Semi-analytical Model Research Articles

Redback: a Bayesian inference software package for electromagnetic transients

ABSTRACT Fulfilling the rich promise of rapid advances in time-domain astronomy is only possible through confronting our observations with physical models and extracting the parameters that best describe what we see. Here, we introduce redback; a Bayesian inference software package for electromagnetic transients. redback provides an object-orientated python interface to over 12 different samplers and over 100 different models for kilonovae, supernovae, gamma-ray burst afterglows, tidal disruption events, engine-driven transients among other explosive transients. The models range in complexity from simple analytical and semi-analytical models to surrogates built upon numerical simulations accelerated via machine learning. redback also provides a simple interface for downloading and processing data from various catalogues such as Swift and FINK. The software can also serve as an engine to simulate transients for telescopes such as the Zwicky Transient Facility and Vera Rubin with realistic cadences, limiting magnitudes, and sky coverage or a hypothetical user-constructed survey or a generic transient for target-of-opportunity observations with different telescopes. As a demonstration of its capabilities, we show how redback can be used to jointly fit the spectrum and photometry of a kilonova, enabling a more powerful, holistic probe into the properties of a transient. We also showcase general examples of how redback can be used as a tool to simulate transients for realistic surveys, fit models to real, simulated, or private data, multimessenger inference with gravitational waves, and serve as an end-to-end software toolkit for parameter estimation and interpreting the nature of electromagnetic transients.

Численно-аналитическая модель для интерпретации результатов индикаторных исследований нефтяных пластов: решение прямой задачи при наличии каналов низкого фильтрационного сопротивления

The article considers the problem of interpretation of tracer tests in oil reservoirs, into which a specific chemical substance - tracer - is injected via an injection well for flow monitoring and tracer concentration measurements in surrounding production wells. The testing data provide evidence of the existence of low resistance channels in the reservoirs, along which the tracer moves at velocities several orders of magnitude higher than in the reservoir. The nature and properties of these channels are unknown, and a semi-analytical model involving two small parameters is proposed to solve this problem. This makes it possible to construct two non-conjugate solutions: universal numerical and analytical. Such an approach allows us to solve both direct and inverse problems. The present article is devoted to solving the direct problem. The problem of pressure distribution in a rectangular reservoir pattern is solved in dimensionless coordinates and is universal, i.e., it does not depend on the size of the area and the pressure drop. This solution is approximated by power functions and is further used to determine the mass transfer between channel and reservoir. The problem of tracer slug propagation through the channel obeys the law of conservation of tracer mass and Darcy's law. Its solution is found by the methods of characteristics under the condition of smallness of the parameter reflecting the ratio of reservoir permeability to channel permeability. The results of the semi-analytical solution are compared with the numerical solutions previously obtained by other authors. The fundamental difference between these solutions is the presence of numerical diffusion when using the finite-difference method of solution, which leads to the «dissipation» of the trace slug edges.

Modelling the galaxy radio continuum from star formation and active galactic nuclei in the Shark semi-analytic model

ABSTRACT We present a model of radio continuum emission associated with star formation (SF) and active galactic nuclei (AGNs) implemented in the Shark semi-analytic model of galaxy formation. SF emission includes free-free and synchrotron emission, which depend on the free-electron density and the rate of core-collapse supernovae with a minor contribution from supernova remnants, respectively. AGN emission is modelled based on the jet production rate, which depends on the black hole mass, accretion rate, and spin, and includes synchrotron self-absorption. Shark reproduces radio luminosity functions (RLFs) at $1.4\, \rm GHz$ and $150\, \rm MHz$ for 0 ≤ z ≤ 4, and scaling relations between radio luminosity, star formation rate, and infrared luminosity of galaxies in the local and distant universe in good agreement with observations. The model also reproduces observed number counts of radio sources from 150 MHz to 8.4 GHz to within a factor of 2 on average, though larger discrepancies are seen at the very bright fluxes at higher frequencies. We use this model to understand how the radio continuum emission from radio-quiet AGNs can affect the measured RLFs of galaxies. We find current methods to exclude AGNs from observational samples result in large fractions of radio-quiet AGNs contaminating the ‘star-forming galaxies’ selection and a brighter end to the resulting RLFs.We investigate how this affects the infrared-radio correlation (IRRC) and show that AGN contamination can lead to evolution of the IRRC with redshift. Without this contamination, our model predicts a redshift- and stellar mass-independent IRRC, except at the dwarf-galaxy regime.

