Homogeneous Medium Research Articles

Estimation of the Soil Water Content Using the Early Time Signal of Ground-Penetrating Radar in Heterogeneous Soil

Ground-penetrating radar (GPR) is an important tool for measuring soil water content (SWC) at the field scale. The amplitude analysis of the early time signal (ETS) of GPR may provide a rapid way to estimate SWC. By assuming a homogeneous medium, various studies have been conducted on the relationship between the amplitude of ETS and the topsoil layer’s electromagnetic parameters (dielectric permittivity and conductivity) through numerical simulations, laboratory experiments, and field experiments. Soil is a typical inhomogeneous medium, and soil cultivation is a factor affecting its heterogeneity. In this context, we discuss the ability of the amplitude of ETS to estimate the water content of heterogeneous soil. First, we establish a multi-scale stochastic medium model with the inhomogeneous distribution of dielectric permittivity and conductivity and simulate the GPR response by the finite-difference time-domain (FDTD) method to observe the influence of medium heterogeneity on the GPR response. The heterogeneity of the soil models is evaluated by a geostatistical analysis described by two parameters, correlation length and variability. Then, we analyze the relationship between variability and the average envelope amplitude (AEA) of ETS. A strong soil heterogeneity increases the error of the AEA method in estimating SWC. Finally, the AEA method is used to estimate the SWC of two adjacent fields with different heterogeneities, which were caused by different cultivation methods. The results of the numerical simulation and field experiment indicate that the soil heterogeneity can have an impact on the estimation of SWC using EST, with an error lower than 3% within a depth range of 1/2 λ to λ (wavelength). This suggests that the EST of GPR can be applied to soil layers with relatively large lateral changes in water content.

Cellulose acylation in homogeneous and heterogeneous media: Optimization of reactions conditions

The dependence of the DS on the acid anhydride/anhydroglucose unit ((RCO)2O/AGU) molar ratio was correlated using second-order polynomials. The regression coefficients of the (RCO)2O/AGU terms showed that increasing the length of the RCO group of the anhydride led to lower values of DS. For acylation under heterogeneous reaction conditions, the following were employed: acid anhydrides and butyryl chloride as acylating agents; iodine as a catalyst; N,N-dimethylformamide (DMF) as a solvent, pyridine, and triethylamine as solvents and catalysts. For acylation using acetic anhydride plus iodine, the values of DS correlate with reaction time by a second-order polynomial. Due to its role as a polar solvent and a nucleophilic catalyst, pyridine was the most effective base catalyst, independent of the acylating agent (butyric anhydride and butyryl chloride).

Strain-based forward modeling and inversion of seismic moment tensors using distributed acoustic sensing (DAS) observations

This study used a waveform inversion of distributed acoustic sensing (DAS) data, acquired in two horizontal monitoring wells, to estimate the moment tensor (MT) of two induced microearthquakes. An analytical forward model was developed to simulate far-field tangential strain generated by an MT source in a homogeneous and anisotropic medium, averaged over the gauge length along a fiber of arbitrary orientation. To prepare the data for inversion, secondary scattered waves were removed from the field observations, using f-k filtering and time-windowing. The modeled and observed primary arrivals were aligned using a cut-and-paste approach. The MT parameters were inverted via a least-squares approach, and their uncertainties were determined through bootstrap analysis. Using simulated data with additive noise derived from the field data and the same fiber configuration as the monitoring wells, the inversion method adequately resolved the MT. Despite the assumption of Gaussian noise, which underlies the least-squares inversion approach, the method was robust in the presence of heavy-tailed noise observed in field data. When the inversion was applied to field data, independent inversion results using P-waves, S-waves, and both waves together yielded results that were consistent between the two events and for different wave types. The agreement of the inversion results for two events resulting from the same stress field illustrated the reliability of the method. The uncertainties of the MT parameters were small enough to make the inversion method useful for geophysical interpretation. The variance reduction obtained from the data predicted for the most probable MT was satisfying, even though the polarity of the P-waves was not always correctly reproduced.

