we consider a fully isotropic and thermalized initial distribution of comets. Results. The comparison revealed that the databases contained several features that were in better agreement with the disk model than with the isotropic model. The Oort Cloud contained an initial disk of objects with perihelia close to the planetary region of the Solar System and aphelia extending out to roughly 20 000 au. Some parts of this disk likely remain in the present Solar System. However, the fit to the disk model is poor. The discrepancy between the observational and synthetic results indicates that some dynamical processes in the current Oort Cloud were not included in either model. Conclusions. This initial shape of the Oort Cloud implies that planetary scattering was crucial during its formation. In addition, the fact that some dynamical features are still detec table 4.5 Gyr after the cloud formation imposes constraints on the role of exosolar effects, such as giant molecular clouds, Galactic tides, and the stellar cluster surrounding the Solar System at the time of its formation.

Modelling of particulate contamination redistribution inside purged cavities

Sophisticated instruments on-board most of satellite payloads, especially scientific ones, are sensitive to particulate contamination since their performance can be affected in terms of straylight or surface obscuration. The surface cleanliness levels have to be minimized on ground. However, even if the deposition rate is controlled in cleanroom, the hardware is continuously exposed to particles and fibers, moving in the airflow and settling according to their various sizes and matter compositions. Thus, depending on the initial surface cleanliness level, the redistribution of particulate contamination can be a concern during integration and tests activities until launch, when venting and/or vibrations occur which results in more or less random fallout of particles. Previous studies identified different steps for the transfer mechanism such as detachment, transport and interaction with the surface (with or without bounce). Therefore, it is paramount to understand the physical phenomena of particle resuspension that happens either inside purged cavities of spacecraft or under fairing in order to be able to model them as for molecular contamination. After performing a state of the art of the existing detachment models, a Computational Fluid Dynamics software, scSTREAM, has been chosen among the most relevant ones for a feasibility study to simulate particles redistribution. This tool was particularly interesting due to the possibility to add specific functions for computation. For the purpose, the Rock’n’Roll (R’n’R) model has been implemented to consider particle resuspension. In parallel, some simple test configurations have been defined and a mock-up with several adjacent cavities has been used to compare theory and experiment when a purging under dry nitrogen was applied in the vicinity of a pre-contaminated surface. The relocation of FluoDust particles, as the source of contamination, deposited on a specific substrate has been evaluated thanks to many collector plates disseminated in one or two cavities and the levels quantified. The impact of different test conditions (flow rate, material of the substrate, presence of leakage, initial contamination level…) has been investigated. This paper presents the comparative results that confirmed the redistribution of the particulate contamination with similar trajectories but also some discrepancies due to the limitations of the R’n’R model and depending on experimental parameters such as initial distribution of particles, adherence force to the substrate…

A Kullback–Leibler divergence method for input–system–state identification

The capability of a novel Kullback–Leibler divergence method is examined herein within the Kalman filter framework to select the input–parameter–state estimation execution with the most plausible results. This identification suffers from the uncertainty related to obtaining different results from different initial parameter set guesses, and the examined approach uses the information gained from the data in going from the prior to the posterior distribution to address the issue. Firstly, the Kalman filter is performed for a number of different initial parameter sets providing the system input–parameter–state estimation. Secondly, the resulting posterior distributions are compared simultaneously to the initial prior distributions using the Kullback–Leibler divergence. Finally, the identification with the least Kullback–Leibler divergence is selected as the one with the most plausible results. Importantly, the method is shown to select the better performed identification in linear, nonlinear, and limited information applications, providing a powerful tool for system monitoring.

