Semi-analytical Model Research Articles

A computationally efficient semi-analytical model for the dust environment of comets and asteroids

We present a model for the distribution of dust ejected by asteroids and comets. Our model incorporates the effects of solar gravity and radiation pressure. In specific cases it can also account for additional forces and the re-impacts of ejected dust onto the source body. The number density of dust at a given point in space was computed as the sum of contributions from a set of point sources placed along a given trajectory, ejecting dust in a temporal sequence that approximates the motion of the source body. The dust ejection from each source was modeled using continuous distributions of the dynamical parameters the dust grains have at ejection. We developed three methods to solve for the dust number density from a single point source that differ in complexity and applicability. We applied the model to investigate the dust environment of the near-Earth asteroid Phaethon, and estimated the number of dust grains that will be observed by the dust detector on the flyby of the forthcoming DESTINY+ mission by JAXA. Additionally, as an illustrative example, we reconstructed an image of comet C/1996 B2 (Hyakutake) to demonstrate the details of working with the model. The implementation of our model, verified with a comparison to independent software, is freely available as a Fortran-95 package, DUDI-heliocentric.

Optimizing Well Trajectories for Enhanced Oil Production in Naturally Fractured Reservoirs: Integrating Particle Swarm Optimization with an Innovative Semi-Analytical Model Framework

Summary Well trajectory optimization is a crucial component in the drilling engineering of naturally fractured reservoirs. The complex heterogeneity and anisotropy of such reservoirs significantly affect the pressure drop distribution within the well and, consequently, the oil well’s output, impacting the economic benefits of the well. Therefore, optimizing the well segment trajectory is key to efficient reservoir development. However, traditional well trajectory optimization methods primarily focus on geological structures and drilling engineering costs, often overlooking future production benefits of the oil well. This paper proposes a new method that first establishes a semi-analytical production prediction model capable of describing complex well trajectories. Although the semi-analytical model has unique advantages in well trajectory description, it typically treats the reservoir as a homogeneous entity, which complicates handling complex reservoir characteristics. To overcome this limitation, we combined optimization algorithms and neural networks to construct a framework for addressing reservoir heterogeneity (Semianalytical Model Framework for Unconventional Wells in Heterogeneous Reservoirs, USAMF-HR), enhancing the semi-analytical model’s ability to describe reservoir heterogeneity. Building on this framework, we applied the particle swarm optimization (PSO) algorithm and introduced constraints on the rationalization of initial well trajectories, as well as limits on particle movement speed and displacement, with the maximization of net present value (NPV) as the objective function, to optimize well trajectory coordinates. Through specific case analysis, the reasonableness and practicality of this method have been verified. The results show that this method can quickly and effectively plan the optimal well trajectory, significantly increasing productivity while reducing costs.

Mining for Protoclusters at z ∼ 4 from Photometric Data Sets with Deep Learning

Protoclusters are high-z overdense regions that will evolve into clusters of galaxies by z = 0, making them ideal for studying galaxy evolution expected to be accelerated by environmental effects. However, it has been challenging to identify protoclusters beyond z = 3 only by photometry due to large redshift uncertainties hindering statistical study. To tackle the issue, we develop a new deep-learning-based protocluster detection model, PCFNet, which considers a protocluster as a point cloud. To detect protoclusters at z ∼ 4 using only optical broadband photometry, we train and evaluate PCFNet with mock g-dropout galaxies based on the N-body simulation with the semianalytic model. We use the sky distribution, i-band magnitude, (g − i) color, and the redshift probability density function surrounding a target galaxy on the sky. PCFNet detects 5 times more protocluster member candidates while maintaining high purity (recall = 7.5% ± 0.2%, precision = 44% ± 1%) than conventional methods. Moreover, PCFNet is able to detect more progenitors ( Mhaloz=0=1014−14.5M⊙ ) that are less massive than supermassive clusters like the Coma cluster. We apply PCFNet to the observational photometric data set of the Hyper Suprime-Cam Strategic Survey Program Deep/UltraDeep layer (∼17 deg2) and detect 121 protocluster candidates at z ∼ 4. We find that the rest-UV luminosities of our protocluster member candidates are brighter than those of field galaxies, which is consistent with previous studies. Additionally, the quenching of satellite galaxies depends on both the core galaxy’s halo mass at z ∼ 4 and accumulated mass until z = 0 in the simulation. PCFNet is very flexible and can find protoclusters at other redshifts or in future extensive surveys by Euclid, Legacy Survey of Space and Time, and Roman.