Immiscible viscous fingering in time-dependent fluids: A linear stability analysis

When a less viscous fluid displaces a more viscous fluid, the interface between the two fluids becomes unstable. The instability exhibits itself as a large number of fingers of the displacing fluid penetrating the displaced fluid. This phenomenon is called viscous fingering or Saffman–Taylor instability, and plays a key role in oil industry, among others. The present study aims at investigating the immiscible viscous fingering of inelastic time-dependent fluids (i.e., fluids for which viscosity varies with time even at a fixed shear rate) in a homogeneous saturated porous medium. To represent such fluids, in the present work, use is made of the Quemada model. As an inelastic structural-kinetic rheological model, it can capture both thixotropy and anti-thixotropy through proper setting of model parameters. The model incorporates a natural time, which, in dimensionless form, is represented by a nominal Deborah number. Using this rheological model, the generalized Darcy’s law is derived, which is used to derive the basic flow. The interfacial instability is investigated by using the linear temporal stability analysis; that is, infinitesimally-small, normal-mode perturbations are introduced to the basic flow and their evolution in time is monitored. Using the Young–Laplace equation, the generalized dispersion relation is derived, which is solved numerically. The results show that the thixotropy and anti-thixotropy stabilize the Newtonian/time-dependent and time-dependent/Newtonian displacements, respectively. On the other hand, the Newtonian/time-dependent and time-dependent/Newtonian displacements are destabilized by the anti-thixotropy and thixotropy, respectively.

An Implementation Method of the Complex Frequency-Shifted Uniaxial/Multi-Axial PML Technique for Viscoelastic Seismic Wave Propagation

ABSTRACT A numerical implementation method of the complex frequency-shifted uniaxial/multi-axial PML (CFS UPML/MPML) is developed for modeling half-space viscoelastic wave propagation. A mixed CFS PML combining CFS UPML and CFS MPML is designed to improve PML’s performances in avoiding evanescent waves at grazing incidence and stabilizing long-time simulation of low-frequency viscoelastic wave propagation. Two numerical examples’ results showed that the developed method for the mixed CFS PML can implement elimination of evanescent waves at grazing incidence near the PML interface, long-time accurate simulation of low-frequency viscoelastic wave propagation and efficient absorption of the near-fault outgoing seismic waves in homogeneous earth medium.

Rapid radio brightening of GRB 210702A

ABSTRACT We observed the rapid radio brightening of GRB 210702A with the Australia Telescope Compact Array (ATCA) just 11 h post-burst, tracking early-time radio variability over a 5 h period on ∼15 min time-scales at 9.0, 16.7, and 21.2 GHz. A broken power law fit to the 9.0 GHz light curve showed that the 5 h flare peaked at a flux density of 0.4 ± 0.1 mJy at ∼13 h post-burst. The observed temporal and spectral evolution is not expected in the standard internal–external shock model, where forward and reverse shock radio emission evolves on much longer time-scales. The early-time (<1 d) optical and X-ray light curves from the Neil Gehrels Swift Observatory demonstrated typical afterglow forward shock behaviour, allowing us to use blast wave physics to determine a likely homogeneous circumburst medium and an emitting electron population power-law index of p = 2.9 ± 0.1. We suggest that the early-time radio flare is likely due to weak interstellar scintillation (ISS), which boosted the radio afterglow emission above the ATCA sensitivity limit on minute time-scales. Using relations for ISS in the weak regime, we were able to place an upper limit on the size of the blast wave of ≲6 × 1016 cm in the plane of the sky, which is consistent with the theoretical forward shock size prediction of 8 × 1016 cm for GRB 210702A at ∼13 h post-burst. This represents the earliest ISS size constraint on a gamma-ray burst (GRB) blast wave to date, demonstrating the importance of rapid (<1 d) radio follow-up of GRBs using several-hour integrations to capture the early afterglow evolution and to track the scintillation over a broad frequency range.

