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We have investigated the performance of anisotropic flows $\langle v_n^2 \rangle$, transverse momentum fluctuations $\langle \delta p_T^2 \rangle $, and their correlations $\langle v_n^2 \delta p_T \rangle$ in central collisions at relativistic energies as probes of deformation parameters $\beta_n$ of colliding nuclei, if these nuclei are light nuclei with large $\beta_n$ and different configurations of $\alpha$ clusters. The effects from higher-order $\beta_n$ terms are illustrated by derived relations based on the overlap of two nuclei with uniform density distributions and by dynamic simulations of collisions of heavy nuclei whose density distributions are of a deformed Woods-Saxon (WS) form. While the linear relations between $\beta^2_n$, $\langle v_n^2 \rangle$, and $\langle \delta p_T^2 \rangle$ and that between $\beta^3_n$ and $\langle v_n^2 \delta p_T \rangle$ can be violated for extremely large $\beta_{n}$, they are mostly valid for realistic values of $\beta_n$, as long as the density distribution of colliding nuclei can be described by a deformed WS form. However, these linear relations are generally not valid with more realistic density distributions of light nuclei with $\alpha$ clusters, and the amount of deviation depends on the detailed $\alpha$-cluster configurations. Care must be taken when one tries to extract the deformation of light nuclei, and specific probes for $\alpha$-cluster structures in these nuclei are very much needed., Comment: 15 pages, 7 figures

Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In the paper, we construct an integral solution operator $T[f]$ for any $\overline{\partial}$ closed $(0,1)$-form $f\in L^p_{(0,1)}(D^n)$ solving the Cauchy-Riemain equation $\overline{\partial} u=f$ on the product domains $D^n$ and obtain the $L^p$-estimates for all $1

Optically addressable defect qubits in wide band gap materials are favorable candidates for room temperature quantum information processing. The two-dimensional (2D) hexagonal boron nitride (hBN) is an attractive solid state platform with a great potential for hosting bright quantum emitters with quantum memories with leveraging the potential of 2D materials for realizing scalable preparation of defect qubits. Although, room temperature bright defect qubits have been recently reported in hBN but their microscopic origin, the nature of the optical transition as well as the optically detected magnetic resonance (ODMR) have been remained elusive. Here we connect the variance in the optical spectra, optical lifetimes and spectral stability of quantum emitters to donor-acceptor pairs (DAP) in hBN by means of ab initio calculations. We find that DAPs can exhibit ODMR signal for the acceptor counterpart of the defect pair with S=1/2 ground state at non-zero magnetic fields depending on the donor partner. The donor-acceptor pair model and its transition mechanisms provide a recipe towards defect qubit identification and performance optimization in hBN for quantum applications.

For users in hotspot region, orbital angular momentum (OAM) can realize multifold increase of spectrum efficiency (SE), and the flying base station (FBS) can rapidly support the real-time communication demand. However, the hollow divergence and alignment requirement impose crucial challenges for users to achieve air-to-ground OAM communications, where there exists the line-of-sight path. Therefore, we propose the air-to-ground cooperative OAM communication (ACOC) scheme, which can realize OAM communications for users with size-limited devices. The waist radius is adjusted to guarantee the maximum intensity at the cooperative users (CUs). We derive the closed-form expression of the optimal FBS position, which satisfies the antenna alignment for two cooperative user groups (CUGs). Furthermore, the selection constraint is given to choose two CUGs composed of four CUs. Simulation results are provided to validate the optimal FBS position and the SE superiority of the proposed ACOC scheme.

The gas-phase metallicity distribution within galaxies records critical information about galactic evolution. In this work we investigate how active galactic nuclei (AGN) influence this distribution by measuring the two-point correlation functions of gas-phase metallicity in 95 non-AGN and 37 AGN-host galaxies from the Calar Alto Legacy Integral Field spectroscopy Area integral field spectrographic survey. We measure metallicity using a novel Bayesian method that properly includes both stellar and AGN contributions to emission line fluxes and allows us to measure metallicities in both AGN-host and non-AGN galaxies in a single, consistent framework. We find that the two-point correlation functions of both AGN-host and non-AGN galaxies are well-fit by a simple injection-diffusion model, and that the correlation lengths $l_\mathrm{corr}$ we derive for the non-AGN galaxies are reasonably consistent with those obtained in earlier work. The AGN-host galaxies generally have smaller $l_\mathrm{corr}$ than non-AGN galaxies at fixed stellar mass, but similar $l_\mathrm{corr}$ at fixed star formation rate (SFR), suggesting that the primary effect of hosting an AGN in this sample is a reduction in SFR at fixed stellar mass, and that this in turn suppresses the correlation length. Our findings further indicate that, while both SFR and stellar mass are positively correlated with metallicity correlation length $l_\mathrm{corr}$, the former is more fundamental, implying that fluctuations in the metallicity distribution within galaxies are driven more by short-term responses to physical processes such as star formation that can change much faster than a Hubble time., Comment: 13 pages, 10 figures, submitted to MNRAS

