Energy Density Spectrum Research Articles

General backreaction force of cosmological bubble expansion

The gravitational-wave energy-density spectra from cosmological first-order phase transitions crucially depend on the terminal wall velocity of asymptotic bubble expansion when the driving force from the effective potential difference is gradually balanced by the backreaction force from the thermal plasma. Much attention has previously focused on the backreaction force acting on the bubble wall alone but overlooked the backreaction forces on the sound shell and shock-wave front, if any, which have been both numerically and analytically accomplished in our previous studies but only for a bag equation of state. In this paper, we will generalize the backreaction force on bubble expansion beyond the simple bag model. Published by the American Physical Society 2024

Constraints on primordial curvature power spectrum with kination era: Insights from NANOGrav 15-year data set

The stochastic signal detected by the NANOGrav, PPTA, EPTA, and CPTA collaborations can be attributed to gravitational waves induced by the primordial curvature perturbations generated during inflation. These scalar-induced gravitational waves provide valuable insights into the small-scale inflation and reheating epochs. In this paper, we assume an equation of state of w=1 during reheating and adopt a log-normal form for the primordial curvature power spectrum to elucidate the observed stochastic signal. The inflation and reheating scenarios are rigorously constrained utilizing Bayesian methods applied to the NANOGrav 15-year data set. The analysis yields constraints on the reheating temperature, indicating Trh≳0.01Gev, a result consistent with constraints derived from Big Bang nucleosynthesis. Furthermore, the NANOGrav 15-year data set necessitates the primordial curvature power spectrum's amplitude and width to satisfy A∼0.01 and Δ≲0.1, respectively. Due to the change in the equation of state w, there exists a turning point in the energy density spectrum of scalar-induced gravitational waves. This suggests that if more data about the scalar-induced gravitational waves is observed, it could potentially provide constraints on the time when the reheating epoch transitions to radiation domination.

Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity f NL and g NL considered

Investigation of primordial non-Gaussianity holds immense importance in testing the inflation paradigm and shedding light on the physics of the early Universe. In this study, we conduct the complete analysis of scalar-induced gravitational waves (SIGWs) by incorporating the local-type non-Gaussianity f NL and g NL. We develop Feynman-like diagrammatic technique and derive semi-analytic formulas for both the energy-density fraction spectrum and the angular power spectrum. For the energy-density fraction spectrum, we analyze all the relevant Feynman-like diagrams, determining their contributions to the spectrum in an order-by-order fashion. As for the angular power spectrum, our focus lies on the initial inhomogeneities, giving rise to anisotropies in SIGWs, that arise from the coupling between short- and long-wavelength modes due to primordial non-Gaussianity. Our analysis reveals that this spectrum exhibits a typical multipole dependence, characterized by C̃ ℓ ∝ [ℓ(ℓ + 1)]-1, which plays a crucial role in distinguishing between different sources of gravitational waves. Depending on model parameters, significant anisotropies can be achieved. We also show that the degeneracies in model parameters can be broken. The findings of our study underscore the angular power spectrum as a robust probe for investigating primordial non-Gaussianity and the physics of the early Universe. Moreover, our theoretical predictions can be tested using space-borne gravitational-wave detectors and pulsar timing arrays.

Internal waves generated from asymmetric topographies

Previous experimental and theoretical research on tidally generated internal waves over oceanic topography has often used symmetric topographic profiles. However, due to the complex nature of real ocean topography, the effect of asymmetry cannot be overlooked. Studies have shown that topographic complexities, including asymmetry, can have a significant impact on internal wave generation, but topographic asymmetry has not yet been explored in a systematic manner. This work presents a comparison of tidally generated internal waves from nine different two-dimensional asymmetric topographies, consisting of a steeper Gaussian curve on one side, and a wider Gaussian curve on the other. The amplitude of the wider curve varies from 60% of the steeper curve to its equivalent. Two oscillation frequencies are tested. Kinetic energy density in tidally generated internal waves on each side of the topography is compared qualitatively and quantitatively, in both physical and Fourier space. When compared to similar symmetric topographies, waves generated by the asymmetric topographies varied distinctly in both magnitude and wavenumber distribution of kinetic energy density. Waves on the relatively steep side of the topography contain up to 50% more kinetic energy than on the wider side. However, there is very little kinetic energy at the higher wavenumbers associated with the steeper topography. Instead, the internal wavefield is dominated by lower wavenumbers, 50%–90% of the kinetic energy density is contained in wavelengths corresponding to the wider side of the topography. Decreasing the amplitude of the wider curve does not make an appreciable difference in the kinetic energy density spectrum. Thus, the differences quantified here are due solely to changing slope and show the effect which relatively slight asymmetry has on internal wave generation.