On the (Non-)Scalability of Target Media for Evaluating the Performance of Ancient Projectile Weapons

Abstract When they work, controlled experiments can efficiently and clearly reveal essential characteristics of the functions and performance of ancient hunting and fighting weapons. However, homogenous target media must be carefully validated to ensure that controlled tests capture the same variables that made weapons effective in their original application. Although homogenous flesh simulants have proven effective for studying firearms, the same simulants cannot be assumed to be effective when testing low-velocity cutting/piercing projectiles, which have significantly different performance characteristics than bullets. We build on past research showing that two flesh simulants that are commonly used by archaeologists, ballistics gelatin and pottery clay, fail to capture how atlatl darts and arrows perform when penetrating biological tissues. In accord with forensic research of knife-thrust attacks, natural and polymeric skin simulants may prove effective in future experiments, but this requires further research.

Dynamical friction of a massive black hole in a turbulent gaseous medium

The orbital decay of massive black holes in galaxies in the aftermath of mergers is at the heart of whether massive black holes successfully pair and merge, leading to emission of low-frequency gravitational waves. The role of dynamical friction sourced from the gas distribution has been uncertain because many analytical and numerical studies have either focussed on a homogeneous medium or have not reached resolutions below the scales relevant to the problem, namely the Bondi-Hoyle-Lyttleton radius. We performed numerical simulations of a massive black hole moving in a turbulent medium in order to study dynamical friction from turbulent gas. We find that the black hole slows down to the sound speed, rather than the turbulent speed, and that the orbital decay is well captured if the Bondi-Hoyle-Lyttleton radius is resolved with at least five resolution elements. We find that the larger the turbulent eddies, the larger the scatter in dynamical friction magnitude, because of the stochastic nature of the problem, and also because of the larger over- and under-densities encountered by the black hole along its trajectory. Compared to the classic solution in a homogeneous medium, the magnitude of the force depends more weakly on the Mach number, and dynamical friction is overall more efficient for high Mach numbers, but less efficient towards and at the transonic regime.

The impact of flow induced by rotating magnetic fields on processes in a molten conductive medium

This paper studies a method of stirring liquid metal by the action of rotating magnetic fields using two ring inductors placed next to each other. These inductors generate magnetic fields rotating in opposite directions. The aim of this study is numerical investigation of the generated fluid flow and its impact on the homogenization of a two-phase medium, as well as on the crystallization process. The impact of these electromagnetic forces proves to cause the generation of intense poloidal flow component. The arising flow is accompanied by oscillatory motion of vortex structures and their interaction resulting in effective mixing of the liquid metal. The moderate values of the force parameter have been found to lead to the most homogeneous medium under stirring. Under non-stationary action, the force parameter modulations in a certain frequency range have practically no effect on the homogeneity occurrence time and the homogeneity value. The positive effect of stirring by magnetic fields of complex topology on the rate and homogeneity of metal solidification is stated. The obtained results are relevant for improving the quality of foundry ingots.

Investigation of reflections of terahertz waves from an inhomogeneous planar layer of a chiral metamaterial with allowance for frequency dispersion

The main purpose of this work is to develop a method for calculating the reflections of linearly polarized waves from an inhomogeneous planar layer of a chiral metamaterial. A mathematical model of a homogeneous inhomogeneous chiral medium is considered taking into account the frequency dispersion of material parameters. The moduli of the reflection coefficients of the main and cross-polarized field components from an inhomogeneous layer with parabolic and linear profiles of changes in the resonant frequency of a chiral metamaterial are calculated. It is shown that inhomogeneous planar structures of chiral metamaterials can significantly reduce the level of reflection of cross-polarized waves in the optical and terahertz ranges.

Microwave-accelerated Eco-friendly Performance of the Knoevenagel Condensation Reaction with Various Active Methylene Derivat-ives evaluation of Electrochemical Properties

