Semi-analytical Model Research Articles

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.

Optimal computation of integrals in the Half-Space Matching method for modal simulation of SHM/NDE in 3D elastic plate

Simulating structural health monitoring (SHM) or nondestructive evaluation (NDE) methods based on elastic guided waves (GW) is very helpful to handle their complexity (co-existence of several GW modes, frequency dependence of wavespeed) and to further design optimal methods of inspection offering high sensitivity to the sought flaws. The half-space matching (HSM) method has been established for the development of a model that hybridizes local finite element (FE) computations for GW scattering by a flaw, with a modal semi-analytical model for GW radiation and propagation in flawless plate-like structures. Highly oscillatory Integral formulae appear in the HSM method that radiate the scattered field away from the FE zone as the superimposition of modal contributions, which computation can be time-consuming. The present work is concerned with their optimal computation. Integral of this form can be efficiently computed under the far-field approximation but this classical technique fails at predicting accurately wavefields at relatively short distances (small number of wavelengths). The method developed herein relies on the complexification of the integrals to be computed and on specific deformation of integration paths in the complex plane, as detailed in the paper. It allows the evaluation of the integrals without approximation other than that of numerical quadratures, ensuring high accuracy while offering high computing performances. It indifferently applies in the far-field and in the near-field. The method of computation is validated by comparing its predictions with a reference solution of GW scattering. Its computational performances are also demonstrated, compared to those of the standard computation of the HSM integral formulae.

Investigating ANU and ICE-6G Ice Model Relative Sea Level Misfits to Determine Viscosity Constraints since the Last Glacial Maximum

Abstract Glacial isostatic adjustment (GIA) incorporates glacial rebound and gravitational potential to calculate sea level rise. However, many ice models struggle to accurately represent these effects in relative sea level (RSL) predictions. Two widely used ice models that incorporate GIA effects, ANU and ICE-6G, require further analysis to gauge their validity. In this thesis, we compare the model predictions of RSL of the ANU and ICE-6G models against six distinct RSL field datasets using a semi-analytic GIA model. To predict RSL, a GIA model requires an ice model and models of the Earth’s mantle viscosity, density, and elastic structure. While mantle density and elastic structures are reliably constructed from seismology studies, mantle viscosity is not well constrained. We developed 864 simulated mantle viscosity models to run with the ANU and ICE-6G ice models to obtain the predicted RSL data. We analyzed the Root Mean Square (RMS) misfits of the simulated test RSL outputs against the observed RSL field data. We showed that RMS demonstrates error quality of field data is critically important to the GIA modeling process. We also showed the strengths and weaknesses of each ice model through further RMS analysis. Lay Summary Sea level change is not only a critical aspect of our climate’s response, but also a novel gateway to understanding the structure of the Earth’s mantle. This understanding is made possible by studying sea level changes over long timescales, such as since the Last Glacial Maximum. The Earth’s crust responds to increased (or decreased) weight of ice on its surface by deforming (or rebounding) and reaching a new equilibrium state over thousands of years. The response time and altered geometryof the crust give information about mantle viscosity. Observations and calculations of sea level over time geospatially constrain historical ice models, creating an opportunity to determine the most appropriate viscosity. This research identified two widely used ice models (ANU and ICE-6G) to reconstruct present day sea level, combined with varying values for the Earth’s upper and lower mantle. Findings were then compared with observations to identify minimum misfits—calculations that are closest to observation values. By understanding the factors that influence these discrepancies, the researchers hope to improve the accuracy of future models and predictions of sea level changes. For the full text and references, please visit https://scholar.colorado.edu/concern/undergraduate_honors_theses/z603qz79c.