Semi-analytical modeling and vibration analysis of bolted frame structure under non-uniform pretension

Most of the frame structures in mechanical equipment are connected by bolts, and the non-uniform pretension among the bolts will have an obvious impact on the vibration characteristic parameters of the frame structure. In this paper, semi-analytical modeling and vibration analysis of a frame structure considering non-uniform pretension of bolts are carried out based on the Timoshenko beam theory and Rayleigh-Ritz method. Specifically, a method is proposed to decompose the frame structure into several substructures and model them respectively, and further the coupling springs are applied among the substructures. Through the vibration test of a beam lap structure with a bolted joint, the analytical expressions between bolt pretension and bolted joint stiffness and damping parameters are obtained. Moreover, the method of simulating the non-uniform pretension among each bolted joint is proposed. Considering the external factors such as reinforcing rib structures and flexible rod exciter, and a complete semi-analytical dynamic model of the bolted frame structure introducing the non-uniform pretension is further established. A case study is carried out on a frame structure that contains four connecting bolts with non-uniform pretension. The natural characteristics of the frame structure are solved by using the developed modeling method, and the rationality of the analysis results is verified by experiments. Based on this, the increasing trends of the resonant frequencies and the resonant response of the frame structure under different pretension conditions are analyzed from two aspects of experiment and simulation.

A novel semi-analytical model for laterally loaded piles

A new model for laterally loaded piles is proposed, consisting of a linear part and a non-linear iterative part. The linear part is based on the Green's function method, which strictly satisfies the displacement and stress continuity conditions at the pile-soil interface and leads to a rigorous solution. The non-linear iterative part assumes that the shear modulus of the soil around the pile decreases with the average strain of the soil layer. Only two soil parameters need to be calibrated, including the initial shear modulus of the soil and the reference shear strain at half the initial modulus. Compared to the finite element model, the advantage of this model is that it converges quickly while maintaining accuracy, which greatly improves computational efficiency. The advantage of this model over the p-y curve model is that it does not have the difficulty of selecting p-y spring parameters, especially for monopiles. The accuracy of this model is verified by comparison with three-dimensional finite element models and nine existing studies, including numerical models, field tests and centrifuge tests. These cases cover various piles with diameters of D∼0.273–10 m and aspect ratios of L/D∼3–40, installed in sand or clay by driving, jacking or vibration.

Extrapolating time development curves of clear-water scour around piles: From empirical fitting to physics-based approach

The currently available prediction formulas for the scour development around a pile predominantly rely on empirical fittings, lacking clear physical mechanisms. This study integrates the principle of sediment mass conservation, the flat-bed sediment transport model, and the phenomenological theory of turbulence to propose a semi-analytical model for predicting clear-water scour development around circular piles. This model overcomes scale-related issues and is governed by three fundamental parameters: the equilibrium scour depth, the characteristic time, and the ratio of the scour depth coefficient to the primary horseshoe vortex coefficient. The results demonstrate that the proposed model is consistent with experimental data. The proposed model offers significant improvements by addressing two critical issues observed in existing models: (i) empirical formulas expressed purely in mathematical terms exhibit low prediction accuracy for long-term scour, resulting in underestimation of the extrapolated equilibrium scour depth and premature attainment of equilibrium conditions; (ii) other models exhibit a divergence phenomenon, where the extrapolated equilibrium scour depth greatly exceeds the pile diameter, contradicting prevailing understanding. Applying the proposed model allows for a substantial reduction in test duration while accurately capturing the subsequent scour development process.