The energy distribution of the first supernovae

ABSTRACT The nature of the first Pop III stars is still a mystery and the energy distribution of the first supernovae is completely unexplored. For the first time we account simultaneously for the unknown initial mass function (IMF), stellar mixing, and energy distribution function (EDF) of Pop III stars in the context of a cosmological model for the formation of a MW-analogue. Our data-calibrated semi-analytic model is based on a N-body simulation and follows the formation and evolution of both Pop III and Pop II/I stars in their proper time-scales. We discover degeneracies between the adopted Pop III unknowns, in the predicted metallicity and carbonicity distribution functions and the fraction of C-enhanced stars. None the less, we are able to provide the first available constraints on the EDF, $dN/dE_\star \propto E_{\star }^{-\alpha _e}$ with 1 ≤ αe ≤ 2.5. In addition, the characteristic mass of the Pop III IMF should be mch < 100 M⊙, assuming a mass range consistent with hydrodynamical simulations (0.1–1000 M⊙). Independent of the assumed Pop III properties, we find that all $\rm [C/Fe]\gt +0.7$ stars (with $\rm [Fe/H]\lt -2.8$) have been enriched by Pop III supernovae at a $\gt 20~{{\ \rm per\ cent}}$ level, and all $\rm [C/Fe]\gt +2$ stars at a $\gt 95~{{\ \rm per\ cent}}$ level. All very metal-poor stars with $\rm [C/Fe]\lt 0$ are predicted to be predominantly enriched by Pop III hypernovae and/or pair instability supernovae. To better constrain the primordial EDF, it is absolutely crucial to have a complete and accurate determination of the metallicity distribution function, and the properties of C-enhanced metal-poor stars (frequency and [C/Fe]) in the Galactic halo.

Analysis of homogeneity and rheological properties of filling slurry during the mixing process through electrical resistance tomography

Mixing is a key process in the paste filling technology. This study utilized electrical resistance tomography and rheological experiments to examine the particle distribution and rheological properties of filling slurry at different shearing speeds, concentrations, and initial particle size distributions. The results indicated that filling slurry flow could be categorized into three states under different shearing speeds: insufficient mixing, full mixing, and excessive mixing. In combination with the rheological characteristics, the radial index and the filling slurry index could be used to measure homogenization. As the shearing speed increases, the homogeneity of the filling slurry improves, and the dynamic yield stress also changes. Increasing shearing speed has a negative impact on particle distribution as homogeneity is reached. The homogenization of the filling slurry is related to particle migration. Additionally, the mechanical response to shearing is discussed. Material and shearing conditions determine the interaction between particles.

Identification of a 4.3 billion year old asteroid family and planetesimal population in the Inner Main Belt

Context. Understanding the conditions that lead to the formation of planetesimals – the building blocks of planets - and their initial size distribution is a central problem of modern planetology. While most of these original planetesimals were accreted onto the terrestrial planets and the cores of the giant planets, some were also stranded in the main belt, where 4.5 Gyr of collisional evolution broke most of them into families of collisional asteroid fragments. However, some planetesimals survived, and are still hidden amongst asteroid fragments in the main belt. Aims. We make use of astronomical data to identify these leftover planetesimals amongst all other asteroids. Our search is based on separating planetesimal survivors from families of asteroids generated by collisions. Namely, we aim to identify and “clean” the main belt of collisional family members: by doing so, we would be left with the surviving members of the original planetesimals. Methods. We focus here on the inner portion of the main belt for asteroids with intermediate to high albedo. It is known that current asteroid family catalogs are not suitable for the aforementioned cleaning; they are conservative and only one-quarter of the known asteroids are associated with the approximately 120 distinct asteroid families. We therefore developed methods to inclusively link asteroids to known collisional families in order to better capture their extent. Namely, we apply a hierarchical clustering method (HCM) on asteroids filtered according to the V-shape of the Yarkovsky drift of each family in order to reassess family membership (V-shape-constrained HCM). The identified families were removed and the remaining background population was searched for previously undetected collisional families. Results. We succeed in using our V-shape-constrained HCM to link family “halos” to their cores. After removing these reassessed families from the asteroid population, our V-shape search reveals a previously unknown collisional family of S-type asteroids in the inner main belt with an age of 4.3 ± 1.7 Gyr and a significance level of 3.4σ. When this ancient collisional family is removed, 34 planetesimals are identified and their size-frequency distribution is presented. Conclusions. The asteroid belt has two components: planetesimals and collisional fragments. The cumulative size-frequency distribution of planetesimals has a steep power-law index for bodies larger than 100 km in diameter and a much smaller power-law index for planetesimals smaller than 100 km.