Modeling and vibration analysis of bolted composite conical-conical shells with flanges

This paper proposes a general semi-analytical modeling method of bolted composite conical-conical shells with flanges based on the first-order shear deformation theory. The coupling connections between conical shells and flanges are achieved by using the penalty function method. A bolted joint model that considers the non-uniform distribution of interface pressure is proposed, which can efficiently simulate any number of bolt connections between flanges and boundaries and between flanges and flanges. The correctness and effectiveness of the proposed modeling method are confirmed through step-by-step comparisons with finite element analysis and experimental testing. Then, the influence of various parameters on the frequency trajectories and modal shapes of bolted composite conical-conical shells with flanges is analyzed, with a particular focus on frequency veering and modal coupling vibration behaviors in these structures. The analyses indicate that the proposed modeling method can flexibly adjust structural geometric parameters, material parameters, bolt parameters, fiber layer parameters, and so on, which can efficiently guide the dynamic design of bolted composite conical shell structures with flanges.

A semi-analytical time-domain model with explicit fluid force expressions for fluidelastic vibration of a tube array in crossflow

It is widely acknowledged that fluidelastic instability (FEI), among other mechanisms, is of the greatest concern in the flow-induced vibration (FIV) of tube bundles in steam generators and heat exchangers. A range of theoretical models have been developed for FEI analysis, and, in addition to the earliest semi-empirical Connors' model, the unsteady model, the quasi-steady model and the semi-analytical model are believed to be three advanced models predominant in the literature. The unsteady and the quasi-static models share the merits of having explicit fluid force expressions and ease of being implemented but require more experimental inputs, whereas the semi-analytical model requires fewer parameters due to its analytical nature but is hard, if not prohibitive, to derive explicit fluid force expressions. Since the fluid force formulations set in the core of development of FEI models, the understanding and in particular the implementation of the semi-analytical model has been impaired by the nonexistence of explicit fluid force expression. This issue becomes more profound in time-domain analysis whereby the simple harmonic assumption is discarded. Here we report a new semi-analytical time-domain (SATD) FEI model with explicit fluid force expressions. The new model allows a consistent frequency-domain stability analysis and more importantly a truly time-domain response analysis. The theory was validated by calculating linear stability thresholds of two typical tube array patterns and comparing against reported experimental data. We then present a nonlinear time-domain analysis of a single loosely-supported tube with piece-wise linear stiffness. The nonlinear and nonsmooth dynamics was probed in details by utilizing various techniques, playing an emphasis on characterizing and distinguishing the chaotic vibration. We found that the system follows a quasi-periodic route to chaos. Such an in-depth study of the nonlinear dynamics of tubes in crossflow has never been reported in the context of SATD model. Our results enrich the theory and provide a different approach for linear and nonlinear dynamics of tube bundles, which are essential for the subsequent fretting wear analysis.

A modified virtual time reversal method for enhancing monitoring sensitivity of bolt preloads based on ultrasonic guided waves

Bolted joints are prone to loosening due to inaccurate initial preloads and time-varying service conditions. Real-time monitoring of bolt preloads is therefore an important means to warrant the reliability and safety of a bolted structure, though it remains a daunting task to implement precise monitoring of early bolt loosening. A modified virtual time reversal (MVTR) method is developed in this study, aimed at enhanced sensitivity of bolt preload monitoring. To begin with, the frequency response function (FRF) of an intact bolted structure is ascertained using the excitation wave and the received wave signal through the bolt. Then a received wave signal captured from the bolted structure under monitoring is time-reversed, and a refocused signal is calculated in virtue of the time-reversed signal and the FRF in the intact state. Bolt tightness indices are established by the peak amplitude or energy of the refocused wave packet. To facilitate interpretation of the principle of the proposed MVTR, a semi-analytic model is developed, which combines the waveform superposition method and finite element method. With the model, the effects of interface contact length, wave mode and signal frequency on the tightness indices are investigated. The effectiveness of the proposed MVTR is experimentally verified using three representative bolted lap structures featuring single bolt or multiple bolts. The results confirm the findings from the semi-analytic model, demonstrating that the MVTR enhances monitoring sensitivity compared to prevailing approaches using linear or nonlinear guided wave features.