Stability of a reinforced concrete column under compression with torsion caused by accidental action

Under emergency situations associated with sudden failures of the load-bearing elements of the structure, torques may additionally occur in the columns due to the specifics of the structural design of the buildings. Thus, the columns may be in a complex stress-strain state. The objective of this study was to develop a semi-analytical design model for analysis of the stability of reinforced concrete columns subjected to compression with torsion as a result of an accidental action. For achieving the objective, authors formulated the initial hypotheses, developed the determining equations for calculating the stability of a reinforced concrete column subjected to compression with torsion. To validate the reliability of the proposed model, it has been compared with the results of modeling in the software complex Ansys. Analysis of the data showed that the largest difference between the results was up to 8.08% for the case P = 0.4·Pcr,e = 126.6 kN. The smallest difference of 3.6% was for the case P = 0.9·Pcr,e = 284.85 kN. It has been shown that as the torque increases, there is a decrease in the value of the critical force causing loss of stability. This is due both to the action of the torsional pair of forces during the distortion of the rod and to the decrease in the mechanical properties of concrete under the combined action of normal and tangential stresses.

A Novel Approach for Accurate Determination of Laminar Burning Velocity Using the Constant Volume Method in a Cylindrical Vessel with Full Optical Access

ABSTRACT The constant volume method (CVM) is a potential method for determining laminar burning velocity (LBV) at high pressures and temperatures. However, CVM using spherical vessels gives no optical access to the flame; in cylindrical vessels, with full optical access, the flame does not remain spherical. In either case, one has to rely on semi-analytical models, which have limitations in accuracy, to obtain burned gas volume (BGV) needed for LBV calculation. This study presents a novel approach for accurate determination of BGV and flame surface area (FSA) of non-spherical flames in cylindrical vessels from the measured end-view flame radius. Through CFD simulation, normalized relationships are developed to relate the measured flame end-view radius to the actual FSA and BGV. It is shown that these relationships are purely geometry-dependent and are independent of vessel size and combustion reactions in the vessel. This facilitates accurate determination of LBV using CVM in an optically accessible cylindrical vessel, eliminating the requirement to estimate burned gas mass fraction using burned gas mass fraction models. Experiments using CVM were performed for a stoichiometric methane-air mixture at 1.0 bar and 300 and 350 K. This new approach is demonstrated by using it to determine the LBV of stoichiometric methane-air mixture accurately. The present methodology is expected to provide a way to calculate accurate LBV without the need for additional thermodynamic models for burned gas mass fraction.

Novel semi-analytical model for solving the C*-integral of specimens with mode-I crack under various constraints

The energy rate line integral C* is an essential fracture parameter that characterizes the stress and strain rate field intensity at a crack tip for materials undergoing creep deformation, and is also a crucial parameter describing the creep crack growth rate. This study proposes a method for determining the characteristic parameters of the creep displacement rate model for specimens with mode-I crack under various constraints. Based on the displacement rate model, a semi-analytical model of the C*-integral related to the displacement rate, load, specimen sizes, and Norton's law parameters of materials is proposed. Furthermore, finite element analysis (FEA) models were established for compact tension (CT), single-edged notched bending (SEB), C-shaped tension (CST), and single-edge notched tension (SET) specimens, and the proposed models were verified using FEA results and those predicted by the ASTM method. The explicit correlation between the creep displacement rate and crack length a in the model can contribute to developing novel testing methods for real-time crack length and creep crack growth rate.

A multidimensional AI-trained correction to the 1D approximate model for Airborne TDEM sensing

The computational resources required to solve the full 3D inversion of time-domain electromagnetic data are immense. To overcome the time-consuming 3D simulations, we construct a surrogate model, more precisely, a data-driven statistical model to replace the 3D simulations. It is trained on 3D data and predicts the approximate output much faster. We construct a surrogate model that predicts the discrepancy between a 1D subsurface model and a deviation of the 1D assumption. The latter response is fastly computable with a semi-analytical 1D forward model. We exemplify the approach on a two-layered case. The results are encouraging even with few training samples. Given the computational cost related to the 3D simulations, there are limitations in the number of training samples that can be generated. In addition, certain applications require a wide range of parameters to be sampled, such as the electrical conductivity parameters in a saltwater intrusion case. The challenge of this work is achieving the best possible accuracy with only a few thousand samples. We propose to view the performance in terms of learning gain, representing the gain from the surrogate model whilst still acknowledging a residual discrepancy. Our works open new avenues for effectively simulating 3D TDEM data.

