Semi-analytical Model Research Articles

Developing a semi-analytical model for estimating mechanical properties of sandstone reservoirs: Enhancing applications in hydrocarbon production and underground gas storage

Rock mechanical properties, encompassing the static Young's modulus, bulk modulus, and shear modulus, influence strategic decision-making operations, such as drilling programs and well completion designs. When precisely calculated, these variables can significantly affect drilling cost-efficiencies and production economic returns. Even though these attributes are significant, the conventional estimation method is core-lab testing, which is expensive and limited to covering the entire reservoir strata. To address this challenge, we propose a new semi-analytical model with direct equations to estimate the elastic rock properties primarily anchored around porosity. In particular, we developed an analytical framework using generalized equations for bulk and shear modulus to calculate static rock mechanical properties as porosity-driven functions. We employed lab-tested core data from 55 core samples to validate the new model's efficiency. The model's innovative design allows computing all elastic properties solely based on porosity. Impressively, the results closely matched the lab measurements. The new semi-analytical model's equations yielded a good root mean square error (RMSE) in the calculated rock mechanical properties. Specifically, the new static Young's modulus equation has the lowest RMSE, 1.489, compared to 45.168 for the Edimann equation and 3.043 for the Zhang equation. The newly developed static shear modulus equation had an RMSE of 0.497, lower than Zhang's empirical equation's 1.262. However, the Zhang equation has an RMSE of 0.891 versus 2.029, slightly outperforming the new equation. According to the RMSE values, the discrepancy between the core sample-based measured, new semi-analytical model-calculated static modulus was caused by the fact that the core samples were collected from clean sand oil-bearing reservoir intervals. However, the derived equations used porosity ranges that covered shale and sand. In essence, the new semi-analytical model provides a fast and precise estimation of rock mechanical properties, easily solving drilling concerns. This research not only advances knowledge of drilling and geomechanics, but also makes strategies more efficient and cost-effective.

Design and analysis of 2D one-way splitter waveguide based on topological photonics

We present a new high-efficiency splitter waveguide design based on photonic topological insulators. The system’s robust edge states allow electromagnetic waves to propagate in the 2D waveguide without backscattering, resulting in almost 100% transmission in the outputs. We also study resonating modes in the structure and show that introducing specific defects can create such modes. We consider four domains with rods of varying magneto-optical properties to provide edge modes in the system. By eliminating rows and columns of rods, we calculate the transmission at the outputs, revealing resonating modes in the middle of the structure with spatial symmetry. Our calculations indicate that the most promising resonating mode occurs when two rods and two columns are eliminated, with a quality factor Q = 1.02 × 106 at frequency f = 8.23 GHz and almost zero transmission at this frequency to the outputs. We further confirm our results using the transmission line resonator model as a semi-analytical model, which agrees well with our findings.

Magnetars as powering sources of gamma-ray burst associated supernovae, and unsupervized clustering of cosmic explosions

ABSTRACT We present the semi-analytical light curve modelling of 13 supernovae associated with gamma-ray bursts (GRB-SNe) along with two relativistic broad-lined (Ic-BL) SNe without GRB association (SNe 2009bb and 2012ap), considering millisecond magnetars as central-engine-based power sources for these events. The bolometric light curves of all 15 SNe in our sample are well-regenerated utilizing a χ2-minimization code, MINIM, and numerous parameters are constrained. The median values of ejecta mass (Mej), magnetar’s initial spin period (Pi), and magnetic field (B) for GRB-SNe are determined to be ≈5.2 M⊙, 20.5 ms, and 20.1 × 1014 G, respectively. We leverage machine learning (ML) algorithms to comprehensively compare the three-dimensional parameter space encompassing Mej, Pi, and B for GRB-SNe determined herein to those of H-deficient superluminous SNe (SLSNe-I), fast blue optical transients (FBOTs), long GRBs (LGRBs), and short GRBs (SGRBs) obtained from the literature. The application of unsupervized ML clustering algorithms on the parameters Mej, Pi, and B for GRB-SNe, SLSNe-I, and FBOTs yields a classification accuracy of ∼95 per cent. Extending these methods to classify GRB-SNe, SLSNe-I, LGRBs, and SGRBs based on Pi and B values results in an accuracy of ∼84 per cent. Our investigations show that GRB-SNe and relativistic Ic-BL SNe presented in this study occupy different parameter spaces for Mej, Pi, and B than those of SLSNe-I, FBOTs, LGRBs, and SGRBs. This indicates that magnetars with different Pi and B can give birth to distinct types of transients.