Predicting Stellar Masses of the First Galaxies Using Graph Neural Networks

Theoretical models of galaxy formation and evolution are primarily investigated through cosmological simulations and semi-analytical models. The former method consumes O(106) core-hours explicitly modeling the dynamics of the galaxies, whereas the latter method only requires O(103) core-hours foregoing directly simulating internal structure for computational efficiency. In this work, we present a proof-of-concept machine learning regression model, using a graph neural network architecture, to predict the stellar mass of high-redshift galaxies solely from their dark matter merger trees, trained from a radiation hydrodynamics cosmological simulation of the first galaxies.

Semi-Analytical Solution Model for Bending Deformation of T-Shaped Aviation Aluminium Alloy Components under Residual Stress

Structures composed of aviation aluminium alloys, characterized by their limited rigidity and thin-walled configurations, frequently exhibit deformation after processing. This paper presents an investigation into T-shaped components fabricated from pre-stretched 7075-T7451 aviation aluminium alloy sheets, examining the effects of residual stress and the geometrical parameters of T-shaped components on their deformational behavior. A semi-analytical model, developed to elucidate the bending deformation of T-shaped components subjected to residual stress, was validated through finite element analysis and empirical cutting experiments. The experimental results revealed that the bending deformation deflection of the T-shaped specimen was 0.920 mm, deviating by a mere 0.011 mm from the prediction provided by the semi-analytical model, resulting in an inconsequential error margin of 1.2%. This concordance underscores the precision and accuracy of the semi-analytical model specifically designed for T-shaped components. Moreover, the model’s simplicity and ease of application make it an effective tool for predicting the bending deformation of thin-walled T-shaped components under a range of residual stresses and dimensional variations, thereby demonstrating its significant utility in engineering applications.

The First Quenched Galaxies: When and How?

Many quiescent galaxies discovered in the early Universe by JWST raise fundamental questions on when and how these galaxies became and stayed quenched. Making use of the latest version of the semianalytic model GAEA that provides good agreement with the observed quenched fractions up to z ∼ 3, we make predictions for the expected fractions of quiescent galaxies up to z ∼ 7 and analyze the main quenching mechanism. We find that in a simulated box of 685 Mpc on a side, the first quenched massive (M ⋆ ∼ 1011 M ⊙), Milky Way–mass, and low-mass (M ⋆ ∼ 109.5 M ⊙) galaxies appear at z ∼ 4.5, z ∼ 6.2, and before z = 7, respectively. Most quenched galaxies identified at early redshifts remain quenched for more than 1 Gyr. Independently of galaxy stellar mass, the dominant quenching mechanism at high redshift is accretion disk feedback (quasar winds) from a central massive black hole, which is triggered by mergers in massive and Milky Way–mass galaxies and by disk instabilities in low-mass galaxies. Environmental stripping becomes increasingly more important at lower redshift.

Detectability of gravity changes on the sea surface due to magma accumulation beneath submarine volcanoes

SUMMARY This study estimated the gravity change expected on the sea surface due to magma accumulation beneath submarine volcanoes. For calculation, a semi-analytical model describing the deformation of an infinite elastic cone was considered, in which a point spherical source was embedded on the axis. The expected gravity change exceeds 0.2 mGal in certain scenarios when $\delta V = 10^8\, \mathrm{m^3}$ of source volume change occurs 2 km below the summit, and the summit is shallower than 300 m below the sea surface. The steeper the slope of a submarine volcano, the greater the expected gravity change. 0.2 mGal of gravity variation can be detected with recent marine gravimeters such as cold atom interferometers. The computation method for the gravity change based on the integral transform (Mellin type) is elaborated in this paper.

Cosmological parameters estimated from peculiar velocity–density comparisons: calibrating 2M++