Quenching massive galaxies across cosmic time with the semi-analytic model shark v2.0

ABSTRACT We introduce version 2.0 of the shark semi-analytic model of galaxy formation after many improvements to the physics included. The most significant being (i) a model describing the exchange of angular momentum (AM) between the interstellar medium and stars; (ii) a new active galactic nuclei feedback model which has two modes, a wind and a jet mode, with the jet mode tied to the jet energy production; (iii) a model tracking the development of black hole (BH) spins; (iv) more sophisticated modelling of environmental effects on satellite galaxies; and (v) automatic parameter exploration using Particle Swarm Optimization. We focus on two timely research topics: the structural properties of galaxies and the quenching of massive galaxies. For the former, sharkv2.0 is capable of producing a more realistic stellar size–mass relation with a plateau marking the transition from disc- to bulge-dominated galaxies, and scaling relations between specific AM and mass that agree well with observations. For the quenching of massive galaxies, sharkv2.0 produces massive galaxies that are more quenched than the previous version, reproducing well the observed relations between star formation rate (SFR) and stellar mass, and specific SFR and BH mass at z = 0. shark v2.0 produces a number density of massive-quiescent galaxies >1 dex higher than the previous version, in good agreement with JWST observations at z ≤ 5; predicts a stellar mass function of passive galaxies in reasonably good agreement with observations at 0.5 < z < 5; and environmental quenching to already be effective at z = 5.

Characterizing ultra-high-redshift dark matter halo demographics and assembly histories with the gureft simulations

ABSTRACT Dark matter halo demographics and assembly histories are a manifestation of cosmological structure formation and have profound implications for the formation and evolution of galaxies. In particular, merger trees provide fundamental input for several modelling techniques, such as semi-analytic models (SAMs), sub-halo abundance matching (SHAM), and decorated halo occupation distribution models. Motivated by the new ultra-high-redshift (z ≳ 10) frontier enabled by JWST, we present a new suite of Gadget at Ultrahigh Redshift with Extra-Fine Timesteps (gureft) dark matter-only cosmological simulations that are carefully designed to capture halo merger histories and structural properties in the ultra-z universe. The simulation suite consists of four 10243-particle simulations with box sizes of 5, 15, 35, and 90 Mpc h−1, each with 170 snapshots stored between 40 ≥ z ≥ 6. With the unprecedented number of available snapshots and strategically chosen dynamic range covered by these boxes, gureft uncovers the emerging dark matter halo populations and their assembly histories in the earliest epochs of cosmic history. In this work, we present the halo mass functions (HMF) between z ∼ 20 and 6 down to log (Mvir/M⊙) ∼ 5, and show that at high redshift, these robust HMFs can differ substantially from commonly used analytic approximations or older fitting functions in the literature. We also present key physical properties of the ultra-high z halo population, such as concentration and spin, as well as their mass growth and merger rates, and again provide updated fitting functions.

Star Formation and Dust in the Cosmic Web

The large-scale environment of the cosmic web is believed to impact galaxy evolution, but there is still no consensus regarding the mechanisms. We use a semi-analytic model (SAM) galaxy catalog to study the star formation and dust content of local galaxies in different cosmic environments of the cosmic web—namely voids, filaments, walls, and nodes. We find a strong impact of the environment only for galaxies with M stars ≲ 1010.8 M ⊙: the less dense the environment, the larger the star formation rate and dust content at fixed stellar mass. This is attributed to the fact that galaxies in less dense environments typically feature younger stellar populations, a slower evolution of their stellar mass, and delayed star formation compared to galaxies in denser environments. As for galaxies with M stars ≳ 1010.8 M ⊙, the differences among environments are milder, due to the disk-instability-driven supermassive black hole (SMBH) growth implemented in the SAM, which makes SMBH growth, and thus galaxy quenching, environment-insensitive. We qualitatively test our predictions against observations by identifying environments in Sloan Digital Sky Survey Data Release 16 using dust masses derived from the GAMA survey. The agreement is encouraging, particularly at logMstars/M⊙≳10.5–11 , where the specific star formation rates and dust masses appear quite environment-insensitive. This result confirms the importance of in situ growth channels of SMBHs.