This note demonstrates that we can stably recover rank $r$ Toeplitz matrix $\pmb{X}\in\mathbb{R}^{n\times n}$ from a number of rank one subgaussian measurements on the order of $r\log^{2} n$ with an exponentially decreasing failure probability by employing a nuclear norm minimization program. Our approach utilizes descent cone analysis through Mendelson's small ball method with the Toeplitz constraint. The key ingredient is to determine the spectral norm of the random matrix of the Topelitz structure, which may be of independent interest.This improves upon earlier analyses and resolves the conjecture in Chen et al. (IEEE Transactions on Information Theory, 2015)., Comment: 14pages

Recently, multilingual artificial intelligence assistants, exemplified by ChatGPT, have gained immense popularity. As a crucial gateway to human-computer interaction, multilingual automatic speech recognition (ASR) has also garnered significant attention, as evidenced by systems like Whisper. However, the proprietary nature of the training data has impeded researchers' efforts to study multilingual ASR. This paper introduces MSR-86K, an evolving, large-scale multilingual corpus for speech recognition research. The corpus is derived from publicly accessible videos on YouTube, comprising 15 languages and a total of 86,300 hours of transcribed ASR data. We also introduce how to use the MSR-86K corpus and other open-source corpora to train a robust multilingual ASR model that is competitive with Whisper. MSR-86K will be publicly released on HuggingFace, and we believe that such a large corpus will pave new avenues for research in multilingual ASR., Comment: Accepted by InterSpeech 2024

Boron nitride exhibits diverse crystal structures, predominantly a layered arrangement with strong intraplanar covalent bonds and weak interplanar van der Waals bonds. While commonly referred to as hexagonal BN (hBN), the sp$^2$-bonded BN atomic planes can also arrange in other configurations like Bernal (bBN) or rhombohedral (rBN) stacking orders. Variations in the orientation and translation of successive atomic layers lead to changes in crystal symmetry, potentially resulting in piezoelectric, pyroelectric or ferroelectric effects. However, distinguishing between different polytypes using conventional methods like X-ray diffraction or Raman spectroscopy presents a significant challenge. In this work, we demonstrate that the optical response of the 4.1 eV defect can serve as an indicator of the polytype. To this end, we study BN samples grown by metalorganic vapor phase epitaxy (MOVPE), which contain different polytypes. The identification of the polytypes was achieved by X-ray diffraction and transmission electron microscopy. Photoluminescence and cathodoluminescence measurements with a high spatial resolution allowed for the deconvolution of the signal into two components from which we can extract a zero-phonon line (ZPL) at 4.096 eV (302.6 nm) for hBN and 4.143 eV (299.2 nm) for rBN. We performed calculations that enable us to identify the defect as a carbon dimer CBCN (C2) and show that the ZPL shift reflects differences in the crystal environment for different polytypes. Furthermore, we demonstrate that different polytypic composition ratios of hBN and rBN can be achieved by MOVPE, which could pave the way for future applications in large-area van der Waals heterostructures.

Motivated by the null results of current dark matter searches and the small-scale problems, we study a dark sector charged by a spontaneous broken gauge $U(1)'$. To explore the parameter space of this model, in addition to the consideration of the small-scale data, we also consider the theoretical bounds on the dark Higgs mass, with the upper bound coming from the tree-level perturbative unitarity and the lower bound from the one-loop Linde-Weinberg bound. We deeply examine the dependence of the Linde-Weinberg bound on gauge choice and energy scale, and present a Linde-Weinberg bound that is gauge and scale independent. Combining the theoretical and observational constraints, we obtain the following ranges for the parameter space: the dark matter mass is 10-500 GeV, the mediator (dark photon) mass is 0.5-5 MeV, the dark Higgs mass is 0.05-50 MeV, and the dark fine-structure constant is 0.001-0.4. We conclude that the dark Higgs in this model cannot be ignored in the phenomenological study of the dark sector., Comment: 45 pages, 7 figures