Constraints on non-Gaussian primordial curvature perturbation from the LIGO-Virgo-KAGRA third observing run

The scalar-induced gravitational wave (SIGWs), arising from large amplitude primordial density fluctuations, provide a unique observational test for directly probing the epoch of inflation. In this work, we provide constraints on the SIGW background by taking into account the non-Gaussianity in the primordial density fluctuations, using the first three observing runs (O1-O3) data of the LIGO-Virgo-KAGRA collaboration. We find that the non-Gaussianity gives a non-negligible effect on the GW energy density spectrum and starts to affect the analysis of the O1-O3 data when the non-Gaussianity parameter is F NL > 3.55. Furthermore, the constraints exhibit asymptotic behavior given by F NL Ag = const. at large F NL limit, where Ag denotes the amplitude of the curvature perturbations. In the limit of large F NL, we placed a 95% credible level upper limit F NL Ag ≤ 0.115, 0.106, 0.112 at fixed scales of 1016, 1016.5, 1017 Mpc-1, respectively.

Probing scalar induced gravitational waves with PTA and LISA: the importance of third order correction

We revisit the calculation of third order scalar induced gravitational waves (SIGWs) and extend it from a monochromatic primordial power spectrum to a more general log-normal one. We investigate the impact of third order SIGWs on signal-to-noise ratio (SNR) of Laser Interferometer Space Antenna (LISA) and pulsar timing array (PTA) observations, and find that third order SIGWs significantly contribute to the total energy density spectrum of gravitational waves (GW) in high-frequency region. For a primordial power spectrum amplitude of Aζ = 10-2 ∼ 10-1, the effects of third order SIGWs lead to a 40% to 400% increase in the SNR for LISA. Additionally, our PTA data analysis reveals that third order SIGWs diminish both the amplitude Aζ and the peak frequency f * of the primordial power spectrum.

Energy density source levels of underwater explosive charges

This paper presents experimental measurements of energy density source levels of small explosive charges for high frequencies to 18 kHz. The experiments were carried out using Signals Underwater Sound (SUS) charges deployed at a deep water site in a coastal fiord north of Vancouver BC. The waveform of an underwater explosion is characterized by a high intensity shock wave signal followed by a series of bubble pulses of decreasing intensity. The bubble pulses dominate the SUS energy density spectrum at frequencies below 1 kHz, but at higher frequencies the spectrum is dominated by the characteristics of the decay envelope of the shock wave signal. The explosive material in SUS charges is packed in a thin cylindrical cavity, resulting in a non-uniform decay envelope with secondary pulses when detonated, and a non-spherical distribution of the radiated sound. The impact of the cylindrical charge shape on energy density source level was investigated experimentally. Data were recorded for SUS deployments that generated in-line and broadside sound propagation to the receiver with respect to the axis of the cylindrical charge. Experimental measurements indicate significant differences in the high frequency SUS energy density spectrum depending upon the SUS and receiver geometry.

A comprehensive study of large eddy simulation models in capturing the dynamics of gas-particle turbulent suspensions

The particle phase attenuates the fluid fluctuations with an increase in volume fraction, and a sudden collapse in the turbulence is observed at a particular particle volume fraction, called critical particle volume loading (CPVL) [P. Muramulla et al. J. Fluid Mech. 889, A28 (2020)]. The present study reports the capability of two different classes of large eddy simulation (LES), viz. anisotropic and eddy viscosity-based, models to capture the turbulence modulation and the sudden disruption of the fluid fluctuations in the particle-laden vertical channel flows. The simulations are performed at two bulk Reynolds numbers of 3300 and 5600 based on the channel width and the bulk averaged fluid velocity. Our study on different LES models shows that approximate deconvolution (ADM) and scale similarity (SS) models accurately predict the critical loading for the Reynolds number of 3300. However, these models predict the critical loading qualitatively only for the Reynolds number of 5600 in the sense that they fail to predict the discontinuity as shown by the direct numerical simulation (DNS) study. The coherent structure model (CSM) predicts the critical loading with an 80% accuracy at both Reynolds numbers. The energy spectral density, production, and particle-induced dissipation spectra are plotted to analyze the distribution across wavenumbers. For all the LES models, a decrease in more than one order of magnitude is observed in the energy spectrum density at the critical loading compared to the unladen flow. The energy density decreases more in the channel center than in the near-wall region for the same particle volume loading. The mean component of particle-induced dissipation is almost two orders of magnitude larger than the particle dissipation spectra of fluctuating energy. The magnitude of streamwise and spanwise dissipation spectra of fluctuating components is higher in the near-wall region than the channel center. However, the magnitude of wall-normal dissipation spectra is higher in the channel center than near the wall region.

