Homogeneous Background Research Articles

Inverse problems of the wave equation for media with mixed but separated heterogeneous parts

In this article, the inverse problems for the wave equation in a medium in which multiple types of cavities and inclusion exist in a mixture are considered. From the point of view of the indicator function of the enclosure method, there are two types of heterogeneous parts: “minus group” and “plus group.” For example, cavities with the Dirichlet boundary condition belong to the minus group, while inclusions with smaller propagation velocity belong to the plus group. The heterogeneous part of the minus group gives a negative sign to the indicator function, and the heterogeneous part of the plus group gives a positive sign. In general, the presence of many types of heterogeneous parts causes cancelation of the sign of the indicator function. Such cases are referred to as “mixed cases.” Here, we consider the case that the shortest length obtained from the indicator function is attained only by heterogeneous parts of the same group. This case is called the “mixed but separated case,” and it is shown that the method of elliptic estimates developed by Ikehata works well. We also show that the case of a two‐layered background medium with a flat layer can be considered in the same way as the case of a homogeneous background medium.

Time-lapse difference seismic inversion based on scattering theory

Time-lapse seismic monitoring technology is an effective tool for quantitatively estimating subsurface medium variations and plays a crucial role in resource and engineering explorations. Among existing time-lapse inversion methods, the difference inversion technique offers higher accuracy but requires linear inversion operators. During linearization, the background is often approximated as a homogeneous medium, resulting in the loss of effective information. Additionally, merely using reflection wave information is not conducive to improving inversion accuracy. However, the true structure of the subsurface is often complex and inhomogeneous, which can easily generate complex wavefields, such as scattering waves, thereby hindering the resolution of differences between time-lapse models. Therefore, incorporating more comprehensive wavefield information is essential for enhancing the accuracy of time-lapse seismic inversion. To address this issue, a wave-equation-based time-lapse difference inversion method is proposed to retrieve the production-induced property perturbation. In the proposed method, the forward operator is formulated through the scattering wave equation, the operator is linearized through the Born approximation, and the WKBJ method is used to approximate Green's function with high accuracy for the inhomogeneous background. In this study, time-lapse seismic parallel inversion and difference inversion are conducted using the proposed forward operator. Both numerical experiments and application of field seismic data indicate that the proposed time-lapse difference inversion method can realize a more accurate quantitative characterization of time-lapse variations.

Performance analysis of mean level CFAR detectors in homogeneous gamma-distributed radar clutter

ABSTRACT In this paper, a novel and exact mathematical formulation of three mean level constant false alarm rate (CFAR) detectors has been developed considering a homogeneous gamma-distributed (GM) clutter. These detectors include the cell averaging (CA), the greatest-of (GO), and the smallest-of (SO)-CFAR detection schemes. To do so, we derived closed-form expressions for the probability density function (pdf), and the cumulative distribution function (cdf) of the sum of an exponential fluctuating target submerged in gamma-distributed sea clutter. Then, we developed exact and explicit expressions for the probability of false alarm (P fa ) and probability of detection (P d ) of the optimal fixed threshold detector and the three considered CFAR detectors. The correctness of our expressions is then examined and validated via numerical simulations. Assuming a homogeneous GM background, the detection performance of these three detectors is carried out, discussed, and compared with that of the optimal detector. Experimental results with Sentinel-1 synthetic aperture radar (SAR) data demonstrate the effectiveness of the proposed closed-form expressions and show that the considered CFAR schemes are efficient for ship detection in sea clutter backgrounds.

Far field operator splitting and completion in inverse medium scattering

Abstract We study scattering of time-harmonic plane waves by compactly supported inhomogeneous objects in a homogeneous background medium. The far field operator associated to a fixed scatterer describes multi-static remote observations of scattered fields corresponding to arbitrary superpositions of plane wave incident fields at a single frequency. In this work we consider far field operators for systems of two well-separated scattering objects, and we discuss the nonlinear inverse problem to recover the far field operators associated to each of these two scatterers individually. This is closely related to the question whether the two components of the scatterer can be distinguished by means of inverse medium scattering in a stable way. We also study the restoration of missing or inaccurate components of an observed far field operator and comment on the benefits of far field operator splitting in this context. Both problems are ill-posed without further assumptions, but we give sufficient conditions on the diameter of the supports of the scatterers, the distance between them, and the size of the missing or corrupted data component to guarantee stable recovery whenever sufficient a priori information on the location of the unknown scatterers is available. We provide algorithms, error estimates, a stability analysis, and we demonstrate our theoretical predictions by numerical examples.