Development of a Semi-Analytical Dynamic Force Model

A moving water mass generates force which is exerted on its moving path. Cyclone generated storm surge or earthquake generated tsunami are specific examples of moving water mass generated force along the coasts. In addition to human lives, these moving water masses cause severe damages to the coastal infrastructure due to tremendous force exerted on these structures. To assess the damage on these infrastructures, an essential parameter is the resultant force exerted on these structures. To evaluate the damages, there is hardly any quantitative method available to compute this force. In this paper we have developed a semi-analytical model, named as Dynamic Force Model (DFM), by using Variational Iteration Method to compute this force. We have derived the governing equation on the basis of Saint-Venant equations which are basically 1D shallow water equations derived from the Navier-Stokes equations. DFM is verified, calibrated, validated, and applied in Bangladesh coastal zone to compute dynamic thrust force due to tropical cyclone SIDR.

Semi-analytical and experimental heat input study of additively manufactured Zr-based bulk metallic glass: Insights into nano- and global-scale relaxation and crystallization

Laser powder bed fusion (LPBF) of Zr-based bulk metallic glasses (BMGs) has recently attracted attention due to its capacity for microstructure control, the potential for custom-tailored properties, and its versatile applicability across various industries. It is crucial to strike a balance between relative density, relaxation, and crystallinity tailored to a specific application when 3D printing amorphous components. However, prior findings have not revealed an exclusive study concerning low fractions of crystallinity (<5 vol%) and atomic-scale effects during the LPBF process, e.g. the relaxation degree of the amorphous structure. This study employs a systematic experimental approach, complemented by semi-analytical modeling, to comprehensively recognize the nano- and macro-scale amorphous structure and the associated mechanical behavior. Differential scanning calorimetry (DSC) along with flexural stress-strain measurements disclose that the highest relaxation and crystallization enthalpies, which are obtained for samples printed with lower heat input, are not in correlation with the desired mechanical properties. On the contrary, samples printed with a heat input of ΔH=44 reveal the maximum density range (up to 99.97 %) and showcase laboratory-XRD amorphous structure. This results in the highest flexural strength (up to 2080 MPa) and elastic deformation range (up to 2.6 %), along with the lowest Young’s modulus span (60–70 GPa). In this case, the crystallinity (0.02–0.2 vol%) associated with the desired mechanical properties is calculated from the modeling results. The outcomes indicate increased heating/ cooling rates corresponding to the amplified heat input, with cooling rates reaching up to 5×104 °C/s and heating rates up to 6×105 °C/s. However, underlying layers are subjected to reduced heating and cooling rates. This observation not only validates the intricate thermal dynamics in LPBF but also elucidates the crystalline formation in heat-affected zones (HAZs) with associated lower heating and cooling rates.