In this paper, we first propose a unified approach for analyzing the stability of the phaseless operator for both amplitude and intensity measurement on an arbitrary geometric set, thus characterizing the robust performance of phase retrieval via the empirical minimization method. We introduce the random embedding of concave lifting operators in tangent space to characterize the unified analysis of any geometric set. Similarly, we investigate the structured matrix recovery problem through the robust injectivity of a linear rank one measurement operator on an arbitrary matrix set. The core of our analysis is to establish a unified empirical chaos process characterization for various matrix sets. Talagrand's $\gamma_{\alpha}$-functionals are introduced to characterize the connection between the geometric constraints and the number of measurements needed to guarantee stability or robust injectivity. Finally, we construct adversarial noise to demonstrate the sharpness of the recovery bounds in the above two scenarios., Comment: 26 pages

Microstructure uniformity of the Al-Nd target materials with Al11Nd3 significantly affects the performance of the fabricated film, which is widely used as wiring material in largesize thin-film transistor liquid crystal display (TFT-LCD) panels. Understanding the inherent mechanical properties and chemical bonds of Al11Nd3 is crucial for homogenizing the Al-Nd target. Here, by a combined experimental and ab-initio theoretical study, the microstructure and deformability of the Al-3wt%Nd alloy and the inherent mechanical properties and chemical bonds of Al11Nd3 are investigated comprehensively. The Al-3wt%Nd alloy is composed of the pre-eutectic {\alpha}-Al matrix and the eutectic {\alpha}-Al and a high stable {\alpha}-Al11Nd3 phases. During the plastic deformation, the eutectic microstructure transforms from a cellular to a lamellar shape, while the morphology and dimension of {\alpha}-Al11Nd3 are not changed significantly. By examining ideal tensile strength, elastic moduli, hardness and brittleness-ductility, the hardnessbrittleness of {\alpha}-Al11Nd3 is quantitatively evaluated, accounting for its difficulties of plastic deformation and fragmentation. Combining band structure, population analysis, topological analysis and crystal orbital Hamilton population, it is revealed that {\alpha}-Al11Nd3 possesses two types of chemical bonds: the Nd-Al and Al-Al bonds. The former is a typical ionic bond with electron transfer from Nd to Al, while the latter, dominated by both 3s-3p and 3p-3p interactions, is a weak covalent bond. The mixed chemical bond is responsible for the high hardness-brittleness of {\alpha}-Al11Nd3. This work is expected to lay a foundation for Al-Nd alloy and catalyze the fabrication of high-quality Al-Nd target materials., Comment: 11 figures,5 tables

Spin-to-photon interfaces from defects in silicon hold great promise towards realizing quantum repeaters with the combination of advanced semiconductor and photonics technologies. Recently, controlled creation and erasure of simple carbon interstitial defects have been successfully realised in silicon. This defect has a stable structure near room temperature and emits in the wave-length where the signal loss is minimal in optical fibres used in communication technologies. Our in-depth theoretical characterization confirms the assignment of the observed emission to the neutral charge state of this defect. We find that the emission is due to the recombination of a bound exciton. We also discovered a metastable triplet state that could be applied as a quantum memory. Based on the analysis of the electronic structure of the defect and its similarities to a known optically detected magnetic resonance centre in silicon, we propose that a carbon interstitial can act as a quantum bit and may realize a spin-to-photon interface in CMOS-compatible platforms., Comment: 2 figures and 2 tables