Thermal performance analysis of a deep coaxial borehole heat exchanger with a horizontal well based on a novel semi-analytical model

This study introduces a novel semi-analytical model for deep coaxial borehole heat exchanger with a horizontal well(H-DBHE), which incorporates the effects of formation stratification and transient heat conduction within the pipe walls. Initially, the model's validity was checked through a comparison with the results derived from the published numerical models. This semi-analytical approach significantly reduces computational time while ensuring calculation accuracy. Subsequently, the study quantitatively examined the influence of the operation parameters, structural characteristics and the thermal capacity within the borehole on the dynamic heat extraction of H-DBHE. The numerical results demonstrate that the thermal capacity within the borehole significantly influences the heat extraction performance during intermittent operations of H-DBHE. Based on this finding, the study further investigated the effects of intermittent operation and heating time on the heat recovery performance of the system. Additionally, the study compared the long-term operational performance and thermal attenuation between H-DBHE and deep coaxial borehole heat exchanger (DBHE) over a ten-year simulation period. This research introduces a novel semi-analytical model for H-DBHE, which is of significant theoretical guidance for accurately predicting the heat extraction performance of H-DBHE and scientifically designing geothermal utilization systems.

Modeling the Multiwavelength Detection of Protoclusters. I. An Excess of Submillimeter Galaxies in Protocluster Cores

Studies of galaxy protoclusters yield insights into galaxy cluster formation complementary to those obtained via “archaeological” studies of present-day galaxy clusters. Submillimeter-selected galaxies (SMGs) are one class of sources used to find high-redshift protoclusters. However, due to the rarity of protoclusters (and thus the large simulation volume required) and the complexity of modeling dust emission from galaxies, the relationship between SMGs and protoclusters has not been adequately addressed in the theoretical literature. In this work, we apply the L-GALAXIES semianalytic model (SAM) to the Millennium N-body simulation. We assign submillimeter flux densities to the model galaxies using a scaling relation from previous work, in which dust radiative transfer was performed on high-resolution galaxy zoom simulations. We find that the fraction of model galaxies that are submillimeter-bright is higher in protocluster cores than in both protocluster “outskirts” and the field; the fractions for the latter two are similar. This excess is not driven by an enhanced starburst frequency. Instead, the primary reason is that overdense environments have a relative overdensity of high-mass halos and thus “oversample” the high-mass end of the star formation main sequence relative to less-dense environments. The fraction of SMGs that are optically bright is dependent on stellar mass and redshift but independent of the environment. The fraction of galaxies for which the majority of star formation is dust-obscured is higher in protocluster cores, primarily due to the dust-obscured fraction being correlated with stellar mass. Our results can be used to guide and interpret multiwavelength studies of galaxy populations in protoclusters.