Method for vibration and acoustic radiation analysis of underwater stiffened plates with acoustic coatings

Based on the effective medium theory as well as the three-dimensional viscoelastic theory, a semi-analytical model of the three-dimensional underwater vibration and acoustic radiation with cavity-type stiffened plate structures covered with acoustic coatings is established to solve the issues related to underwater vibration and acoustic radiation calculation of the stiffened plate and shell structure with complex acoustic coatings. By comparing the far-field acoustic radiation characteristics of the proposed semi-analytical model and the finite element numerical model, this research verifies the validity and accuracy of the proposed model. On such a basis, this research preliminarily investigates the coupling effect exerted by stiffeners and parent plates in stiffened plates as well as the vibroacoustic characteristics of acoustic coatings, thereby providing a valuable idea for the prediction of vibroacoustic characteristics concerning underwater structures.

Secular evolution of resonant planets in the coplanar case

Aims. We study the secular evolution of two planets in mutual deep mean-motion resonance (MMR) in the planar elliptic three-body problem framework for different mass ratios. We do not consider any restriction in the eccentricity of the inner planet e1 or in the eccentricity of the outer planet e2. Methods. The method we used is based on a semi-analytical model that consists of calculating the averaged resonant disturbing function numerically. It is assumed for this that all the orbital elements (except for the mean longitudes) of both planets are constant on the resonant timescale. In order to obtain the secular evolution inside the MMR, we make use of the adiabatic invariance principle, assuming a zero-amplitude resonant libration. We constructed two phase portraits, called the ℋ1 and ℋ2 surfaces, in the three-dimensional spaces (e1, Δϖ, σ) and (e2, Δϖ, σ), where Δϖ is the difference between the planetary longitude of perihelia and σ is the critical angle. These surfaces, which are related through the angular moment conservation, allow us to find the apsidal corotation resonances (ACRs) and to predict the secular evolution of e1, e2, Δϖ, and σ (libration center). Results. While studying the 1:1, 2:1, 3:1, and 3:2 MMR, we found that large excursions in eccentricity can exist in some particular cases. We compared the secular variations of e1, e2, Δϖ, and σ predicted by the model with a numerical integration of the exact equations of motion for different mass ratios. We obtained good matches. Finally, the model was applied to study the secular evolution of the resonant exoplanet systems HD 73526 and HD 31527. They both have a pair of planets and are very close to the deep MMR condition. In the first system, we found that the pair of planets that constitutes the system evolves in a symmetrical ACR, whereas in the second system, we found that planets c and d, which are in an unusual 16:3 MMR, are close to an ACR, but outside its dynamical region, where Δϖ circulates.

Semi-Analytical and Data-Driven Models of Electric Field Strength Considering the Actual Structure of Medium Frequency Transformers

Semi-Analytical and Data-Driven Models of Electric Field Strength Considering the Actual Structure of Medium Frequency Transformers

Model Prediction and Experimental Validation of Transverse Permeability of Large-Tow Carbon Fiber Composites.

Large-tow carbon fiber (LCF) meets the low-cost requirements of modern industry. However, due to the large and dense number of monofilaments, there are problems with uneven and insufficient infiltration during material preparation. The permeability of large-tow carbon fibers can be used as a two-scale expression of resin flow during infiltration, making it an important factor to consider. This paper provides support for the study of pore formation. A two-dimensional model of randomly bundled large-filament carbon fibers is generated based on scanning electron microscope (SEM) maps. Microstructure size parameters are obtained, and a semi-analytical model of the transverse permeability of large-filament-bundled carbon fibers is established. Permeability values are then obtained. The analysis shows that the monofilaments in the tow are arranged randomly, and their periodic arrangement cannot be used to calculate permeability. Additionally, the number of monofilaments in a carbon fiber tow of the same volume fraction affects the permeability of the tow. Therefore, the permeability model of large-tow carbon fibers is reliable.