Background: The present work describes sustainable Knoevenagel condensation reac-tion of aryl/ heterocyclic aldehyde with various active methylene derivatives such as malono-nitrile, dimedone, ethyl cyanoacetate, ethyl acetoacetate, barbituric acid, and thiobarbituric acid is reported. The protocol was developed using water extract of mango peel ash (WEMPA), an agro-waste that emerged as a greener solvent media and in combination with microwave irradiation gave high-yield product isolation. The method noticed added advantages for the reaction faster reaction rate, inexpensive extract media, simple work-up, and not required chromatographic puri-fication. The present method synthesized various Knoevenagel condensation derivatives benzyli-dinemalononitrile, ethyl benzylidenecyanoacetate, ethyl benzylideneacetoacetate, benzalbarbituric acid, benzylidene-2-thiobarbituric acid, and 5,5-dimethylcyclohexane-1,3-diones were character-ized by FT-IR, 1H- & 13C-NMR, and mass spectrometry. Further, selected derivatives were inves-tigated for their electrochemical studies using cyclic voltammetry, and showed comparable oxida-tion and reduction potential properties. Objective: The objective of this work is to develop a green methodology synthesis of various active methylene derivatives via Knoevenagel condensation to give the product of benzylidine-malononitrile, ethyl benzylidenecyanoacetate, ethyl benzylideneacetoacetate, benzalbarbituric acid, benzylidene-2-thiobarbituric acid and 5,5-dimethylcyclohexane-1,3-diones. Methods: We have demonstrated WEMPA as a greener homogenous agro-waste catalytic medi-um for the economic synthesis of Knoevenagel condensation products. The developed method was found robust, non-toxic and solvent-free with a simple work-up to give the target product. The selected derivatives were investigated for their electrochemical studies using the cyclic volt-ammetry method. Results: The agro-waste-based catalyst developed avoids the use of the external organic or inor-ganic base for the Knoevenagel condensation reaction under microwave irradiation. The de-scribed method found faster, eco-friendly, simple filtration and recrystallization excellent yield, and purity of the Knoevenagel product. Further, the selected compounds (8a-8d, 9a- 9d, 10a-10d, 11a,-11c, 12a, 12b, and 13a-13c) were subjected to electrochemical behavior studies and showed good oxidation and reduction properties. Conclusion: In summary, we have established an efficient, simple, inexpensive agro-waste based catalytic approach for the synthesis of benzylidinemalononitrile, ethyl benzylidenecyanoacetate, ethyl benzylideneacetoacetate, benzalbarbituric acid, benzylidene-2-thiobarbituric acid and 5,5-dimethylcyclohexane-1,3-diones derivatives under microwave irradiation described. The catalyst is agro-waste derived, which is abundant in nature and recyclable without loss of activity after the four-run of the reaction, thus making the present approach a greener one. The advantages of the approach are inexpensive, chemical base free, requiring no external metal catalyst, short reaction time, and simple work-up isolated excellent yields of the product. For the first time, herein, we reported the electrochemical behavior of the products prepared, and showed good oxidation and reduction properties, and these molecules will emerge as good antioxidant agents. other: NA

Predictive modeling of oil and water saturation during secondary recovery with supervised learning

In the petroleum reservoir, the secondary oil recovery (SOR) process is employed by injecting water into wells to enhance the moment of oil toward the production wells. The SOR process gives rise to the instability (fingering) phenomena due to the injecting force and the difference in the wettability and viscosity of the oil and water at the common interface. Since the late 1800s, mathematical models of petroleum reservoirs have been extensively used in the oil and gas industry. In this paper, we investigated the saturation of two immiscible fluid (oil and water) flows through homogeneous porous media during the SOR process by solving the modeled partial differential equation using the supervised machine learning algorithm based on feedforward back-propagated neural networks (FFBNNs) and Levenberg–Marquardt (LM) optimization algorithm. The designed scientific computing technique (FFBNN-LMA) is further employed to study the detailed sensitivity analysis of the approximate solutions. Performance measures like average absolute deviations, Theils' inequality measure, regression, and Nash–Sutcliffe model efficiency coefficient.

Contaminated water flow modelling through the porous media by using fractional advection-dispersion equation (FADE)

ABSTRACT This study aims to evaluate the validity of Fractional Advection-Dispersion equation (FADE) in breakthrough curves in saturated homogenous soil media, i.e. clay, and to examine the three primary restraints, pore water velocity, dispersion coefficient, and order of fractional differentiation which are impacting solute transport behavior (Fickian or Non-Fickian). In this study, the FADE framework used to characterize the transport process at depth 50 cm soil (clay). FADE Main based on FORTRAN, to estimate the parameters of FADE including fractional differentiation (λ), the dispersive coefficient (D), and the average pore-water velocity (v). If the value of is equal to or greater than 2, the transport is said to be Fickian otherwise is non-Fickian. In this study, the fractional differentiation of non-Fickian behavior was found 1.85 which is less than 2. On the other hand, early long-time tailing to the soil media showed an increase in the dispersion coefficient (D) for FADE and higher values in differentiation coefficient (λ = 1.85–1.99). The results of breakthrough curves (BTCs) of relative concentration (C/C0) show that it is best fitted by using FADE. For the assessment of fitting, Root Mean Square Error (RMSE) and determination Coefficient was used to find the quality of fit. .