Galaxies' stellar masses, gas-phase oxygen abundances (metallicity), and star formation rates (SFRs) obey a series of empirical correlations, most notably the mass-metallicity relation (MZR) and fundamental metallicity relation (FZR), which relates oxygen abundance to a combination of stellar mass and SFR. However, due to the difficulty of measuring oxygen abundances and SFRs in galaxies that host powerful active galactic nuclei (AGN), to date it is unknown to what extent AGN-host galaxies also follow these correlations. In this work, we apply Bayesian methods to the MaNGA integral field spectrographic (IFS) survey that allow us to measure oxygen abundances and SFRs in AGN hosts, and use these measurements to explore how the MZR and FZR differ between galaxies that do and do not host AGN. We find similar MZRs at stellar masses above $10^{10.5} \mathrm{M}_\odot$, but that at lower stellar masses AGN hosts show up to $\sim 0.2$ dex higher oxygen abundances. The offset in the FZR is significantly smaller, suggesting that the larger deviation in the MZR is a result of AGN-host galaxies having systematically lower SFRs at fixed stellar mass. However, within the AGN-host sample there is little correlation between SFR and oxygen abundance. These findings support a scenario in which an AGN can halt efficient gas accretion, which drives non-AGN host galaxies to both higher SFR and lower oxygen abundance, resulting in the galaxy evolving off the star-forming main sequence (SFMS). As a consequence, as the SFR declines for an individual system its metallicity remains mostly unchanged., Comment: 18 pages, 14 figures, accepted for publication in MNRAS

We identify a fading AGN SDSS J220141.64+115124.3 from the internal Product Launch-11 (MPL-11) in Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. The central region with a projected radius of $\sim$2.4 kpc is characterized as LINER-like line ratios while the outskirts extended to $\sim$15 kpc show Seyfert-like line ratios. The [OIII]$\lambda$5007 luminosity of the Seyfert regions is a factor of 37 (2) higher than the LINER regions without (with) dust attenuation correction, suggesting that the AGN activity decreases at least $\sim$8 $\times$ 10$^3$ yrs ($\sim$2.4 kpc/light-speed) ago. We model the emission line spectra in the central region with double Gaussian components (a narrow core and a broad wing) and analyze the properties of each component. The narrow core component mostly co-rotates with the stellar disc, whereas the broad wing component with a median of the velocity dispersion $\sim$300 km s$^{-1}$ is related to a wind outflow. The kinematic position angle (PA) of the ionized gas shows a $\sim$20{\deg} twist from the galaxy center to 1.5 effective radius. The median of the PA difference between the gas and stellar components is as large as $\sim$50{\deg} within 0.4 effective radius. The tidal feature in DESI image and star-gas misalignment suggest this galaxy is a merger remnant. Combining all these observational results as well as public available X-ray and MIR luminosities, we confirm this is a fading AGN, the merger process kick-started the central engine to quasar phase which ionized gas composed of tidal debris, and now the activity of the central black hole decreases. The discontinuity in [OIII]$\lambda$5007 flux and EQW maps is due to multiple AGN outbursts triggered by merger remnant gas inflows., Comment: Accepted for publication in MNRAS. 12 pages, 10 figures, 1 table

In this paper, we study two generalized constrained integrable hierarchies, which are called the $c$-$k$ constrained KP and BKP hierarchies. The Fermionic picture of the $c$-$k$ constrained KP hierarchy is given. We give some solutions for the $c$-$k$ constrained KP hierarchy by using the free Fermion operators and define its additional symmetries. Its additional flows form a subalgebra of the Virasoro algebra. Furthermore, the additional flows acting on eigenfunctions $q_{i}(t)$ and adjoint eigenfunctions $r_{i}(t)$ of the $c$-$k$ constrained KP hierarchy are presented. Next, we define the $c$-$k$ constrained BKP hierarchy and obtain its bilinear identity and solutions. The algebra formed by the additional symmetric flow of the $c$-$k$ constrained BKP hierarchy that we defined is still a subalgebra of the Virasoro algebra and it is a subalgebra of the algebra formed by the additional flows of the $c$-$k$ constrained KP hierarchy.

Quantum Griffiths singularity (QGS) has been experimentally observed in a range of two-dimensional (2D) superconducting systems. Although it is theoretically suggested that the QGS also exists in three-dimensional (3D) superconductors, there is almost no experimental support to the theoretical prediction. In the present paper, we observe the occurrence of QGS in a series of $\sim$80-nm-thick Mo$_{0.8}$Ti$_{0.2}$N$_x$ ($0.84 \lesssim x \lesssim 1.12$) superconducting films near the field-driven superconductor-metal transition (SMT). These films have a NaCl structure and are 3D with respect to the superconductivity. For each film, the low-temperature magnetoresistance isotherms, measured at magnetic fields being perpendicular or parallel to the film plane, do not cross at a single point but at a clear wide region. The dynamical critical exponents $z\nu_{\perp}$ (for perpendicular field) and $z\nu_{\parallel}$ (for parallel field) obtained by analyzing the related magnetoresistance isotherms increase with decreasing temperature and tend to diverge as $T\rightarrow 0$ K. In addition, the effective resistivity data for the perpendicular and parallel field in the vicinity of the SMTs both obey an activated scaling based on the random transverse-field Ising model. We also fabricate a $\sim$80-nm-thick (Mo$_{0.8}$Ti$_{0.2}$)$_2$N$_{1.06}$ superconducting film with face-centered cubic structure at low nitrogen partial pressure. It is found that the low-temperature magnetoresistance isotherms for the perpendicular (parallel) field cross at a single point and the resistivity data for the perpendicular (parallel) field in the vicinity of the field-induced SMT obey the power-law scaling deduced from the dirty-boson model. Our results provide unambigous experimental evidence for the existence of QGS in 3D superconductors., Comment: 11 pages and 9 Figures