Integrated Magnetic and Geochemical Assessment of the Soil from the Steam Power Plant Area of South Kalimantan Province

Abstract The magnetic proxy approach has proven to be efficient in the assessment of pollution by potentially toxic elements when targeting soils or areas with a homogeneous background where anthropogenic magnetic signals can be easily distinguished. It’s crucial to conduct research on the impact of fly ash on the vicinity of the PLTU in this particular area, as it’s a previously unexplored area. The unique thing about this research is that this PLTU uses coal containing Fe, Pb, and Mg as fuel and has a fairly high susceptibility value for fly ash and bottom ash. This study is due to an analysis of the magnetic susceptibility and heavy metal content in the soil of the area around the Asam-Asam steam power plant (PLTU) of South Kalimantan Province, where geogenic input and fly ash can influence it. Heavy metals that have passed the threshold at all locations are Ti, Cr, Mn, Fe, Ni, Cu, V, and Al. Most of the correlation coefficients are strong and significant between magnetic susceptibility values and heavy metal concentrations at each location. The correspondence between magnetic susceptibility values and heavy metal content reflects the potential of magnetic proxy methods at polluted spots, provided that the lithological conditions are carefully considered.

Numerical analysis of resonant axion-photon mixing

Many present-day axion searches attempt to probe the mixing of axions and photons, which occurs in the presence of an external magnetic field. While this process is well understood in a number of simple and idealized contexts, a strongly varying or highly inhomogeneous background can impact the efficiency and evolution of the mixing in a nontrivial manner. In an effort to develop a generalized framework for analyzing axion-photon mixing in arbitrary systems, we focus in this work on directly solving the axion-modified form of Maxwell’s equations across a simulation domain with a spatially varying background. We concentrate specifically on understanding resonantly enhanced axion-photon mixing in a highly magnetized plasma, which is a key ingredient for developing precision predictions of radio signals emanating from the magnetospheres of neutron stars. After illustrating the success and accuracy of our approach for simplified limiting cases, we compare our results with a number of analytic solutions recently derived to describe mixing in these systems. We find that our numerical method demonstrates a high level of agreement with one, but only one, of the published results. Interestingly, our method also recovers the mixing between the axion and magnetosonic-t and Alfvén modes; these modes cannot escape from the regions of dense plasma but could nontrivially alter the dynamics in certain environments. Future work will focus on extending our calculations to study resonant mixing in strongly variable backgrounds, mixing in generalized media (beyond the strong magnetic field limit), and the mixing of photons with other light bosonic fields, such as dark photons. Published by the American Physical Society 2024

COULOMB DRAG RESISTIVITY IN DOUBLE-LAYER GRAPHENE: INHOMOGENEITY EFFECTS

We investigate Coulomb drag resistivity in a double-layer system consisting of two parallel monolayer graphene sheets. In calculations, we employ the random-phase approximation to determine the polarizability functions of the graphene layers and the frequency-dependent dielectric function of the structure, taking into account inhomogeneity effects of the background dielectric. Our numerical calculations reveal that Coulomb drag resistivity in double-layer graphene systems steadily increases with increasing temperature but quickly decreases as the interlayer separation increases. The drag resistivity between the two layers in the case of an inhomogeneous background dielectric is substantially larger than that in the case of a homogeneous one. In addition, both the value and the imbalance in carrier density in the layers lead to noticeable changes in Coulomb drag resistivity in the system. Our study results are useful in graphene-based structure applications.

Optimization of reconstruction in quantitative brain PET images: Benefits from PSF modeling and correction of edge artifacts.