ABSTRACT Cosmological parameters can be measured by comparing peculiar velocities with those predicted from a galaxy density field. Previous work has tested the accuracy of this approach with N-body simulations, but generally on idealized mock galaxy surveys. However, systematic biases may arise solely due to survey selection effects such as flux-limited samples, edge-effects, and complications due to the obscuration of the Galactic plane. In this work, we explore the impact of each of these effects individually as well as collectively using the semi-analytic models from numerical simulations to generate mock catalogues that mimic the 2M++ density field. We find the reconstruction and analysis methods used for our 2M++ mocks produce a value of fσ8 that is biased high by a factor 1.04 ± 0.01 compared to the true value. Moreover, a cosmic volume matching that of 2M++ has a cosmic variance uncertainty in fσ8 of $\sim 5~{{\ \rm per\ cent}}$. The systematic bias is a function of distance: it is unbiased close to the origin but is biased slightly high for distances in the range 100–180 h−1 Mpc. Correcting for this small bias, we find that recent peculiar velocity samples yield $f\sigma _8^{\textrm {lin}} = 0.362\pm 0.023$, a value that is in tension with the extrapolations from cosmic microwave background measurements. The predicted peculiar velocities from 2M++ have an error of 170 km s−1 that slowly increases with distance, exceeding 200 km s−1 only at distances of 180–200 h−1Mpc. Finally, the residual bulk flow speeds found in previous work are shown to be not in conflict with those expected in the Λ cold dark matter model.

Towards digitally programmed nonlinear electroacoustic resonators for low amplitude sound pressure levels: Modeling and experiments

Passive acoustic foams have limitations in efficiently reducing low-frequency noise below 800 Hz due to the associated wavelengths for reasonable material thickness. To address this challenge, passive or semi-active resonators are commonly employed solutions. Linear resonators are very efficient within a narrow frequency bandwidth. However, nonlinear oscillators can broaden this bandwidth, but activation of their nonlinear responses typically requires high excitation amplitudes, beyond human hearing tolerance amplitudes. Furthermore, the specific type of nonlinearity in such devices is often predetermined by the inherent properties of the resonator. In this study, we employ a novel digital control algorithm, allowing to activate the nonlinear response of the electroacoustic resonator at low excitation amplitudes. This algorithm, which relies on real-time integration, facilitates the creation of nonlinear resonators featuring polynomial or diverse non-polynomial nonlinearities within the range of low amplitudes. The nonlinear control is carried out on a loudspeaker equipped with a microphone. Our research highlights the potential to create nonlinear resonators with different, versatile and programmable behaviors. Unprecedented non-polynomial nonlinear behaviors are experimentally exhibited, we consider cubic, piece-wise linear, and logarithmic nonlinearities. These behaviors are implemented and compared to a semi-analytic model to control an acoustic mode of a tube under conditions of low excitation amplitudes and frequencies.

The semi-analytical model of capacitive imaging (CI) sensors based on the renormalization group method

Purpose This study aims to design and validate a theoretical model for capacitive imaging (CI) sensors that incorporates the interelectrode shielding and surrounding shielding electrodes. Through experimental verification, the effectiveness of the theoretical model in evaluating CI sensors equipped with shielding electrodes has been demonstrated. Design/methodology/approach The study begins by incorporating the interelectrode shielding and surrounding shielding electrodes of CI sensors into the theoretical model. A method for deriving the semianalytical model is proposed, using the renormalization group method and physical model. Based on random geometric parameters of CI sensors, capacitance values are calculated using both simulation models and theoretical models. Three different types of CI sensors with varying geometric parameters are designed and manufactured for experimental testing. Findings The study’s results indicate that the errors of the semianalytical model for the CI sensor are predominantly below 5%, with all errors falling below 10%. This suggests that the semianalytical model, derived using the renormalization group method, effectively evaluates CI sensors equipped with shielding electrodes. The experimental results demonstrate the efficacy of the theoretical model in accurately predicting the capacitance values of the CI sensors. Originality/value The theoretical model of CI sensors is described by incorporating the interelectrode shielding and surrounding shielding electrodes into the model. This comprehensive approach allows for a more accurate evaluation of the detecting capability of CI sensors, as well as optimization of their performance.