We study deterministic matrix completion problem, i.e., recovering a low-rank matrix from a few observed entries where the sampling set is chosen as the edge set of a Ramanujan graph. We first investigate projected gradient descent (PGD) applied to a Burer-Monteiro least-squares problem and show that it converges linearly to the incoherent ground-truth with respect to the condition number \k{appa} of ground-truth under a benign initialization and large samples. We next apply the scaled variant of PGD to deal with the ill-conditioned case when \k{appa} is large, and we show the algorithm converges at a linear rate independent of the condition number \k{appa} under similar conditions. Finally, we provide numerical experiments to corroborate our results., Comment: 41 pages, 3figures

In current studies for testing Bell inequalities at colliders, the reconstruction of spin correlations from scattering cross-sections relies on the bilinear form of the spin correlations, but not all local hidden variable models (LHVMs) have such a property. To demonstrate that a general LHVM cannot be rule out via scattering cross-section data, we propose a specific LHVM, which can exactly duplicate the same scattering cross-section for particle production and decay as the standard quantum theory, making it indistinguishable at colliders in principle. Despite of this, we find that reconstructing spin correlations through scattering cross-sections can still exclude a broad class of LHVMs, e.g., those models employing classical spin correlations as a surrogate for quantum spin correlations., Comment: 14 pages, 2 figures

We propose to use spectator particle yield ratios to probe the configuration of $\alpha$ clusters in $^{12}$C and $^{16}$O by their collisions at RHIC and LHC energies. The idea is illustrated based on initial density distributions with various $\alpha$-cluster configurations generated by a microscopic cluster model, and without $\alpha$ clusters from mean-field calculations. The multifragmentation of the spectator matter produces more spectator light nuclei including $\alpha$ clusters in collisions of nuclei with chain structure of $\alpha$ clusters, compared to those of nuclei with a more compact structure. The yield ratio of free spectator neutrons to spectator particles with mass-to-charge ratio $A/Z=2$ scaled by their masses can be practically measured by the zero-degree calorimeter (ZDC) at RHIC and LHC, serving as a clean probe free from modeling the complicated dynamics at midrapidities., Comment: 6 pages, 4 figures

We investigate the phase retrieval problem perturbed by dense bounded noise and sparse outliers that can change an adversarially chosen $s$-fraction of the measurement vector. The adversarial sparse outliers may exhibit dependence on both the observation and the measurement. We demonstrate that the nonlinear least absolute deviation based on amplitude measurement can tolerate adversarial outliers at a fraction of $s^{*,1}\approx0.2043$, while the intensity-based model can tolerate a fraction of $s^{*,2}\approx0.1185$. Furthermore, we construct adaptive counterexamples to show that the thresholds are theoretically sharp, thereby showing the presentation of phase transition in the adversarial phase retrieval problem when the corruption fraction exceeds the sharp thresholds. This implies that the amplitude-based model exhibits superior adversarial robustness in comparison with the intensity-based model. Corresponding experimental results are presented to further illustrate our theoretical findings. To the best of our knowledge, our results provide the first theoretical examination of the distinction in robustness performance between amplitude and intensity measurement. A crucial point of our analysis is that we explore the exact distribution of some combination of two non-independent Gaussian random variables and present the novel probability density functions to derive the sharp thresholds., Comment: 32 pages

Test of the no-hair theorem is the primary target with gravitational waves from binary black holes. In this Letter, we analyze gravitational-wave data from the LIGO-Virgo-KAGRA detection of binary black-hole mergers using the PSI_FD model, which is a non-general relativity full waveform template for arbitrary axisymmetric black holes. By analyzing two high signal-noise-ratio events, GW150914 and GW200129, the no-hair theorem is tested at a significance level of 95%, which is the best constraint until now. Especially, we find a significant deviation from the Kerr black hole in GW200129. More events and further analysis are needed to validate this deviation., Comment: 5 pages, 4 figures and 1 table