Crack growth in homogeneous media using an adaptive isogeometric fourth-order phase-field model

By using the threshold on the phase-field variable as an error indicator, an adaptive fourth-order phase-field method in the framework of isogeometric analysis is proposed for fracture simulation. The spatial and geometric discretization is based on locally refined non-uniform rational B-splines (LR NURBS), which have the ability for local refinement. The C1 continuous LR NURBS basis function is employed as the fourth-order phase field which requires higher-order derivatives. A hybrid formulation is adopted, and the coupled elasticity and phase-field equations are solved using a staggered method. The simulation starts with a coarse discretization and the spatial discretization is adaptively refined on the fly. The robustness and the reliability of the adaptive fourth-order phase-field model based on isogeometric analysis are demonstrated with a few standard benchmark problems. From the numerical study, it is inferred that the proposed framework yields accurate results without compromising accuracy. Further, the fourth-order phase-field model gives a narrow diffusive region, which reduces the region to be refined that improves the computational efficiency.

Thermal-optical mechanical waves of the microelongated semiconductor medium with fractional order heat time derivatives in a rotational field

Outlined here is an innovative method for characterizing a layer of microelongated semiconductor material under excitation. Fractional time derivatives of a heat equation with a rotational field are used to probe the model during photo-excitation processes. Micropolar-thermoelasticity theory, which the model implements, introduces the microelongation scalar function to characterize the processes occurring inside the microelements. When the microelongation parameters are considered following the photo-thermoelasticity theory, the model investigates the interaction scenario between optical-thermo-mechanical waves under the impact of rotation parameters. During electronic and thermoelastic deformation, the key governing equations have been reduced to dimensionless form. Laplace and Fourier's transformations are used to solve this mathematical problem. Isotropic, homogeneous, and linear microelongated semiconductor medium's general solutions to their respective fundamental fields are derived in two dimensions (2D). To get complete solutions, several measurements must be taken at the free surface of the medium. As an example of numerical modeling of the important fields, we will use the silicon (Si) material’s physicomechanical characteristics. Several comparisons were made using different values of relaxation time and rotation parameters, and the results were graphically shown.

Photothermal effects of semiconducting medium with non-local theory

A generalized magnetothermoelastic half-space problem is considered for a homogeneous, isotropic and semiconducting medium under the non-local heat equation with dual-phase-lag model. The boundary surface of the medium is subjected to a prescribed time-dependent and exponential order compression along with a prescribed temperature and carrier intensity gradient. Two integral transformations, Laplace transform for time variable and Fourier transform for space variable, are employed to the equations of motion and the heat conduction equation for formulation of a vector-matrix differential equation which is then solved by using eigenvalue approach. Inversion processes for the two integral transforms are carried out numerically. Finally, the effects of physical field variables and stress components are analyzed and illustrated graphically under the variation of different physical parameters.

Pore-scale Ostwald ripening of gas bubbles in the presence of oil and water in porous media

HypothesisOstwald ripening of gas bubbles is a spontaneous mass transfer process that can impact the storage volume of trapped gas in the subsurface. In homogeneous porous media with identical pores, bubbles evolve toward an equilibrium state of equal pressure and volume. How the presence of two liquids impacts ripening of a bubble population is less known. We hypothesize that the equilibrium bubble sizes depend on the surrounding liquid configuration and oil/water capillary pressure. Method and numerical experimentsWe investigate ripening of nitrogen bubbles in homogeneous porous media containing decane and water using a level set method that alternately simulates capillary-controlled displacement and mass transfer between bubbles to eradicate chemical-potential differences. We explore impacts of initial fluid distribution and oil/water capillary pressure on the bubble evolution. FindingsRipening in three-phase scenarios in porous media stabilizes gas bubbles to sizes that depend on their surrounding liquids. Bubbles in oil decrease in size while bubbles in water increase in size with increasing oil/water capillary pressure. Bubbles in oil reach local equilibrium before the three-phase system stabilizes globally. A potential implication for field-scale gas storage is that the trapped gas fractions in oil and water vary with depth in the oil/water transition zone.