Variation of the stellar initial mass function in semi-analytical models

Context. In our previous work, we derived the CR-IGIMF, which is a new scenario for a variable stellar initial mass function (IMF) that combines numerical results on the role played by cosmic rays (CR) in setting the thermal state of star-forming gas with the analytical approach of the integrated galaxy-wide IMF (IGIMF). Aims. In this work, we study the implications of this scenario for the properties of local early-type galaxies (ETG) as inferred from dynamical, photometric, and spectroscopic studies. Methods. We implemented a library of CR-IGIMF shapes in the framework of the galaxy evolution and assembly (GAEA) model. GAEA provides predictions for the physical and photometric properties of model galaxies and for their chemical composition. Our realization includes a self-consistent derivation of the synthetic spectral energy distribution for each model galaxy, which allows a direct derivation of the mass fraction in the mean IMF of low-mass stars (i.e., the dwarf-to-giant ratio, fdg) and a comparison with IMF-sensitive spectral features. Results. The predictions of the GAEA model implementing the CR-IGIMF confirm our previous findings: It correctly reproduces both the observed excess of z ∼ 0 dynamical mass (mass-to-light ratio) with respect to spectroscopic (photometric) estimates assuming a universal MW-like IMF, and the observed increase in [α/Fe] ratios with stellar mass in spheroidal galaxies. Moreover, this realization reproduces the increasing trends of fdg and IMF-sensitive line strengths with velocity dispersion, although the predicted relations are significantly shallower than the observed ones. Conclusions. Our results show that the CR-IGIMF is a promising scenario that reproduces at the same time dynamical, photometric, and spectroscopic indications of a varying IMF in local ETGs. The shallow relations found for spectral indices suggest that either a stronger variability as a function of galaxy properties or additional dependences (e.g., as a function of star forming gas metallicity) might be required to match the strength of the observed trends.

Electron trapping efficiency of a magnetron sputtering cathode

A common feature of all types of magnetron sputtering (MS) assemblies is an effective confinement of electrons by an appropriate combination of electric and magnetic fields. Therefore, studying the motions of electrons in the fields of magnetron assemblies is of particular importance. Here, we systematically analyze the electrons motions in front of a typical DC MS cathode. We first calculate the profiles of the magnetron’s magnetic field for balanced and two types of unbalanced configurations. Then, we compute the profiles of the cathode’s electric field before the gas discharge and after the plasma formation. A semi-analytical model is utilized to compute the plasma potential. We then track the motions of electrons released from the target and electrons produced through impact ionization of the background gas in the prescribed fields. A Monte Carlo model is implemented to consider electron-gas collisions and a mixed boundary condition is employed to account for electron-wall interactions. The study analyzes the impact of field profiles on the cathode’s efficiency in trapping electron by examining electron escape from the magnetic trap and electron recapture at the target surface. It is shown that the presence of plasma in all configurations leads to a significant increase in the trapping efficiency and the ionization performance, as well as a decrease in the recapture probability. These effects are attributed to the high electric field developed in the cathode sheath. Moreover, we statistically analyze the trapping efficiency by illustrating the spatial distributions of electrons locations in both axial and radial dimensions. It is demonstrated that during their azimuthal drift motion, the electrons released from the middle region at the target surface have the smallest range of axial and radial locations, in all configurations in the absence of plasma. Finally, the impact of field profiles on the average energies of electrons is discussed.

The AGORA High-resolution Galaxy Simulations Comparison Project. IV. Halo and Galaxy Mass Assembly in a Cosmological Zoom-in Simulation at z ≤ 2

In this fourth paper from the AGORA Collaboration, we study the evolution down to redshift z = 2 and below of a set of cosmological zoom-in simulations of a Milky Way mass galaxy by eight of the leading hydrodynamic simulation codes. We also compare this CosmoRun suite of simulations with dark matter-only simulations by the same eight codes. We analyze general properties of the halo and galaxy at z = 4 and 3, and before the last major merger, focusing on the formation of well-defined rotationally supported disks, the mass–metallicity relation, the specific star formation rate, the gas metallicity gradients, and the nonaxisymmetric structures in the stellar disks. Codes generally converge well to the stellar-to-halo mass ratios predicted by semianalytic models at z ∼ 2. We see that almost all the hydro codes develop rotationally supported structures at low redshifts. Most agree within 0.5 dex with the observed mass–metallicity relation at high and intermediate redshifts, and reproduce the gas metallicity gradients obtained from analytical models and low-redshift observations. We confirm that the intercode differences in the halo assembly history reported in the first paper of the collaboration also exist in CosmoRun, making the code-to-code comparison more difficult. We show that such differences are mainly due to variations in code-dependent parameters that control the time stepping strategy of the gravity solver. We find that variations in the early stellar feedback can also result in differences in the timing of the low-redshift mergers. All the simulation data down to z = 2 and the auxiliary data will be made publicly available.