Modern PET reconstruction algorithms incorporate point-spread-function (PSF) correction to mitigate partial volume effect. However, PSF correction can introduce edge artifacts that lead to quantification errors. Consequently, current international guidelines advise against using PSF correction in brain PET reconstruction. We aimed to investigate PSF-induced quantification errors in recent digital PET systems and identify conditions that mitigate them. This study utilized brain PET imaging with alginate-based realistic phantoms, simulating lesion-to-background activity ratios of 10:1 and 2:1, with eleven reconstruction parameter sets. Phantoms were prepared using a commercial anthropomorphic head phantom and two homemade inserts. Each insert contained a homogeneous 18F-FDG alginate background with hot spheres of varying diameter (3, 4, 6, 8, 10, 12, and 15mm). PET imaging was conducted on a digital PET-CT system Biograph Vision 600 (Siemens), with a 10 min scan duration. Imaging was performed with and without PSF correction, with 2, 4, 6, 12, 18, or 24 iterations in reconstruction, and with or without additional Gaussian postfiltering. We assessed the recovery coefficient (RC), contrast recovery coefficient (CRC), variability, and CRC-to-variability ratios for each sphere size and reconstruction parameter set. PSF-corrected images of the 10:1 spheres exhibited a nonmonotonic CRC-to-sphere diameter relationship due to edge artifacts overshoot in the 10mm-diameter sphere. In contrast, PSF images of the 2:1 spheres showed a monotonically increasing relationship. Non-PSF images of both phantoms showed an expected monotonically increasing CRC-to-sphere diameter relationship but with lower CRC values compared to PSF images. The nonmonotonic relationship observed with 10:1 spheres was mitigated by applying a 3-mm FWHM Gaussian postfiltering. For both phantoms, reconstructions with 6 iterations, PSF correction, and additional 3-mm FWHM Gaussian postfiltering demonstrated the highest CRC-to-variability ratios. Our findings indicate that Gaussian postfiltering suppresses PSF artifacts. This parameter set corrected the nonmonotonic CRC-to-sphere diameter relationship and improved the CRC-to-variability ratio compared to non-PSF reconstructions. Therefore, to enhance lesion detectability without compromising quantification accuracy, PSF correction coupled with Gaussian postfiltering should be used in brain PET.

On the absence of the chiral magnetic effect in equilibrium QCD

In this paper we investigate the chiral magnetic effect (CME): the generation of an electric current due to a homogeneous background magnetic field and a homogeneous chiral imbalance in QCD. We demonstrate that the leading coefficient describing the CME vanishes in equilibrium, both for free fermions as well as in full QCD. Our full QCD results are based on continuum extrapolated lattice simulations using dynamical staggered quarks with physical masses as well as quenched Wilson quarks. We show that it is crucial that a gauge invariant ultraviolet regularization is used to compute the CME and elaborate on why some of the existing in-equilibrium calculations of this effect gave a nonzero result. We stress that our findings imply the absence of a time-independent CME current flowing in equilibrium QCD, but do not concern the CME as an out-of-equilibrium, time-dependent effect.

Proton acceleration in plasma turbulence driven by high-energy lepton jets

Abstract The interaction of high energy lepton jets composed of electrons and positrons with background electron-proton plasma is investigated numerically based upon particle-in-cell simulation, focusing on the acceleration processes of background protons due to the development of electromagnetic turbulence. Such interaction may be found in the universe when energetic lepton jets propagate in the interstellar media. When such a jet is injected into the background plasma, the Weibel instability is excited quickly, which leads to the development of plasma turbulence into the nonlinear stage. The turbulent electric and magnetic fields accelerate plasma particles via the Fermi II type acceleration, where the maximum energy both for electrons and protons can be accelerated to much higher than that of the incident jet particles. Because of background plasma acceleration, a collisionless electrostatic shock wave is formed, where some pre-accelerated protons are further accelerated when passing through the shock wave front. Dependence of proton acceleration on the beamplasma density ratio and beam energy is investigated. For a given background plasma density, the maximum proton energy generally increases both with the density and kinetic energy of the injected jet. Moreover, for a homogeneous background plasma, the proton acceleration both via turbulent fields and collisionless shocks is found to be significant. In the case of an inhomogeneous plasma, the proton acceleration in the plasma turbulence is dominant. Our studies illustrate a scenario where protons from background plasma can be accelerated successively by the turbulent fields and collisionless shocks.