Phase Retrieval for Radar Constant–Modulus Signal Design Based on the Bacterial Foraging Optimization Algorithm

Optimizing the energy spectrum density (ESD) of a transmitted waveform can improve radar performance. The design of a time–domain constant–modulus signal corresponding to the transmitted waveform ESD is practically important because constant–modulus signals can maximize transmission power and meet the hardware requirements of radar transmitters. Here, we present a time–domain signal design under dual constraints of energy and constant modulus. The mutual information (MI)–based waveform design method is used to design transmitted waveform ESD under the energy constraint. Then, the bacterial foraging optimization algorithm (BFOA) is proposed to design the time–domain constant–modulus signal. We use minimum mean square error (MMSE) in the frequency domain as the cost function. The BFOA monotonously decreases the MMSE with increasing iterations, which makes the ESD of the time–domain constant–modulus signal close to the MI–based optimal waveform ESD. The simulation results indicate that the proposed algorithm has advantages, including insensitivity to initial phases, rapid convergence, smaller MI loss, and MMSE compared with the iterative reconstruction algorithm.

CoDA-Based Geo-Electrochemical Prospecting Prediction of Uranium Orebodies in Changjiang Area, Guangdong Province, China

In order to achieve a breakthrough in the exploration of uranium orebodies in the Changjiang area of Guangdong province in China, the geo-electrochemical exploration method is used for mineral resource prediction. The logarithmically and isometric log-ratio (ilr) transformations are applied to the geo-electrochemical data in this study area to extract geochemical anomalies. The relationship between element associations and mineralization is revealed through descriptive statistical analysis and further biplot analysis. Then, the energy spectrum density–area fractal model (S-A model) is used to identify geochemical backgrounds and anomalies. The results show that: (i) the logarithmically and ilr-transformed data are more uniform, and they more or less obey the rules of normal distribution; (ii) the biplot shows that the ilr-transformed data eliminates the closure effect, and the robust principal component analysis (RPCA) has a better indicative significance for element associations—PC1 reveals the mineralization element association dominated by U and the multiple periods of hydrothermal activity; (iii) the S-A method could extract the local anomalies from different geochemical backgrounds, which indicates mineralization is more reliable. Finally, four favorable prospecting targets are delineated based on the geological and geochemical indicators.

An SZ-like effect on cosmological gravitational wave backgrounds

Cosmological gravitational wave backgrounds (CGWBs) are the conglomeration of unresolved gravitational wave signals from early Universe sources, which make them a promising tool for cosmologists. Because gravitons decouple from the cosmic plasma early on, one can consider interactions between gravitons and any particle species that were present in the very early Universe. We show that analogous to the cosmic microwave background, elastic scattering on any cosmological background will induce small distortions in its energy density spectrum. We then quantify the magnitude of these spin-dependent spectral distortions when attributed to the dark matter in the early Universe. Lastly, we give estimates for potentially measurable distortions on CGWBs due to gravitational scattering by primordial black holes.

Exact solution for anisotropic Dirac materials interacting with position-dependent electric and magnetic fields

The interaction between massless Dirac fermions in anisotropic Dirac materials and position-dependent electric and magnetic fields is discussed here. The effect of the electric field strength in the energy spectrum and probability density of the eigenstates of the system is analyzed. Results show that the Landau levels are dispersive and the external electric field induces a collapse on them.

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence

AbstractThe immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use data sets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (a) a form of Nonlinear Vector Autoregression (NVAR), and (b) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi‐Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures.