A two-dimensional semi-analytic thermal model for global temperature distribution predicting and hot spot monitoring in interior permanent magnet synchronous motor

A two-dimensional semi-analytical thermal model (SATM) is presented, aiming to quickly and accurately achieve global temperature distribution predicting and hot spot monitoring for interior permanent magnet synchronous motor (IPMSM). Thereby, it provides a reliable analysis tool for thermal behavior evaluation and prevents undesired consequences induced by excessive temperature rise, which is of great worth and significance in promoting the flourishing of IPMSM. SATM combines the analytical method, lumped parameter thermal network, and finite element analysis to obtain an analytical solution for thermal behavior through mathematical derivation by considering the complicated configuration, heat source distribution, heat dissipation condition, and material thermal dependence. Through SATM, it is possible to observe the global temperature distribution as well as the location and size of hot spots in each element. The temperature distribution gradient on the static is more pronounced than that on the dynamic; secondly, the area with the most severe heating is mainly found on the winding; furthermore, the hot spot on the winding is mainly located a little bit inside the center. Moreover, the thermal behavior of IPMSM at rated load is investigated by numerical analysis and experiments. A comprehensive comparison with SATM is done. The computational deviations between SATM and numerical analysis regarding the hot spot, minimum, and average temperatures on each element are all within 4.06 %. However, SATM consumes only 20.92 % of the time and 68.29 % of the storage of the numerical analysis. The measured data also fully prove the reliability and validity of the comparison. It is certain that SATM can well break through the limitation of the existing non-numerical technique to quickly and accurately achieve global temperature distribution predicting and hot spot monitoring of IPMSM. It provides researchers and engineers engaged in thermal behavior evaluation with good analysis means, design guidance, and optimization direction.

Impact of property covariance on cluster weak lensing scaling relations

ABSTRACT We present an investigation into a hitherto unexplored systematic that affects the accuracy of galaxy cluster mass estimates with weak gravitational lensing. Specifically, we study the covariance between the weak lensing signal, ΔΣ, and the ‘true’ cluster galaxy number count, Ngal, as measured within a spherical volume that is void of projection effects. By quantifying the impact of this covariance on mass calibration, this work reveals a significant source of systematic uncertainty. Using the MDPL2 simulation with galaxies traced by the SAGE semi-analytic model, we measure the intrinsic property covariance between these observables within the three-dimensional vicinity of the cluster, spanning a range of dynamical mass and redshift values relevant for optical cluster surveys. Our results reveal a negative covariance at small radial scales (R ≲ R200c) and a null covariance at large scales (R ≳ R200c) across most mass and redshift bins. We also find that this covariance results in a $2{\!-\!}3~{{\ \rm per\ cent}}$ bias in the halo mass estimates in most bins. Furthermore, by modelling Ngal and ΔΣ as multi-(log)-linear equations of secondary halo properties, we provide a quantitative explanation for the physical origin of the negative covariance at small scales. Specifically, we demonstrate that the Ngal–ΔΣ covariance can be explained by the secondary properties of haloes that probe their formation history. We attribute the difference between our results and the positive bias seen in other works with (mock)-cluster finders to projection effects. These findings highlight the importance of accounting for the covariance between observables in cluster mass estimation, which is crucial for obtaining accurate constraints on cosmological parameters.

Analytic approximations for the primordial power spectrum with Israel junction conditions

This work compares cosmological matching conditions used in approximating generic pre-inflationary phases of the Universe. We show that the joining conditions for primordial scalar perturbations assumed by Contaldi [] are inconsistent with the physically motivated Israel junction conditions; however, performing general relativistic matching with the aforementioned constraints results in unrealistic primordial power spectra. Eliminating the need for ambiguous matching, we look at an alternative semianalytic model for producing the primordial power spectrum allowing for finite duration cosmological phase transitions. Published by the American Physical Society 2024

Natural frequencies and stability for Z-shaped fluid-conveying pipes with constrained-layer damping – Semi-analytic modeling with experimental validation