Multiple states of two-dimensional turbulence above topography

The recent work of Siegelman & Young (Proc. Natl Acad. Sci. USA, vol. 120, issue 44, 2023, e2308018120) revealed two extreme states reached by the evolution of unforced and weakly damped two-dimensional turbulence above random rough topography, separated by a critical kinetic energy $E_\#$ . The low- and high-energy solutions correspond to topographically locked and roaming vortices, surrounded by non-uniform and homogeneous background potential vorticity (PV), respectively. However, we found that these phenomena are restricted to the particular intermediate length scale where the energy was initially injected into the system. Through simulations initialized by injecting the energy at larger and smaller length scales, we found that the long-term state of topographic turbulence is also dependent on the initial length scale and thus the initial enstrophy. If the initial length scale is comparable to the domain size, the long-term flow field resembles the minimum-enstrophy state proposed by Bretherton & Haidvogel (J. Fluid Mech., vol. 78, issue 1, 1976, pp. 129–154), with very few topographically locked vortices; the long-term enstrophy is quite close to the minimum value, especially when the energy is no larger than $E_\#$ . As the initial length scale becomes smaller, more vortices nucleate and become more mobile; the long-term enstrophy increasingly deviates from the minimum value. Simultaneously, the background PV tends to homogenization, even if the energy is below $E_\#$ . These results complement the phenomenology of topographic turbulence documented by Siegelman & Young, by showing that the minimum-enstrophy and background PV homogenization states can be adequately approached by large- and small-scale initial fields, respectively, with relatively arbitrary energy.

Total Magnetic Field Perturbations at Martian Low Altitudes (≤500 km): MAVEN Observations in 2014–2023

AbstractMagnetic perturbations in the Martian ionosphere are often considered as representing plasma irregularities, but thorough statistical comparisons between the two independent phenomena have been rarely conducted. In this study, we investigate the statistical relationship between total magnetic field perturbations and those of O2+ density as observed by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft at altitudes below 500 km in 2014–2023. From the 1 Hz time series of magnetic field strength, perturbation intensity is estimated by subtracting a signal smoothed with a Savitzky‐Golay filter (window size ∼36 km). Statistically, the magnetic perturbations are stronger on the dayside than at night, in the local summer hemisphere than in winter, and away from crustal magnetic anomalies than nearby. Also, day‐to‐day variability of the magnetic perturbations exhibits a weak but significant correlation with that of solar wind electron density. The statistical behavior of total magnetic field perturbations is not the same as that of O2+ density perturbations: that is, the former is not a perfect proxy for the latter. The seemingly counter‐intuitive discrepancy can be explained by effects of inhomogeneous background magnetic field strength (participating in total pressure balance across plasma perturbations) and localized ionospheric currents at altitudes unreachable by MAVEN.

Temperature and inhomogeneous background affect plasmons in four-layer graphene structures

We employ the random-phase approximation to investigate the effects of temperature and the inhomogeneity of background dielectric on the collective excitations and respective broadening functions in 4-MLG structures. Computations present that the systems have four plasmon modes, corresponding to one in-phase and three out-of-phase oscillations of charged particles. We obtain that plasmon frequency and respective broadening functions behave as increasing functions of temperature with sufficiently large wave vectors. Dissimilarly, in small wave vector regions, the increase in temperature slightly decreases plasmon energy, but further increases in temperature increase this parameter. In addition, as the separation increases, both plasmon frequency and broadening functions significantly reduce, and the inhomogeneity of the dielectric background strongly decreases plasmon energy and its loss. We observe that both temperature and the environment's inhomogeneity should be considered in calculations.