A Quantification of the Effects Using Different Stellar-population Synthesis Models for Epoch of Reionization

The luminosity and spectral energy distribution of high-z galaxies are sensitive to the stellar-population synthesis (SPS) models. In this paper, we study the effects of different SPS models on the measurements of high-z galaxies and the budget of ionizing photons during the epoch of reionization by employing each of them in the semianalytical galaxy formation model L-Galaxies 2020. We find that the different SPS models lead to ≲0.5 dex differences on the amplitudes of UV luminosity functions, while two modes of the same SPS model with and without the inclusion of binary stars lead to similar UV luminosity functions at z ≥ 6. Instead, the binary stars produce ∼40% more ionizing photons than the single stars, while such differences are smaller than those caused by different SPS models; for example, the BPASS model produces ∼100% more ionizing photons than other models.

Devouring the Centaurus A Satellites: Modeling Dwarf Galaxies with Galacticus

For the first time, systematic studies of dwarf galaxies are being conducted throughout the Local Volume, including the dwarf satellites of the nearby giant elliptical galaxy Centaurus A (NGC 5128). Given Centaurus A's mass (roughly 10 times larger than that of the Milky Way), AGN activity, and recent major mergers, investigating the dwarf galaxies of Centaurus A and their star formation physics is imperative. However, simulating the faintest dwarfs around a galaxy of Centaurus A's mass with sufficient resolution in a hydrodynamic simulation is computationally expensive and currently infeasible. In this study, we seek to reproduce the properties of Centaurus A dwarfs using the semianalytic model Galacticus to model dwarfs within a 700 kpc region around Centaurus A, corresponding approximately to its splashback radius. We investigate the effects of host halo mass and environment and predict observable properties of Centaurus A dwarfs using astrophysical prescriptions and parameters previously tuned to match properties of the Milky Way’s satellite galaxies. This approach allows us to approximately replicate cumulative luminosity functions, and luminosity–metallicity and luminosity–half-light-radii relations observed in the Centaurus A satellites. We provide predictions for the velocity dispersions, and star formation histories of Centaurus A dwarfs. The agreement between our predicted star formation histories for Centaurus A dwarfs and those of the Milky Way dwarfs implies the presence of universal processes governing star formation in dwarf galaxies. Overall, our findings shed light on the star formation physics of dwarf galaxies in the Centaurus A system, revealing insights into their properties and dependence on the host environment.

Connecting low-redshift LISA massive black hole mergers to the nHz stochastic gravitational wave background

Pulsar Timing Array (PTA) experiments worldwide recently reported evidence of a nHz stochastic gravitational wave background (sGWB) compatible with the existence of slowly inspiralling massive black hole (MBH) binaries (MBHBs). The shape of the signal contains valuable information about the evolution of z &lt; 1 MBHs above 108 M⊙, suggesting a faster dynamical evolution of MBHBs towards the gravitational-wave-driven inspiral or a larger MBH growth than usually assumed. In this work, we investigate if the nHz sGWB could also provide constraints on the population of merging lower-mass MBHBs (&lt; 107 M⊙) detectable by LISA. To this end, we use the L-Galaxies semi-analytical model applied to the Millennium suite of simulations. We generate a population of MBHs compatible simultaneously with current electromagnetic and nHz sGWB constraints by including the possibility that, in favourable environments, MBHs can accrete gas beyond the Eddington limit. The predictions of this new model for the sGWB show that the global (integrated up to high-z) LISA detection rate is not significantly affected when compared to a fiducial model whose nHz sGWB signal is ∼2 times smaller. In both cases, the global rate yields ∼12 yr−1 and is dominated by systems of 105 − 6 M⊙. The main differences are limited to low-z (z &lt; 3), high-mass (&gt; 106 M⊙) LISA MBHBs. The model compatible with the latest PTA results predicts up to ∼1.6 times more detections, with a rate of ∼1 yr−1. We find that these LISA MBHB systems have 50% probability of shining with bolometric luminosities &gt; 1043 erg s−1. Hence, in case PTA results are confirmed and given the current MBH modelling, our findings suggest there will be higher chances to perform multimessenger studies with LISA MBHB than previously expected.