Semianalytical Calculation Model for Winding Loss of Litz Wire in High-Frequency Transformer

Semianalytical Calculation Model for Winding Loss of Litz Wire in High-Frequency Transformer

Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks

The observed dust rings and gaps in protoplanetary disks could be imprints of forming planets. Even low-mass planets in the 1-10 Earth-mass regime, which have not yet carved deep gas gaps, can generate such dust rings and gaps by driving a radially-outward gas flow, as shown in previous work. However, understanding the creation and evolution of these dust structures is challenging due to dust drift and diffusion, requiring an approach beyond previous steady state models. Here we investigate the time evolution of the dust surface density influenced by the planet-induced gas flow, based on post-processing three-dimensional hydrodynamical simulations. We find that planets larger than a dimensionless thermal mass of m = 0.05, corresponding to 0.3 Earth mass at 1 au or 1.7 Earth masses at 10 au, generate dust rings and gaps, provided that solids have small Stokes numbers (St ≲ 10−2) and that the disk midplane is weakly turbulent (αdiff ≲10−4). As dust particles pile up outside the orbit of the planet, the interior gap expands with time when the advective flux dominates over diffusion. Dust gap depths range from a factor of a few to several orders of magnitude, depending on planet mass and the level of midplane particle diffusion. We constructed a semi-analytic model describing the width of the dust ring and gap, and then compared it with the observational data. We find that up to 65% of the observed wide-orbit gaps could be explained as resulting from the presence of a low-mass planet, assuming αdiff = 10−5 and St = 10−3. However, it is more challenging to explain the observed wide rings, which in our model would require the presence of a population of small particles (St = 10−4). Further work is needed to explore the role of pebble fragmentation, planet migration, and the effect of multiple planets.

Calculation and measurement of motor and converter losses according to IEC 61800-9-2 ED2

Calculated and measured motor and converter losses are compared using the example of a four-pole asynchronous motor with a rated output of 110 kW, operated on a standard converter. The determination of the motor losses using the polynomial approach to describe the motor losses in the field weakening range shows a clear deviation from the measurements. To calculate the converter losses, an equation for calculating the losses in DC link chokes was shown. The polynomial approach to describe the motor losses as a function of torque and speed can also be used for converters in the constant flux range. The semi-analytical model for calculating the converter losses shows satisfactory accuracy even when the motor is operated in the field weakening range.

Pulsational mode stability in complex EiBI-gravitating polarized astroclouds with (r,q)-distributed electrons

The pulsational mode of gravitational collapse (PMGC) originating from the combined gravito-electrostatic interaction in complex dust molecular clouds (DMCs) is a canonical mechanism leading to the onset of astronomical structure formation dynamics. A generalized semi-analytic model is formulated to explore the effects of the Eddington-inspired Born-Infeld (EiBI) gravity, non-thermal (r,q)-distributed electrons, and dust-polarization force on the PMGC stability concurrently. The thermal ions are treated thermo-statistically with the Maxwellian distribution law and the non-thermal electrons with the (r,q)-distribution law. The constitutive partially ionized dust grains are modeled in the fluid fabric. A spherical normal mode analysis yields a generalized linear PMGC dispersion relation. Its oscillatory and propagation characteristics are investigated in a judicious numerical platform. It is found that an increase in the polarization force and positive EiBI parameter significantly enhances the instability, causing the DMC collapse and vice versa. The electron non-thermality spectral parameters play as vital stabilizing factors, and so on. Its reliability and applicability are finally outlined in light of astronomical predictions previously reported in the literature.

Machine learning model based on the time domain regular perturbation-based theory for performance estimation in arbitrary heterogeneous optical links

To meet the required high demands for the capacity of optical networks, there are several efforts in recent years to further reduce the system margin. To achieve this goal, a fast and reliable QoT estimation tool is needed. The key module of such QoT tool is the nonlinear interference variance estimation. This paper presents a novel machine learning tool to speed up the exact model by six orders of magnitude without scarifying the accuracy and the scalability of this semi-analytical model. Moreover, to further enhance the scalability of the model, we used the cross-correlation functions to re-write the equations. The proposed ML-based framework KerrNet, based on a bank of small ANNs, can handle any arbitrary heterogeneous link up to ten thousand km composed of different fiber span. The transmitting C-band WDM channels in both fully loaded and sparsely occupied configurations are evaluated. The crucial steps for the machine learning algorithm to converge, which are the data preparation and the choice of training data, are presented in detail.