As the common fluid-conveying component, pipe structures are susceptible to excessive vibration due to internal fluid and external excitation. Constrained-layer damping (CLD) is commonly applied to suppress structural vibrations. However, effective modeling and vibration suppression analysis for Z-shaped fluid-conveying pipes are lacking to explore novel dynamic behaviors. This paper presents a dynamic model for analyzing the three-dimensional vibration of Z-shaped fluid-conveying pipes treated by partial CLD based on the semi-analytical method. Utilizing Timoshenko beam theory and calculating the centrifugal, Coriolis, and inertial force of fluids, the energy of straight and curved fluid-conveying pipes treated by CLD is derived. Based on the Lagrangian energy function, the equation of motion is obtained by using the Rayleigh-Ritz method. The improved artificial spring set is deployed to model the interaction of pipe sections and the non-uniform constraint distribution of clamps. Modal parameters are obtained by solving characteristic equations. The proposed method is verified by comparisons with references and modal experiment results. Frequency parameters, damping effects, and stability are analyzed under various fluid, geometric, and CLD parameters. In conclusion, a novel dynamic model is provided for analyzing the vibration and stability of the Z-shaped fluid-conveying pipe treated by CLD, which lays a foundation for vibration suppression research of fluid-conveying pipe systems.

Three-dimensional frictional contact within the framework of couple stress elasticity

This work investigates a three-dimensional size-dependent frictional contact problem of a rigid spherical punch sliding on an elastic half-space. The size-dependent material behaviors are governed by the couple stress theory, and the corresponding frequency response functions, which include two additional length-related elastic parameters, are obtained. Based on the conjugate gradient method and the discrete convolution-fast Fourier transform algorithm, a semi-analytical model is established to predict the frictional size-dependent contact behaviors and then the detailed parameter analysis is performed. The transverse effects of the couple stress, which are induced due to the considerations of the two additional elastic parameters in couple stress theory, are investigated in the contact problems for the first time. And the dependences of the size-dependent contact behavior on the coupling effects of the friction and the two additional elastic parameters are presented.

Flight dynamic modeling and stability of a small-scale side-by-side helicopter for Urban Air Mobility

This paper aims to explore the development of a flight dynamics model for a small-scale side-by-side helicopter and describe its trim and stability characteristics. The helicopter is considered a suitable candidate for Urban Air Mobility (UAM) solutions, because of its reliable design and low noise characteristics, but still very small knowledge is present on the mathematical modeling approaches and dynamic properties. A 14 degrees of freedom nonlinear mathematical model is developed and semi-analytical models are employed to account for the presence of the shrouds. An iterative trim routine is developed and applied with a suitable control mix that allows the use of classic helicopter controls. To control the vertical speed and roll rate, the paper assumes an equal collective pitch and lateral cyclic in the two rotors, while a uniform plus a differential longitudinal cyclic is adopted for pitch and yaw maneuvers. The paper discusses unique characteristics of the side-by-side configuration as obtained from the stability analysis: an unstable high-frequency mode, governed by the vertical velocity and pitch angle arises when the center of gravity (CG) of the vehicle is aligned or placed in front of the two main rotors. Similarly, both lateral phugoid and roll subsidence modes are sensitive to the CG location. The side-by-side configuration presents also a stable spiral mode which needs to be carefully designed.

Semi-analytic modeling and experimental verification of arbitrary aero-engine complex spatial pipeline

In-depth research is imperative for complex spatial pipelines with fluid-structure interaction. A comprehensive and universal three-dimensional semi-analytical modeling method is first established for complex fluid-conveying spatial pipelines under the base excitation with arbitrary connections and configurations under different boundary conditions. The virtual spring technology is used to connect the straight and curved pipeline segments with spatial angles and simulate boundary conditions. For a thorough analysis, the actual stiffness of the bracket-clamp system is experimentally measured for the first time. The multi-level coupling dynamic model of part, component, and system levels under actual boundary conditions is established. An efficient method for solving the fluid-structure coupling pipeline system dynamics considering the base excitation is proposed based on energy method. The mid-plane displacement function of the Fourier series is introduced and solved using the principle of modal superposition. Hammer impact modal experiments, ANSYS software and vibration response experiments are performed on spatial pipelines supported by flexible bracket-clamps; the numerical and experimental results support the semi-analytical results. The degenerate model is verified with the simple plane pipelines in other references, and the errors are less than 5 %. The proposed method exhibits broad applicability and generalizability, making it suitable for various configurations and boundary conditions.