We consider the problem of recovering an unknown signal $\pmb{x}_0\in \mathbb{R}^{n}$ from phaseless measurements. In this paper, we study the convex phase retrieval problem via PhaseLift from linear Gaussian measurements perturbed by $\ell_{1}$-bounded noise and sparse outliers that can change an adversarially chosen $s$-fraction of the measurement vector. We show that the Robust-PhaseLift model can successfully reconstruct the ground-truth up to global phase for any $s< s^{*}\approx 0.1185$ with $\mathcal{O}(n)$ measurements, even in the case where the sparse outliers may depend on the measurement and the observation. The recovery guarantees are based on the robust outlier bound condition and the analysis of the product of two Gaussian variables. Moreover, we construct adaptive counterexamples to show that the Robust-PhaseLift model fails when $s> s^{*}$ with high probability., Comment: The first version of this article was submitted on October 28, 2022 at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4296843

In the realm of natural supersymmetric models, higgsinos are typically the lightest electroweakinos. In gauge-mediated supersymmetry breaking models, the lightest higgsino-dominated particles decay into a $Z$-boson or a Higgs boson ($h$), along with an ultra-light gravitino ($\tilde{G}$) serving as the lightest supersymmetric particle (LSP). This scenario suggests a significant non-resonant $hh$ production. Basing on the recent global fitting results of the $\tilde{G}$-EWMSSM (MSSM with light electroweakinos and an eV-scale gravitino as the LSP) performed by the \textsf{GAMBIT} collaboration, which support a higgsino dominated electroweakino as light as 140 GeV, we develop two simplified models to evaluate their detection potential at the high-luminosity LHC (HL-LHC) with $\sqrt{s} = 14~{\rm TeV}$ and an integrated luminosity of $3000~{\rm fb}^{-1}$. The first model examines the processes where heavier higgsino-dominated states decay into soft $W/Z$ bosons, while the second focuses on direct decays of all three higgsino-dominated electroweakinos into $W/Z/h$ plus a $\tilde{G}$. Our study, incorporating both models and their distinct decay channels, utilizes detailed Monte Carlo simulations for signals and standard model backgrounds. We find that the HL-LHC can probe higgsinos up to 575 GeV, potentially discovering or excluding the natural SUSY scenario in the context of a gravitino LSP. Further, we reinterpret this discovery potential using the GAMBIT global fit samples, and find that the entire parameter space of $|\mu| \leq 500~{\rm GeV}$ with an electroweak fine-tuning measure ($\Delta_{\rm EW}$) under 100 in $\tilde{G}$-EWMSSM is accessible at the HL-LHC., Comment: 31 pages, 12 figures, and 6 tables

Point defects may introduce defect levels into the fundamental band gap of the host semiconductors that alter the electrical properties of the material. As a consequence, the in-gap defect levels and states automatically lower the threshold energy of optical excitation associated with the optical gap of the host semiconductor. It is, therefore, a common assumption that solid state defect emitters in semiconductors ultimately alter the conductivity of the host. Here we demonstrate on a particular defect in 4H silicon carbide that a yet unrecognized class of point defects exists which are optically active but electrically inactive in the ground state., Comment: 7 pages, 4 figures

In order to study the validity of analytical formulas used in the calculation of characteristic physical quantities related to vacuum bubbles, we conduct several numerical simulations of bubble kinematics in the context of cosmological first-order phase transitions to determine potentially existing systematic uncertainties. By comparing with the analytical results, we obtain the following observations: (1) The simulated false vacuum fraction will approach the theoretical one with increasing simulated volume. When the side length of the cubic simulation volume becomes larger than 14.5 $\beta_{th}^{-1}$ , the simulated results do not change significantly; (2) The theoretical expected total number of bubbles do not agree with the simulated ones, which may be caused by the inconsistent use of the false vacuum fraction formula; (3) The different nucleation rate prefactors do not affect the bubble kinetics much; (4) The lifetime distribution in the sound shell model does not obey an exponential distribution, in such a way as to cause a suppression in the gravitational wave spectra., Comment: PRD accepted version, 12 pages, 9 figures