The formation of supermassive black holes from Population III.1 seeds. III. Galaxy evolution and black hole growth from semi-analytic modelling

ABSTRACT We present an implementation of Pop III.1 seeding of supermassive black holes (SMBHs) in a theoretical model of galaxy formation and evolution to assess the growth of the SMBH population and the properties of the host galaxies. The model of Pop III.1 seeding involves SMBH formation at redshifts $z\gtrsim 20$ in dark matter minihaloes that are isolated from external radiative feedback, parametrized by isolation distance $d_{\rm iso}$. Within a standard $\Lambda$CDM cosmology, we generate dark matter haloes using the code pinocchio and seed them according to the Pop III.1 scenario, exploring values of $d_{\rm iso}$ from 50 to 100 kpc (proper distance). We consider two alternative cases of SMBH seeding: a halo mass threshold model in which all haloes $\gt 7\times 10^{10}\,\rm M_\odot$ are seeded with $\sim 10^5\,\rm M_\odot$ black holes; an all light seed model in which all haloes are seeded with low, stellar mass black holes. We follow the redshift evolution of the haloes, populating them with galaxies using the GAlaxy Evolution and Assembly theoretical model of galaxy formation, including accretion on SMBHs and related feedback processes. Here we present predictions for the properties of galaxy populations, focusing on stellar masses, star formation rates, and black hole masses. The local, $z\sim 0$ metrics of occupation fraction as a function of the galaxy stellar mass, galaxy stellar mass function, and black hole mass function all suggest a constraint of $d_{\rm iso}\lt 75\:$ kpc. We discuss the implications of this result for the Pop III.1 seeding mechanism.

The diverse star formation histories of early massive, quenched galaxies in modern galaxy formation simulations

Abstract We present a comprehensive study of the star formation histories of massive-quenched galaxies at z = 3 in three semi-analytic models (Shark, gaea, Galform) and three cosmological hydrodynamical simulations (Eagle, IllustrisTNG, Simba). We study the predicted number density and stellar mass function of massive-quenched galaxies, their formation and quenching timescales and star-formation properties of their progenitors. Predictions are disparate in all these diagnostics, for instance: (i) some simulations reproduce the observed number density of very massive-quenched galaxies ($>10^{11}\, \rm {\rm M}_{\odot }$) but underpredict the high density of intermediate-mass ones, while others fit well the lower masses but underpredict the higher ones; (ii) In most simulations, except for gaea and eagle, most massive-quenched galaxies had starburst periods, with the most intense ones happening at 4 < z < 5; however, only in Shark and IllustrisTNG we do find a large number of progenitors with star formation rates $>300\rm \, {\rm M}_{\odot }\, yr^{-1}$; (iii) quenching timescales are in the range ≈20 − 150 Myr depending on the simulation; among other differences. These disparate predictions can be tied to the adopted Active Galactic Nuclei (AGN) feedback model. For instance, the explicit black-hole (BH) mass dependence to trigger the ‘radio mode’ in IllustrisTNG and Simba makes it difficult to produce quenched galaxies with intermediate stellar masses, also leading to higher baryon collapse efficiencies (≈15 − 30 per cent); while the strong bolometric luminosity dependence of the AGN outflow rate in gaea leads to BHs of modest mass quenching galaxies. Current observations are unable to distinguish between these different predictions due to the small sample sizes. However, these predictions are testable with current facilities and upcoming observations, allowing a ‘true physics experiment’ to be carried out.