Damping of MHD turbulence in a partially ionized medium

ABSTRACT The coupling state between ions and neutrals in the interstellar medium plays a key role in the dynamics of magnetohydrodynamic (MHD) turbulence, but is challenging to study numerically. In this work, we investigate the damping of MHD turbulence in a partially ionized medium using 3D two-fluid (ions + neutrals) simulations generated with the athenak code. Specifically, we examine the velocity, density, and magnetic field statistics of the two-fluid MHD turbulence in different regimes of neutral-ion coupling. Our results demonstrate that when ions and neutrals are strongly coupled, the velocity statistics resemble those of single-fluid MHD turbulence. Both the velocity structures and kinetic energy spectra of ions and neutrals are similar, while their density structures can be significantly different. With an excess of small-scale sharp density fluctuations in ions, the density spectrum in ions is shallower than that of neutrals. When ions and neutrals are weakly coupled, the turbulence in ions is more severely damped due to the ion-neutral collisional friction than that in neutrals, resulting in a steep kinetic energy spectrum and density spectrum in ions compared to the Kolmogorov spectrum. We also find that the magnetic energy spectrum basically follows the shape of the kinetic energy spectrum of ions, irrespective of the coupling regime. In addition, we find large density fluctuations in ions and neutrals and thus spatially inhomogeneous ionization fractions. As a result, the neutral-ion decoupling and damping of MHD turbulence take place over a range of length-scales.

Primordial black hole mass function with mass gap

ABSTRACT Primordial black holes (PBHs) are mainly characterized by their mass function, in which there may be some huge suppression for certain mass spans. If this is the case, the absence of these PBHs will form mass gaps. In this paper, we investigate the PBH mass function with the mass gap. First, to obtain a data-supported PBH mass function with the mass gap for subsolar masses PBHs, we fine-tune the coefficients of a model-independent power spectrum of primordial curvature perturbations. Then we take this unique PBH mass function into consideration and calculate the energy-density spectrum of the stochastic gravitational-wave background from PBH mergers. We find the location of its first peak almost has no relationship with the mass gap and is only determined by the probability distribution of frequencies at which PBH binaries merge. Apart from the first peak, there must be an accompanying smaller trough at a higher frequency resulting from the mass gap. Therefore, the detection of this smaller trough will provide more information about inflation and PBH formation.

Probing the gravitational wave background from cosmic strings with the alternative LISA-TAIJI network

As one of the detection targets of all gravitational wave detectors today, the stochastic gravitational wave background (SGWB) provides an important means of understanding the evolution of our universe. In this paper, we explore the feasibility of detecting the SGWB generated by the loops arising throughout the cosmological evolution of the cosmic string network, using both individual space detectors (LISA and TAIJI) and joint space detectors (LISA-TAIJI). For the joint detectors, we choose three different configurations of TAIJI, namely TAIJIm, TAIJIp, and TAIJIc, to form the LISA-TAIJI networks, and we investigate their ability to detect the SGWB. By comparing the power-law sensitivity (PLS) curves of individual space detectors and joint detectors with the energy density spectrum of SGWB, we find that LISA-TAIJIc has the best sensitivity for detecting the SGWB from cosmic string loops. It thus holds promise for further constraining the tension of cosmic strings Gμ=O(10-17)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G\\mu =O(10^{-17})$$\\end{document}.

Novel Ocean Wave Height and Energy Spectrum Forecasting Approaches: An Application of Semi-Analytical and Machine Learning Models