Modeling Impacts of Implementation Policies of Tradable Credit Schemes on Traffic Congestion in the Context of Traveler’s Cognitive Illusion

A tradable credit scheme (TCS) is a novel traffic demand management (TDM) measure that can effectively mitigate traffic congestion in a revenue-neutral way. Under a given TCS, the cognitive illusion (CI) would occur when travelers instinctively use a specious thinking logic to estimate travel cost. The traveler’s CI would significantly influence his/her route choice behaviors, and thus the regulation effect of TCS on mitigating traffic congestion. To reveal the impacts of implementation policies of TCS on managing network mobility in the context of the traveler’s CI, this study investigated the traffic equilibrium assignment model with consideration of the traveler’s CI and the specific implementation policies of TCS. By incorporating the two types of factors into the generalized path travel cost (GPTC), the coupled user equilibrium (UE) and market equilibrium (ME) conditions are established to describe the equilibrium state of the traffic network under a given TCS. As the implementation policies of TCS are factored in the GPTC, different types of initial credit distribution scheme (ICDS) and the transaction costs (TC) of trading credits can be analyzed within the unified model framework. The coupled UE and ME conditions are then reformulated as an equivalent variational inequality (VI) model, and the sufficient conditions for the uniqueness of UE link flows and ME credit price are also provided. The system optimal (SO) TCS design problem is further investigated to achieve the minimum total travel time (TTT) of the transportation network, and two analytical methods are proposed to obtain the SO TCS in the context of the traveler’s CI. Numerical experiments are presented to verify the proposed model and methods. The results show that the presence of the traveler’s CI has an effect of lowering the ME credit price, and ICDS and TC have a complex network-wide influence on the ME credit price and UE link flows, which depends on the specific values of the relevant parameters.

Spatial distribution, and predictors of late initiation of first antenatal care visit in Ethiopia: Spatial and multilevel analysis.

Despite the proven benefit of early initiation of first antenatal care visits as a means to achieve good maternal and neonatal health outcomes through early detection and prevention of risks during pregnancy, shreds of evidence showed that most of the women in Ethiopia start their ANC visits lately. To determine the spatial distribution and predictors of late initiation of first antenatal care visits among reproductive-age women in Ethiopia. The 2019 Ethiopian Mini Demographic and Health Survey (EMDHS) data were used. A total weighted sample of 2,935 reproductive-age women who gave birth in the five years preceding the survey and who had antenatal care visits for their last child was included. To check the nature of the distribution of late initiation of ANC visits, the global Moran's I statistics were applied. Gettis-OrdGi statistics and spatial interpolation using the Ordinary Kriging method were done to identify the spatial locations and to predict unknown locations of late initiation of first ANC visits, respectively. For the predictors, a multilevel mixed-effect logistic regression model was applied. Finally, statistical significance was declared at a p-value < 0.05. The prevalence of late initiation of first ANC visits in Ethiopia was 62.6%. The spatial analysis showed that the late initiation of first ANC visits significantly varied across regions of Ethiopia. The spatial interpolation predicted the highest rates of late initiation of first ANC visits in the eastern SNNPRs, southern and western Oromia, and some parts of the Somalia region. Being rural residents, attending higher education, having medium wealth status, richer wealth status, richest wealth status, having ≥ 5 family size, a household headed by male, living in SNNPRs, and Oromia regions were significant predictors of late initiation of first ANC visits. A clustered pattern of areas with high rates of late initiation of the first ANC visit was detected in Ethiopia. Public health intervention targeting the identified hotspot areas, and women's empowerment would decrease the late start of the first ANC visit. Furthermore, the identified predictors should be underscored when designing new policies and strategies.