Passive control of vibrations of a beam by means of Herschel–Quincke vibration filters

This work concerns the adaptation of the Herschel–Quincke filters (HQ) known in the case of plane acoustic waves in tubes to the case of bending waves in beams. The objective is to develop new techniques to design vibration filters in thin structures. In acoustics, an HQ filter consists of the insertion of a bifurcation in a primary tube, so as to create two tubes in parallel and of different length. The phase difference creates destructive interference at certain frequencies which gives rise to zero transmission. In the case of the bending waves considered here, the HQ interference is obtained by locally splitting a thin beam into two segments of the same length but of different thickness. The difference in travel time is then created by the difference in bending stiffness between the two segments. A semi-analytical wave decomposition model using Timoshenko’s theory is developed to perform parametric studies of behaviour of such a device. Finite element simulations and experimental demonstrations confirm the predictions of a semi-analytical model. The results highlight the link between the geometric parameters of the device and its filtering properties. Therefore, this paper establishes a novel strategy of design of vibration filters, which utilizes the HQ effect for bending waves in beams.

Size–mass relation of the brightest cluster galaxies at z ∼ 1

ABSTRACT We present the size–mass relation of the brightest cluster galaxies (BCGs) at 0.1 &amp;lt; z &amp;lt; 1.4 using the imaging data obtained by the Hyper Suprime-Cam Subaru Strategic Program. Our sample consists of 471 photometrically selected BCGs with stellar mass logM*/M⊙ = 11–12. We measure the size of the BCGs using i-band imaging and model fits based on a single Sérsic light profile. Stellar masses are determined through spectral energy distribution fitting using Sérsic-modelled photometry data across five optical bands (grizy). The size–mass scaling relation of BCGs is $r_\mathrm{ e}\propto M_*^{0.73-1.00}$ at z &amp;lt; 1, with a slope that does not evolve significantly. The slope of the size–mass relation for BCGs is steeper than other non-BCG galaxies, which implies that BCGs are a special galaxy population. The size of BCGs at a given stellar mass evolves rapidly as ∝ (1 + z)−1.58 ± 0.13 and increases with redshift by a factor of 2.5 from z ∼ 1.2 to z ∼ 0.2. The rapid size growth is in agreement with semi-analytical model results, indicating that the BCG growth is dominated by frequent minor mergers. Furthermore, we explore the size–mass relationship of BCGs with respect to the halo mass of the cluster and find there is no significant correlation, which might imply that a dependence on the environment predominantly affects the outer envelope of the BCGs.

Autoencoding Labeled Interpolator, Inferring Parameters from Image and Image from Parameters

The Event Horizon Telescope (EHT) provides an avenue to study black hole accretion flows on event-horizon scales. Fitting a semianalytical model to EHT observations requires the construction of synthetic images, which is computationally expensive. This study presents an image generation tool in the form of a generative machine-learning model, which extends the capabilities of a variational autoencoder. This tool can rapidly and continuously interpolate between a training set of images and can retrieve the defining parameters of those images. Trained on a set of synthetic black hole images, our tool showcases success in interpolating both black hole images and their associated physical parameters. By reducing the computational cost of generating an image, this tool facilitates parameter estimation and model validation for observations of black hole systems.