Semi-analytical model and vibrational energy recovery efficiency of piezoelectric beams with quasi-periodic additional acoustic black holes

Semi-analytical model and vibrational energy recovery efficiency of piezoelectric beams with quasi-periodic additional acoustic black holes

Triboplasma assisted chemical conversion in granular systems: a semi-analytic model

Abstract We present a semi-analytic model for a novel plasma-assisted chemical conversion pathway using triboplasmas generated in granular flows. Triboelectric charge relaxation is a well known phenomena where the potential generated from contact charging of particles exceeds the breakdown voltage of the background gas. In this work, we extend the triboelectric charge relaxation theory to include non equilibrium plasma energy and particle balance equations to predict the formation of dissociated and excited species that act as precursors to chemical conversion, for example in plasma-assisted ammonia synthesis. 
Our example case study with nitrogen background gas and Teflon/aluminum tribomaterial system yielded high excited nitrogen species densities per collision that are comparable to current plasma-assisted conversion pathways. We also present a regime diagram for various gases where Paschen breakdown parameters are used to determine whether triboplasmas can be formed for a given effective work-function difference between two materials. Our sensitivity studies indicate particle velocity, particle radius, solids fraction and space charge effects play a critical role in overall plasma densities and excited species production.

A comparison of pre-existing ΛCDM predictions with the abundance of JWST galaxies at high redshift

Abstract Observations with the James Webb Space Telescope have revealed a high abundance of bright galaxies at redshift, z ≳ 12, which has been widely interpreted as conflicting with the ΛCDM model. In Cowley et al. (2018) predictions were made – prior to the JWST observations – for the expected abundance of these galaxies using the Durham semi-analytic galaxy formation model, galform, which is known to produce a realistic population of galaxies at lower redshifts including the present day. Key to this model is the assumption of a “top-heavy” initial mass function of stars formed in bursts (required to explain the number counts and redshift distribution of sub-millimetre galaxies). Here, we compare the rest-frame ultraviolet luminosity functions derived from JWST observations with those predicted by the Cowley et al. model up to z = 14 and make further predictions for z = 16. We find that below z ∼ 10, the Cowley et al. predictions agree very well with observations, while agreement at z ≳ 12 requires extending the model to take into account the timescale for the growth of obscuring dust grains at these very early times and its dependence on gas metallicity. We trace the evolution of these galaxies from z = 14 to z = 0 and find that their descendants typically reside in halos with a median mass 2.5 × 1013 h−1 M⊙. The stellar masses of the descendants range from 3.2 × 106 h−1 M⊙ to 3.2 × 1011 h−1 M⊙. Although these galaxies were all central galaxies at z = 14, over half of their descendants end up as satellites in massive halos.

Parameter optimisation of piezoelectric vibration absorber in composite cylindrical shells: A multi-modal approach to mitigate stochastic vibration

This paper investigates the stochastic vibration mitigation of composite cylindrical shells using multi-modal piezoelectric vibration absorbers (PVAs). A novel semi-analytical method is proposed to analyse the stochastic vibration characteristics of composite cylindrical shells equipped with PVAs. The vibration behaviour under stochastic excitations is determined using the modified Ritz method and the pseudo excitation method (PEM). Compared to the finite element method (FEM), the proposed model greatly enhances efficiency by eliminating the need for repeated modelling and meshing, thereby facilitating the optimisation of PVAs. The effects of piezoelectric patch layout and circuit parameters on PVA performance are examined in detail using the proposed electro-mechanical model. Additionally, a multi-modal PVA design procedure, combining the semi-analytical model with a surrogate model-based optimisation algorithm, is presented. The superior stochastic vibration suppression performance of the multi-modal PVA is demonstrated by comparing the dynamic responses of the composite cylindrical shell without PVA, with single-modal PVA, and with multi-modal PVA. The proposed optimisation procedure offers a valuable approach for the design of multi-modal PVAs for stochastic vibration control of cylindrical structures.