Accurate and reliable wave forecasting is crucial for optimizing the performance of various marine operations, such as offshore energy production, shipping, and fishing. Meanwhile, predicting wave height and wave energy is crucial for achieving sustainability as a renewable energy source, as it enables the harnessing of the power of wave energy efficiently based on the water-energy nexus. Advanced wave forecasting models, such as machine learning models and the semi-analytical approach, have been developed to provide more accurate predictions of ocean waves. In this study, the Sverdrup Munk Bretschneider (SMB) semi-analytical approach, Emotional Artificial Neural Network (EANN) approach, and Wavelet Artificial Neural Network (WANN) approach will be used to estimate ocean wave parameters in the Gulf of Mexico and Aleutian Basin. The accuracy and reliability of these approaches will be evaluated, and the spatial and temporal variability of the wave field will be investigated. The available wave characteristics are used to generate hourly, 12-hourly, and daily datasets. The WANN and SMB model shows good performance in the daily prediction of the significant wave height in both case studies. In the SMB model, specifically on a daily time scale, the Nash–Sutcliffe Efficiency (NSE) and the peak deviation coefficient (DCpeak) were determined to be 0.62 and 0.54 for the Aleutian buoy and 0.64 and 0.55 for the Gulf of Mexico buoy, respectively, for significant wave height. In the context of the WANN model and in the testing phase at the daily time scale, the NSE and DCpeak indices exhibit values of 0.85 and 0.61 for the Aleutian buoy and 0.72 and 0.61 for the Gulf of Mexico buoy, respectively, while the EANN model is a strong tool in hourly wave height prediction (Aleutian buoy (NSEEANN = 0.60 and DCpeakEANN = 0.88), Gulf of Mexico buoy (NSEEANN = 0.80 and DCpeakEANN = 0.82)). In addition, the findings pertaining to the energy spectrum density demonstrate that the EANN model exhibits superior performance in comparison to the WANN and SMB models, particularly with regard to accurately estimating the peak of the spectrum (Aleutian buoy (DCpeakEANN= 0.41), Gulf of Mexico buoy (DCpeakEANN = 0.59)).

Revisiting the cosmological phase transitions on the inflationary gravitational waves with BKP18

The effects of the electroweak and the quark-gluon plasma phase transitions are considered in the course of evolution of the universe and the resulting spectrum of primordial gravitational waves normalized with the BICEP/Keck and Planck joint data is obtained. The QGP index n=0.203 leads to a step reduction of ∼17.6% in the amplitude and a step of ∼35% in the energy density spectrum for frequency >1.36×10−8Hz. On the other hand, the EW index w=0.0147 leads to a step of ∼1.47% in the amplitude and a step of ∼2.9% in the energy density spectrum for frequency >10−5Hz. The combined effect of phase transitions on the inflationary gravitational waves leads to about ∼19% reduction in the amplitude and an overall reduction of ∼38% in the energy density as compared to the spectrum without considering these phase transitions. The resulting spectrum for R2 inflation model is found to be well within the BBN bound and its potential detectability is tested with the power-law integrated sensitivity curves of the future LISA, DECIGO, BBO, SKA and IPTA experiments.

Magnetic edge states and edge current in honeycomb zigzag nanoribbons by Kane–Mele–Hubbard model

We investigate spin-dependent edge states of honeycomb zigzag nanoribbons with a focus on electron–electron interaction as the origin of the initial edge magnetism which is assumed to be anti-ferromagnetism order as a stable form. We study the effect of intrinsic spin–orbit interaction (SOI) and also applied in-plane transverse electric field on low energy spectrum and edge spin density. Tight-binding method in the framework of the self-consistent Kane–Mele–Hubbard model has been utilized for exploring electronic properties. Edge currents and electric dipole moments are also calculated. Results show electric field and SOI can dramatically affect the edge states and energy gaps. A transition from a magnetic edge state to a non-magnetic one occurs at critical values of SOI and electric field. Furthermore, the system goes into the topological insulator phase at sufficiently large SOI strengths. The results of edge spin density, electric dipole moment, and spin currents indicate that one can reach the favorite spin-dependent transport by manipulating the electric field and SOI in a zigzag nanoribbon. The outcome may pave the way to further control of spin-based transport in future devices.

Probing dark matter axions using the hyperfine structure splitting of hydrogen atoms

QCD axions can be a substantial part of dark matter if their mass ma∼10−5 eV. Since the axions were created by the misalignment mechanism, their local energy spectrum density is large. Consequently, the axion-induced atomic transition rate is enhanced if the atomic energy gap matches the axion mass. The hyperfine splitting between the spin 0 singlet ground state and the spin 1 triplet state of hydrogen is 0.59×10−5 eV, which is close to the preferred mass of dark matter axions. With an energy gap adjustment by applying a weak Zeeman magnetic field, dark matter axions can induce atomic hydrogen transitions. Furthermore, because the total spins of the hydrogen triplet and singlet differ, the axion-induced transitions are detectable by a Stern–Gerlach apparatus or a sensitive magnetic field detector. A potential realization of the proposed scheme can be similar to existing hydrogen masers.