Comparative Analysis of the Hot Isostatic Pressing Densification Behavior of Uniform and Non-Uniform Distributed Powder

Hot isostatic pressing (HIP) technology can directly produce nearly clean shaped workpieces that meet the requirements while ensuring machining accuracy and surface quality. Usually, people use numerical simulation methods to reduce experimental costs. Generally, a uniform powder relative density distribution of about 65% is used in the simulation. However, in practical engineering, we found that even with additional tools such as vibration tables, the powder filling is not uniform. The non-uniform distribution causes uneven shrinkage of the powder and capsule after HIP. In this paper, a numerical model for HIPing of Ti-6Al-4V powder is developed to improve the prediction by comparing the uniform and non-uniform initial powder distribution. The results show that different initial relative density distributions affect the powder densification process and further affect the deformation of the capsule. It also leads to non-uniform stress distribution after HIP, which increases the risk of capsule rupture. The analysis of the numerical simulation results and the comparison with the experimental results highlights that taking into account the non-uniform powder distribution inside the capsule is vital to improve numerical results and produce near-net shape components. The maximum error of the simulation with the usual initial relative density setting of 65% is 4.2%. However, considering the uneven distribution of initial powder, the maximum error is reduced to 3.16%, and the average error is also less than 2%.

An Intelligent Cost-Reference Particle Filter with Resampling of Multi-Population Cooperation.

Although the cost-reference particle filter (CRPF) has a good advantage in solving the state estimation problem with unknown noise statistical characteristics, its estimation accuracy is still affected by the lack of particle diversity and sensitivity to the particles' initial value. In order to solve these problems of the CRPF, this paper proposed an intelligent cost-reference particle filter algorithm based on multi-population cooperation. A multi-population cooperative resampling strategy based on ring structure was designed. The particles were divided into multiple independent populations upon initialization, and each population generated particles with a different initial distribution. The particles in each population were divided into three different particle sets with high, medium and low weights by the golden section ratio according to the weight. The particle sets with high and medium weights were retained. Then, a cooperative strategy based on Gaussian mutation was designed to resample the low-weight particle set of each population. The high-weight particles of the previous population in the ring structure were randomly selected for Gaussian mutation to replace the low-weight particles in the current population. The low-weight particles of all populations were resampled in turn. The simulation results show that the intelligent CRPF based on multi-population cooperation proposed in this paper can reduce the sensitivity of the CRPF to the particles' initial value and improve the particle diversity in resampling. Compared with the general CRPF and intelligent CRPF with adaptive MH resampling (MH-CRPF), the RMSE and MAE of the proposed method are lower.

Unstable Points, Ergodicity and Born's Rule in 2d Bohmian Systems.

We study the role of unstable points in the Bohmian flow of a 2d system composed of two non-interacting harmonic oscillators. In particular, we study the unstable points in the inertial frame of reference as well as in the frame of reference of the moving nodal points, in cases with 1, 2 and multiple nodal points. Then, we find the contributions of the ordered and chaotic trajectories in the Born distribution, and when the latter is accessible by an initial particle distribution which does not satisfy Born's rule.

Effect of morphological properties on the particle size distribution measurements and modelling of porous and nonspherical aerosol behaviour