Scalar perturbations from inflation in the presence of gauge fields

We study how Abelian-gauge-field production during inflation affects scalar perturbations in the case when the gauge field interacts with the inflaton directly (by means of generic kinetic and axial couplings) and via gravity. The homogeneous background solution is defined by self-consistently taking into account the backreaction of the gauge field on the evolution of the inflaton and the scale factor. For the perturbations on top of this background, all possible scalar contributions coming from the inflaton, the metric, and the gauge field are considered. We derive a second-order differential equation for the curvature perturbation, ζ, capturing the impact of the gauge field, both on the background dynamics and on the evolution of scalar perturbations. The latter is described by a source term in the ζ equation, which is quadratic in the gauge-field operators and leads to non-Gaussianities in the curvature perturbations. We derive general expressions for the induced scalar power spectrum and bispectrum. Finally, we apply our formalism to the well-known case of axion inflation without backreaction. Numerical results show that, in this example, the effect of including metric perturbations is small for values of the gauge-field production parameter ξ>3. This is in agreement with the previous results in the literature. However, in the region of smaller values, ξ≲2, our new results exhibit order-of-unity deviations when compared to previous results. Published by the American Physical Society 2024

Persymmetric direction detector for range‐spread target in subspace interference plus homogeneous and partially homogeneous clutter

AbstractThe problem of detecting the direction of range‐spread targets in the presence of subspace interference, along with homogeneous and partially homogeneous Gaussian clutter backgrounds characterised by an unknown persymmetric covariance matrix, is being investigated. It is assumed that the interference subspace is linearly independent of the signal subspace, and the coordinates of both subspaces are unknown. Leveraging the property of persymmetry, the two‐step Generalised Likelihood Ratio Test and the two‐step Wald test are proposed to formulate three detectors in the presence of subspace interference, homogeneous, and partially homogeneous Gaussian clutter. Theoretical derivations and simulations demonstrate that three proposed detectors maintain a constant false alarm rate with respect to the unknown clutter covariance matrix. In comparison to existing detectors in similar backgrounds, particularly in scenarios with limited training data, these three detectors exhibit superior detection performance.

Time-dependent scalings and Fock quantization of a massless scalar field in Kantowski–Sachs

Abstract We address the issue of inequivalent Fock representations in quantum field theory in a curved homogenous and anisotropic cosmological background, namely Kantowski–Sachs spacetime, which can also be used to describe the interior of a nonrotating black hole. A family of unitarily equivalent Fock representations that are invariant under the spatial isometries and implement a unitary dynamics can be achieved by means of a field redefinition that consists of a specific anisotropic scaling of the field configuration and a linear transformation of its momentum. Remarkably, we show that this kind of field redefinition is in fact unique under our symmetry and unitary requirements. However, the physical properties of the Hamiltonian dynamics that one obtains in this way are not satisfactory, inasmuch as the action of the Hamiltonian on the corresponding particle states is ill defined. To construct a quantum theory without this problem, we need a further canonical transformation that is time- and mode-dependent and is not interpretable as an anisotropic scaling. The old and new Fock representations, nevertheless, are unitarily equivalent. The freedom that is introduced when allowing for this further canonical transformation can be fixed by demanding an asymptotic diagonalization of the Hamiltonian and a minimal absorption of dynamical phases. In this way, the choice of vacuum and the associated Fock representation are asymptotically determined.

Perceptual Benefits of Linguistic Diversity and Language Background: Evidence from Auditory Free Classification of English Dialect Accents and Asian-Accented English

Non-linguistic factors leave a distinct thumbprint on our speech production that is perceptible to listeners. A steadily growing line of research demonstrates that listeners can perceive a contrast between native and non-native (L2) speakers based on accents and further classify these speakers according to dialectal variation, even when they are not native speakers of a language. Most of these studies have focused on dialectal variation within US English speakers, a combination of US and International English dialects, or L2 speakers representing a wide range of languages. Most have also featured listeners who are monolingual native speakers of the target language coming from a homogenous background, or a contrast between these and a targeted set of L2 speakers. We therefore lack knowledge of how exposure to, or familiarity with, diverse accents and languages, or specific native language competence of the native language of L2 speakers, can guide listeners’ accent perception and categorization. In this research, we employed a free classification task, presenting listeners with speech samples of native speakers with accents representing multiple English dialects, and L2 speakers of nine Asian languages across three geographic regions speaking Asian-accented English. There were six groups of listeners: monolingual US English listeners in a diverse linguistic context, monolingual US English listeners in a homogeneous linguistic context, native speakers of a non-Asian language and English (bilinguals), and native speakers of each of the three target Asian language groups who are L2 speakers of English. The results reveal that nearly all listeners are sensitive to accents capturing native/L2 contrasts and dialectal variation in English. While regular exposure to a diversity of accents results in increased classification accuracy, classification of Asian L2-accented English speakers is best performed when there is alignment of similar language family and geographic area, as demonstrated by South Asian listeners.