Constraining the Low-mass End of the Stellar-to-halo Mass Relation with Surveys of Satellite Galaxies

The abundance of satellite galaxies is set by the hierarchical assembly of their host halo. We leverage this to investigate the low-mass end (M H < 1011 M ⊙) of the stellar-to-halo mass relation (SHMR), which is key to constraining theories of galaxy formation and cosmology. We argue that recent analyses of satellite galaxies in the Local Group environment have not adequately modeled the dominant source of scatter in satellite stellar mass functions: the variance in accretion histories for a fixed host halo mass. We present a novel inference framework that not only properly accounts for this halo-to-halo variance but also naturally identifies the amount of host halo mass mixing, which is generally unknown. Specifically, we use the semianalytical SatGen model to construct mock satellite galaxy populations consistent with the third data release of the Satellites Around Galactic Analogs survey. We demonstrate that even under the most idealized circumstances, the halo-to-halo variance makes it virtually impossible to put any meaningful constraints on the scatter in the SHMR. Even a satellite galaxy survey made up 100 hosts can at best only place an upper limit of ∼0.5 dex on the scatter (at the 95% confidence level). This is because the large variance in halo assembly histories dominates over the scatter in the SHMR. This problem can be overcome by increasing the sample size of the survey by an order of magnitude (∼1000 host galaxies), something that should be fairly straightforward with forthcoming spectroscopic surveys.

Structural dynamics of contractile injection systems

The dynamics of many macromolecular machines is characterized by chemically mediated structural changes that achieve large-scale functional deployment through local rearrangements of constitutive protein subunits. Motivated by recent high-resolution structural microscopy of a particular class of such machines, contractile injection systems (CISs), we construct a coarse-grained semianalytical model that recapitulates the geometry and bistable mechanics of CISs in terms of a minimal set of measurable physical parameters. We use this model to predict the size, shape, and speed of a dynamical actuation front that underlies contraction. Scaling laws for the velocity and physical extension of the contraction front are consistent with our numerical simulations and may be generally applicable to related systems.

A semi-analytic universal model on elasticity across wide temperatures and pressures.

A semi-analytic model is presented universally for the elastic constants and moduli of solid phases in a wide range of temperatures and pressures. We derive in detail the model as a function of temperature and pressure, where the characteristic temperature is clearly associated with the Debye temperature. The abundant experiments of thermal elasticity for Cr-Mn-Fe-Co-Ni high entropy alloys are used to estimate the validity of the characteristic temperature of elasticity. The linear process of the analytical part significantly reduces the high computational and experimental cost of elasticity across a wide range of temperatures and pressures. We take the elastic property of beryllium within the range of up to 6000K and 500GPa as a prototype to investigate the accuracy, efficiency and extrapolation of this model. The application to Mg3Al2Si3O12-pyrope and CaSiO3-perovskite in the Earth's mantle further suggests that our model excellently describes the elasticity of different materials across a wide range of temperatures and pressures.

Mechanistic Modeling of Pollutant Mass Redistribution (Sorption/Desorption) in Heterogeneous Systems Explaining Unexpected Slow Kinetics.

Redistribution of pollutants between different solid phases occurs frequently in field and laboratory settings. Examples include the input of urban particles carrying pollutants into soils or rivers with suspended particles or passive sampling. Since multiple mass transfer mechanisms are involved and natural particles typically are very heterogeneous, modeling of sorption/desorption kinetics is challenging. Here, we present a semi-analytical model formulated in the Laplace domain to simulate pollutant redistribution kinetics in heterogeneous systems. The model accounts for a coupled process governed by intraparticle and external boundary layer diffusion, and it considers the heterogeneity of various sorbents (e.g., geometric shape, size, sorption capacity coefficient, and solid and porous particles). The model is validated against data of two batch experiments: (i) the redistribution of phenanthrene in spherical polyethylene particles of different sizes and (ii) redistribution of anthracene-d10 and phenanthrene in a heterogeneous sediment suspension with polyethylene passive samplers. It allows to explain the temporary overshooting of concentrations in the aqueous phase due to different kinetic controls of various particles involved (fast desorption vs. slow sorption) as well as initial fast kinetics followed by surprising long tailing in batch experiments. The approach is very flexible and can be used for many different scenarios.