Modulation of cerebellar cortical, cerebellar nuclear and vestibular nuclear activity using alternating electric currents.

Cerebellar transcranial alternating current stimulation (ctACS) has shown promise as a therapeutic modality for treating a variety of neurological disorders, and for affecting normal learning processes. Yet, little is known about how electric fields induced by applied currents affect cerebellar activity in the mammalian cerebellum under in vivo conditions. Alternating current (AC) stimulation with frequencies from 0.5 to 20 Hz was applied to the surface of the cerebellum in anesthetized rats. Extracellular recordings were obtained from Purkinje cells (PC), cerebellar and vestibular nuclear neurons, and other cerebellar cortical neurons. AC stimulation modulated the activity of all classes of neurons. Cerebellar and vestibular nuclear neurons most often showed increased spike activity during the negative phase of the AC stimulation. Purkinje cell simple spike activity was also increased during the negative phase at most locations, except for the cortex directly below the stimulus electrode, where activity was most often increased during the positive phase of the AC cycle. Other cortical neurons showed a more mixed, generally weaker pattern of modulation. The patterns of Purkinje cell responses suggest that AC stimulation induces a complex electrical field with changes in amplitude and orientation between local regions that may reflect the folding of the cerebellar cortex. Direct measurements of the induced electric field show that it deviates significantly from the theoretically predicted radial field for an isotropic, homogeneous medium, in both its orientation and magnitude. These results have relevance for models of the electric field induced in the cerebellum by AC stimulation.

TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media

We propose to explore the time-reversed absorbing condition (TRAC) method in the case of dissipative homogeneous media. In previous work, the TRAC method was derived from the time-reversibility of the (undamped) wave equation and proved to be efficient in both the time-domain and the frequency-domain. Namely, two main utilisations of the TRAC method have been probed: (a) redatuming, i.e. moving virtually the measurements by reconstructing the wavefield and (b) tracking down the location of a possible inclusion inside the domain. In this paper, we focus on the redatuming application and investigate the feasibility of the TRAC method in the case of dissipation. In particular, we will see that performing the classical TRAC method, i.e. ignoring the dissipation, may give satisfactory results, even for larger values of dissipation. An analysis is provided in the frequency-domain and one-space dimension and shows satisfactory updated versions of the TRAC method. Moreover, a systematic error study in two-space dimension is illustrated via numerical examples.

Optical simulation and experimental investigation of the crystalline silicon/black silicon/perovskite tandem structures

The use of a black silicon (b-Si) interlayer is a promising solution for improving the optical properties of crystalline Si/perovskite solar cells. Optical numerical simulation of the crystalline Si/b-Si/perovskite structures can efficiently optimize their parameters at the initial tandem solar cell design stage. In this work, the optical properties of these structures were modeled using the transfer matrix method, where an array of cone-like nanoneedles of the b-Si interlayer is approximated as a homogeneous optical medium, for which the effective complex refractive index is the weighted average of those for Si and perovskite. Analytical equations are obtained for tandem structures' reflection, transmission, and absorption. The simulated reflectance spectra of the structures were compared with those of structures without the b-Si layer, as well as with experimental data. Numerical calculations and experiments confirm that nanotexturing significantly improves the optical properties of tandem structures. In addition, the nanotextured tandem structures have a wide-angle antireflective characteristic at incidence angles less than 60°, indicating their omnidirectional light-trapping capability. The proposed simulation model satisfactorily describes the optical behavior of crystalline Si/b-Si/perovskite tandem structures and can be used to estimate their optical properties depending on various parameters. As a demonstration, a numerical analysis was performed to study the effect of the b-Si interlayer thickness on the reflection of the tandem structure.