A semi-analytical model for the propagation of a relativistic jet in a magnetized medium

ABSTRACT The merger of two magnetized compact objects, such as neutron stars, forms a compact object which may launch a relativistic and collimated jet. Numerical simulations of the process show that a dense and highly magnetized medium surrounds the system. This study presents a semi-analytical model that models the effects that a static magnetized medium with a tangled field produces in relativistic, collimated, and non-magnetized jets. The model is a first approximation that addresses the magnetic field present in the medium and is based on pressure equilibrium principles between the jet, cocoon, and external medium. A fraction of the ambient medium field is allowed to be entrained in the cocoon. We find that the jet and cocoon properties may be affected by high magnetic fields (≳ 1015 G) and mixing. The evolution of the system may vary up to $\sim 10{{\ \rm per\ cent}}$ (compared to the non-magnetized case). Low-mixing may produce a slower broader jet with a broader and more energetic cocoon would be produced. On the other hand, high-mixing could produce a faster narrower jet with a narrow and less-energetic cocoon. Two-dimensional hydrodynamical simulations are used to validate the model and to constrain the mixing parameter. Although the magnetic field and mixing have a limited effect, our semi-analytic model captures the general trend consistent with numerical results. For high magnetization, the results were found to be more consistent with the low mixing case in our semi-analytic model.

Fluid Structure Interaction Analyses of Elevated Storage Tank under Seismic Load

Elevated storage tanks are used to store fresh and waste water, cereal, oil and petrochemical materials. Therefore they serve in a wide area of utilization in this day and age. Analysis of a half full with water elevated storage tank is performed in the scope of this study. The structure is composed of a steel circular storage tank and frame typed steel stager. The structure is under the effect of earthquake loads as well as operational ones. Numerical model is generated by Finite Elements Analysis (FEA) software including fluid and structure parts. The interaction of the parts is provided by Coupled Eulerian Lagrangian (CEL) technique. While the structure constitutes the Lagrangian part, the fluid constitutes the Eulerian part. Interaction of Eulerian and Lagrangian parts are provided by general contact algorithms. Free surface movement of the water, maximum displacements and natural frequency values with related mode shapes of the structure are obtained after numerical analysis. Numerical results are verified by semi-analytical model, where the structure is modelled as single degree of freedom system. The accordance between results is numerically and visually obtained. The turbulent movement of water under the influence of an earthquake is modelled by utilizing the CEL technique. So, the effect of the dynamic pressure induced by the turbulence on the tank and the structural system has been taken into consideration.

A self-consistent model for dust settling and the vertical shear instability in protoplanetary disks

Abstract The spatial distribution of dust particles in protoplanetary disks affects dust evolution and planetesimal formation processes. The vertical shear instability (VSI) is one of the candidate hydrodynamic mechanisms that can generate turbulence in the outer disk region and affect dust diffusion. Turbulence driven by the VSI has a predominant vertical motion that can prevent dust settling. On the other hand, the dust distribution controls the spatial distribution of the gas cooling rate, thereby affecting the strength of VSI-driven turbulence. Here, we present a semi-analytic model that determines the vertical dust distribution and the strength of VSI-driven turbulence in a self-consistent manner. The model uses an empirical formula for the vertical diffusion coefficient in VSI-driven turbulence obtained from our recent hydrodynamical simulations. The formula returns the vertical diffusion coefficient as a function of the vertical profile of the cooling rate, which is determined by the vertical dust distribution. We use this model to search for an equilibrium vertical dust profile where settling balances with turbulent diffusion for a given maximum grain size. We find that if the grains are sufficiently small, there exists a stable equilibrium dust distribution where VSI-driven turbulence is sustained at a level of αz ∼ 10−3, where αz is the dimensionless vertical diffusion coefficient. However, as the maximum grain size increases, the equilibrium solution vanishes because the VSI can no longer stop the settling of the grains. This runaway settling may explain highly settled dust rings found in the outer part of some protoplanetary disks.