Estimating the time evolution of the suspended aerosol concentration in nuclear reactor containment is critical in assessing the environmental source term during severe accident conditions. Morphological properties of porous and non-spherical aerosol particles are necessary to convert the measured equivalent size distributions to actual size distributions and modelling the aerosol processes. Towards this, the dynamics of liquid PAO (Poly Alpha Olefin) and metal aerosol (non-radioactive fission product equivalent SrO2; and structural steel) are studied individually in a 1 m3 closed chamber. The effect of initial particle size distributions (PSDs) based on different equivalent diameters and the morphological properties on realistic modeling of experimental results is analysed. Electrical Low-Pressure Impactor (ELPI) and Scanning Mobility Particle Sizer (SMPS) are used to measure concentration decay and size growth. The aerosol dynamics model is validated with PAO aerosol data and applied to metal aerosol. Modelled dynamics using both the aerodynamic and effective density (ρe) corrected mobility equivalent PSDs of ELPI (APSD and MEPSD) agree with the measured values within 10% deviation for PAO aerosol, which are spherical with ρe (0.82 g cm−3) slightly differed from 1 g cm−3. Modelled dynamics using APSD significantly deviate around 77.5–137% for the porous and non-spherical/fractal metal aerosols, irrespective of the morphological properties explicitly used to model the aerosol processes with marginal effect. As ρe of SrO2 and steel aerosols (3.16 and 3.34 g cm−3) are >1 g cm−3, aerodynamic distribution underestimates the coagulation phenomenon, the primary aerosol dynamics process to a larger extent. The mobility equivalent size distributions of ELPI model the aerosol dynamics within 6–23% deviation, as supported by SMPS measurements. This study can be extended to ascertain the input parameters required for improved estimations of sodium combustion aerosol dynamics, which has added complexity of hygroscopic growth and time-varying chemical speciation.

Anisotropic sintering shrinkage behavior of stainless steel fabricated by extrusion-based metal additive manufacturing

Metal additive manufacturing (AM) can be achieved by first extruding polymer-based filaments with densely filled metal particles to create the so-called ‘green’ parts and then experiencing debinding and sintering to produce finished metal components. As a critical step, sintering governs the shape dimension, relative density, and resultant strength of final parts. Thus, there is a growing need for research on understanding and quantifying the sintering-induced anisotropic shrinkage. In this work, the underlying behaviors of anisotropic shrinkage during the entire sintering of extrusion-printed stainless steel 316L parts will be understood and quantified through a combination of theoretical study and experimental investigations including three-directional dilatometry, scanning electron microscopy, and X-ray computed tomography. The three-dimensional size evolution of ‘brown’ parts before sintering will be studied through a macroscopic analysis of shrinkage anisotropy factors and microstructure characterizations. Different filling strategies will be integrated with initial pore distribution characterization for anisotropic dimensional change analysis. The heterogeneous pore distribution will be discussed in conjunction with the anisotropic viscous behavior to eventually unveil the shrinkage performance in the course of sintering. The findings of this work will provide insights into the anisotropic sintering mechanisms and fill the knowledge gap of the relations between extrusion-based metal AM process and sintered structures of metal alloys.

Interpretable Policies and the Price of Interpretability in Hypertension Treatment Planning

Problem definition: Effective hypertension management is critical to reducing the consequences of atherosclerotic cardiovascular disease, a leading cause of death in the United States. Clinical guidelines for hypertension can be enhanced using decision-analytic approaches capable of capturing complexities in treatment planning. However, model-generated recommendations may be uninterpretable/unintuitive, limiting their clinical acceptability. We address this challenge by investigating interpretable treatment plans. Methodology/results: We formulate interpretable treatment plans as Markov decision processes (MDPs) and analyze the problems of optimizing monotone policies, which prohibit decreasing treatment intensity for sicker patients, and class-ordered monotone policies, which generalize monotone policies. We establish that both policies depend on initial state distributions and that optimal monotone policies can be generated tractably for many treatment planning problems. Next, we propose exact formulations for optimizing interpretable policies broadly. Then, we analyze the price of interpretability, proving that the class-ordered monotone policy’s price of interpretability does not exceed the monotone policy’s price of interpretability. Finally, we formulate and evaluate MDPs for hypertension treatment planning using a large nationally representative data set of the U.S. population. We compare the structure and performance of optimal monotone policies and class-ordered monotone policies with optimal MDP-based policies and current clinical guidelines. At the patient level, optimal MDP-based policies may be unintuitive, recommending more aggressive treatment for healthier patients than sicker patients. Conversely, monotone policies and class-ordered monotone policies never deescalate treatment, reflecting clinical intuition. Across 66.5 million patients, optimized monotone policies and class-ordered monotone policies outperform clinical guidelines, saving over 3,246 quality-adjusted life years per 100,000 patients, with both policies paying a low price of interpretability. Sensitivity analysis illustrates that monotone policies and class-ordered monotone policies are robust to various definitions of “interpretability.” Managerial implications: Interpretable policies can be tractably optimized, drastically outperform existing guidelines, and perform near optimally—potentially increasing the acceptability of decision-analytic approaches in practice. Funding: L. N. Steimle and W. J. Marrero received support from the National Science Foundation Graduate Research Fellowship [Grant DGE 1256260]. J. B. Sussman received support from the National Institutes of Health [Grants R01NS102715 and RF1AG068410], the U.S. Department of Veterans Affairs [Grants 1I01-HX003304 and 1I50-HX003251], and the Michigan Department of Health and Human Services. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2021.0373 .