Impact of gas hardening on the population properties of hierarchical black hole mergers in active galactic nucleus disks

Hierarchical black hole (BH) mergers in active galactic nuclei (AGNs) are unique among formation channels of binary black holes (BBHs) because they are likely associated with electromagnetic counterparts and can efficiently lead to the mass growth of BHs. Here, we explore the impact of gas accretion and migration traps on the evolution of BBHs in AGNs. We have developed a new fast semi-analytic model, that allows us to explore the parameter space while capturing the main physical processes involved. We find that an effective exchange of energy and angular momentum between the BBH and the surrounding gas (i.e., gas hardening) during inspiral greatly enhances the efficiency of hierarchical mergers, leading to the formation of intermediate-mass BHs (up to 104 M⊙) and triggering spin alignment. Moreover, our models with efficient gas hardening show both an anticorrelation between the BBH mass ratio and the effective spin and a correlation between the primary BH mass and the effective spin. In contrast, if gas hardening is inefficient, the hierarchical merger chain is already truncated after the first two or three generations. We compare the BBH population in AGNs with other dynamical channels as well as isolated binary evolution.

Fitting the light curves of Sagittarius A* with a hot-spot model

Context. Sagittarius A* (Sgr A*) exhibits frequent flaring activity across the electromagnetic spectrum. Signatures of an orbiting hot spot have been identified in the polarized millimeter wavelength light curves observed with ALMA in 2017 immediately after an X-ray flare. The nature of these hot spots remains uncertain. Aims. We expanded existing theoretical hot-spot models created to describe the Sgr A* polarized emission at millimeter wavelengths. We sampled the posterior space, identifying best-fitting parameters and characterizing uncertainties. Methods. Using the numerical radiative transfer code ipole, we defined a semi-analytical model describing a ball of plasma orbiting Sgr A*, threaded with a magnetic field and emitting synchrotron radiation. We then explored the posterior space in the Bayesian framework of dynesty. We fit the static background emission separately, using a radiatively inefficient accretion flow model. Results. We considered eight models with a varying level of complexity, distinguished by choices regarding dynamically important cooling, non-Keplerian motion, and magnetic field polarity. All models converge to realizations that fit the data, but one model without cooling, non-Keplerian motion, and magnetic field pointing toward us improved the fit significantly and also matched the observed circular polarization. Conclusions. Our models represent observational data well and allow testing various effects in a systematic manner. From our analysis, we have inferred an inclination of ∼155 − 160 deg, which corroborates previous estimates, a preferred period of ∼90 min, and an orbital radius of 9 − 12.0 gravitational radii. Our non-Keplerian models indicate a preference for an orbital velocity of 0.6–0.9 times the Keplerian value. Last, all our models agree on a high dimensionless spin value (a* > 0.8), but the impact of spin on the corresponding light curves is subdominant with respect to other parameters.

Modeling Molecular Hydrogen in Low-metallicity Galaxies

We use a suite of hydrodynamics simulations of the interstellar medium (ISM) within a galactic disk, which includes radiative transfer, a nonequilibrium model of molecular hydrogen, and a realistic model for star formation and feedback, to study the structure of the ISM and H2 abundance as a function of local ISM properties. We show that the star formation rate and structure of the ISM are sensitive to the metallicity of the gas with a progressively smoother density distribution with decreasing metallicity. In addition to the well-known trend of the H I–H 2 transition shifting to higher densities with decreasing metallicity, the maximum achieved molecular fraction in the ISM drops drastically at Z ≲ 0.2 Z ⊙ as the formation time of H2 becomes much longer than a typical lifetime of dense regions of the ISM. We present accurate fitting formulae for both volumetric and projected fH2 measured on different scales as a function of gas metallicity, UV radiation field, and gas density. We show that when the formulae are applied to the patches in the simulated galaxy, the overall molecular gas mass is reproduced to better than a factor of ≲1.5 across the entire range of metallicities and scales. We also show that the presented fit is considerably more accurate than any of the previous fH2 models and fitting formulae in the low-metallicity regime. The fit can thus be used for modeling molecular gas in low-resolution simulations and semi-analytic models of galaxy formation in the dwarf and high-redshift regimes.