Nanoparticle Diffusion in Crowded Polymer Nanocomposite Melts.

This study examines nanoparticle diffusion in crowded polymer nanocomposites by diffusing small Al2O3 nanoparticles (NPs) in SiO2-loaded P2VP matrices. Time-of-flight secondary ion mass spectroscopy (ToF-SIMS) measures Al2O3 NP diffusion coefficients within a homogeneous PNC background of larger, immobile SiO2 NPs. By developing a geometric model for the average interparticle distance in a system with two NP sizes, we quantify nanocomposite confinement relative to the Al2O3 NP size with a bound layer. At low SiO2 concentrations, Al2O3 NP diffusion aligns with the neat polymer results. In more crowded nanocomposites with higher SiO2 concentrations where the interparticle distance approaches the size of the mobile Al2O3 NP, the 6.5 nm Al2O3 NPs diffuse faster than predicted by both core-shell and vehicular diffusion models. Relative to our previous studies of NPs diffusing into polymers, these findings demonstrate that the local environment in crowded systems significantly complicates NP diffusion behavior and the bound layer lifetimes.

Significance of a quadratically varying deceleration parameter in scalar field-dominated model and cosmic acceleration

In this study, we explore the enigma of late-time cosmic acceleration in the framework of a general scalar field playing the role of dark energy. Our investigation yields an exact solution to Einstein’s field equations, achieved through a parametrization of the deceleration parameter [Formula: see text] in quadratic form in the homogeneous and isotropic background geometry represented by Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. This parametrization unveils a seamless transition from a decelerated to an accelerated phase in the cosmic evolution. Furthermore, we leverage this parametrization to reconstruct cosmological parameters with respect to redshift z, elucidating their dependency on certain model parameters that govern the universe’s evolutionary trajectory. The model parameters are subsequently constrained using diverse observational datasets. We provide a comprehensive analysis of the evolution of geometrical and physical parameters, complete with the numerically constrained values. To gain deeper insights into the nature of dark energy, we employ Statefinder diagnostics, conducting a thorough examination. Our findings shed light on the intricate interplay between cosmic acceleration, quintessential dark energy and the parametrization of deceleration parameter, offering valuable insights into the fundamental dynamics of the universe.

Epigenetic regulation by TET1 in gene-environmental interactions influencing susceptibility to congenital malformations.

The etiology of neural tube defects (NTDs) involves complex gene-environmental interactions. Folic acid (FA) prevents NTDs, but the mechanisms remain poorly understood and at least 30% of human NTDs resist the beneficial effects of FA supplementation. Here, we identify the DNA demethylase TET1 as a nexus of folate-dependent one-carbon metabolism and genetic risk factors post-neural tube closure. We determine that cranial NTDs in Tet1 -/- embryos occur at two to three times higher penetrance in genetically heterogeneous than in homogeneous genetic backgrounds, suggesting a strong impact of genetic modifiers on phenotypic expression. Quantitative trait locus mapping identified a strong NTD risk locus in the 129S6 strain, which harbors missense and modifier variants at genes implicated in intracellular endocytic trafficking and developmental signaling. NTDs across Tet1 -/- strains are resistant to FA supplementation. However, both excess and depleted maternal FA diets modify the impact of Tet1 loss on offspring DNA methylation primarily at neurodevelopmental loci. FA deficiency reveals susceptibility to NTD and other structural brain defects due to haploinsufficiency of Tet1. In contrast, excess FA in Tet1 -/- embryos drives promoter DNA hypermethylation and reduced expression of multiple membrane solute transporters, including a FA transporter, accompanied by loss of phospholipid metabolites. Overall, our study unravels interactions between modified maternal FA status, Tet1 gene dosage and genetic backgrounds that impact neurotransmitter functions, cellular methylation and individual susceptibilities to congenital malformations, further implicating that epigenetic dysregulation may underlie NTDs resistant to FA supplementation.