Effectiveness of halo and galaxy properties in reducing the scatter in the stellar-to-halo mass relation

ABSTRACT The stellar-to-halo mass relation (SHMR) is a fundamental relationship between galaxies and their host dark matter haloes. In this study, we examine the scatter in this relation for primary galaxies in the semi-analytic l-galaxies model and two cosmological hydrodynamical simulations, EAGLE (Evolution and Assembly of Galaxies and their Environments) and TNG100-1. We find that in low-mass haloes, more massive galaxies tend to reside in haloes with higher concentration, earlier formation time, greater environmental density, earlier major mergers, and, to have older stellar populations, which is consistent with findings in various studies. Quantitative analysis reveals the varying significance of halo and galaxy properties in determining SHMR scatter across simulations and models. In EAGLE and TNG100-1, halo concentration and formation time primarily influence SHMR scatter for haloes with $M_{\rm h}\lt 10^{12}{\, \rm M_\odot }$, but the influence diminishes at high mass. Baryonic processes play a more significant role in LGal. For haloes with $M_{\rm h} \lt 10^{11}{\, \rm M_\odot }$ and $10^{12}{\, \rm M_\odot }\lt M_{\rm h}\lt 10^{13}{\, \rm M_\odot }$, the main drivers of scatter are galaxy star formation rate and age. In the $10^{11.5}{\, \rm M_\odot }\lt M_{\rm h} \lt 10^{12}{\, \rm M_\odot }$ range, halo concentration and formation time are the primary factors. And for haloes with $M_{\rm h} \gt 10^{13}{\, \rm M_\odot }$, supermassive black hole mass becomes more important. Interestingly, it is found that active galactic nucleus feedback may increase the amplitude of the scatter and decrease the dependence on halo properties at high masses.

Active transport of a passive colloid in a bath of run-and-tumble particles

The dispersion of a passive colloid immersed in a bath of non-interacting and non-Brownian run-and-tumble microswimmers in two dimensions is analyzed using stochastic simulations and an asymptotic theory, both based on a minimal model of swimmer-colloid collisions characterized solely by frictionless steric interactions. We estimate the effective long-time diffusivity D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathscr {D}}$$\\end{document} of the suspended colloid resulting from its interaction with the active bath, and elucidate its dependence on the level of activity (persistence length of swimmer trajectories), the mobility ratio of the colloid to a swimmer, and the number density of swimmers in the bath. We also propose a semi-analytical model for the colloid diffusivity in terms of the variance and correlation time of the net fluctuating active force on the colloid resulting from swimmer collisions. Quantitative agreement is found between numerical simulations and analytical results in the experimentally-relevant regime of low swimmer density, low mobility ratio, and high activity.

Longitudinal low-frequency vibration control of a propeller-shafting system using a hydraulic leveraged dynamic anti-resonance vibration isolator: A theoretical and experimental study

The longitudinal fluctuating forces of a propeller are a major cause of sound radiation of an underwater vehicle in the low frequency range. A hydraulic leveraged dynamic anti-resonance vibration isolator (HLVI) is proposed to attenuate the longitudinal vibration of a shaft system transmitted to the hull. The semi-analytical model of the shafting system with and without the isolator is set up by employing the frequency response synthesis method, in which the elasticity of the foundation is taken into consideration. Compared to the traditional isolation scheme and DVA, the proposed control scheme will not change the longitudinal effective stiffness and needs a small mass to attenuate the longitudinal vibration of the shafting system. A parametric study was conducted to investigate the key parameters of the isolator and their impact on its isolation performance. An experimental apparatus is set up to validate the isolation scheme. The acceleration frequency response results of the shafting system under axial excitation with both the frequency sweep method and discrete sinusoidal frequencies are presented and discussed. The results indicate that the proposed method is capable of attenuating the corresponding longitudinal vibration of the shafting system.