Contact Temperature Measurements on Hybrid Aluminum–Steel Workpieces in a Cross-Wedge Rolling Process

The Collaborative Research Center 1153 is investigating a novel process chain for manufacturing high-performance hybrid components. The combination of aluminum and steel can reduce the weight of components and lead to lower fuel consumption. During the welding of aluminum and steel, a brittle intermetallic phase is formed that reduces the service life of the component. After welding, the workpiece is heated inhomogeneously and hot-formed in a cross-wedge rolling process. Since the intermetallic phase grows depending on the temperature during hot forming, temperature control is of great importance. In this paper, the possibility of process-integrated contact temperature measurement with thin-film sensors is investigated. For this purpose, the initial temperature distribution after induction heating of the workpiece is determined. Subsequently, cross-wedge rolling is carried out, and the data of the thin-film sensors are compared to the temperature measurements after heating. It is shown that thin-film sensors inserted into the tool are capable of measuring surface temperatures even at a contact time of 0.041 s. The new process monitoring of the temperature makes it possible to develop a better understanding of the process as well as to further optimize the temperature distribution. In the long term, knowledge of the temperatures in the different materials also makes it possible to derive quality characteristics as well as insights into the causes of possible process errors (e.g., fracture of the joining zone).

On a class of prior distributions that accounts for uncertainty in the data

A new class of prior distributions that can be used to assess the sensitivity of the Bayesian posterior inference to uncertainty in the data is proposed. This class is derived starting from an initial prior distribution and the likelihood function. We establish the mathematical properties of this class and the conditions under which ordering can be established within this class. We show how the sensitivity analysis can be performed using a standard MCMC procedure for any model whose likelihood, or an approximation, is available in a closed form and illustrate using examples. We also discuss how the proposed class is connected to the main ideas behind the Approximate Bayesian Computation (ABC) method. For this reason, we choose to call the new class of prior distributions as the ABC class of prior distributions. Finally, we close by sketching further possible extensions to this work.

Modelling uncertainties in wide binary constraints on primordial black holes

ABSTRACT Dark matter in the form of compact objects with mass Mco ≳ 10 M⊙ can be constrained by its dynamical effects on wide binary stars. Motivated by the recent interest in primordial black hole dark matter, we revisit the theoretical modelling involved in these constraints. We improve on previous studies in several ways. Specifically, we (i) implement a physically motivated model for the initial wide-binary semimajor axis distribution, (ii) include unbound binaries, and (iii) take into account the uncertainty in the relationship between semimajor axis and observed angular separation. These effects all tend to increase the predicted number of wide binaries (for a given compact object population). Therefore, the constraints on the halo fraction in compact objects, fco, are significantly weakened. For the wide binary sample used in the most recent calculation of the constraints, we find the fraction of halo dark matter in compact objects is fco &amp;lt; 1 for $M_{\rm co} \approx 300 \, \mathrm{ M}_{\odot }$, tightening with increasing Mco to fco &amp;lt; 0.26 for $M_{\rm co} \gtrsim 1000 \, \mathrm{ M}_{\odot }$.