Arbitrary Depth Research Articles

Improving the method for assessment of bending stresses in the wall of an underground pipeline

Brief information about modern methods for determining the bending stresses of the extended sections of underground main pipelines without access to the pipeline generatrix is given. The necessity of modernizing methods based on determining the configuration of the pipeline axis from the soil surface with subsequent calculation of bending stresses based on the obtained data is substantiated. A mathematical model that allows to calculate the optimal parameters for surveying the axis of the pipeline from the soil surface for a pipeline of arbitrary configuration and depth, when planning a study, is proposed. Bench tests of the BITA-1 pipeline finder were carried out to determine the error in measuring the depth of the pipeline axis. It is proved that the deviations of the pipeline finder data relative to the true values in narrow depth intervals follow a normal distribution and do not change their sign. The confidence intervals of the error in determining the depth of the pipeline axis for the BITA-1 device are presented.

Target-oriented least-squares reverse-time migration using Marchenko double-focusing: reducing the artefacts caused by overburden multiples

SUMMARY Geophysicists have widely used least-squares reverse-time migration (LSRTM) to obtain high-resolution images of the subsurface. However, LSRTM is computationally expensive and it can suffer from multiple reflections. Recently, a target-oriented approach to LSRTM has been proposed, which focuses the wavefield above the target of interest. Remarkably, this approach can be helpful for imaging below complex overburdens and subsalt domains. Moreover, this approach can significantly reduce the computational burden of the problem by limiting the computational domain to a smaller area. Nevertheless, target-oriented LSRTM still needs an accurate velocity model of the overburden to focus the wavefield accurately and predict internal multiple reflections correctly. A viable alternative to an accurate velocity model for internal multiple prediction is Marchenko redatuming. This method is a novel data-driven method that can predict Green’s functions at any arbitrary depth, including all orders of multiples. The only requirement for this method is a smooth background velocity model of the overburden. Moreover, with Marchenko double-focusing, one can make virtual sources and receivers at a boundary above the target and bypass the overburden. This paper proposes a new algorithm for target-oriented LSRTM, which fits the Marchenko double-focused data with predicted data. The predicted data of the proposed method is modelled by a virtual source term created by Marchenko double-focusing on a boundary above the target of interest. This virtual source term includes all the interactions between the target and the overburden. Moreover, the Marchenko double-focused data and the virtual source term are free of multiples generated in the overburden. Consequently, our target-oriented LSRTM algorithm suppresses the multiples purely generated inside the overburden. Our algorithm correctly accounts for all orders of multiples caused by the interactions between the target and the overburden, resulting in a significant reduction of the artefacts caused by the overburden internal multiple reflections and improves amplitude recovery in the target image compared to conventional LSRTM.

A generalized photon-tracking approach to simulate spectral snow albedo and transmittance using X-ray microtomography and geometric optics

Abstract. A majority of snow radiative transfer models (RTMs) treat snow as a collection of idealized grains rather than an organized ice–air matrix. Here we present a generalized multi-layer photon-tracking RTM that simulates light reflectance and transmittance of snow based on X-ray microtomography images, treating snow as a coherent 3D structure rather than a collection of grains. The model uses a blended approach to expand ray-tracing techniques applied to sub-1 cm3 snow samples to snowpacks of arbitrary depths. While this framework has many potential applications, this study's effort is focused on simulating reflectance and transmittance in the visible and near infrared (NIR) through thin snowpacks as this is relevant for surface energy balance and remote sensing applications. We demonstrate that this framework fits well within the context of previous work and capably reproduces many known optical properties of a snow surface, including the dependence of spectral reflectance on the snow specific surface area and incident zenith angle as well as the surface bidirectional reflectance distribution function (BRDF). To evaluate the model, we compare it against reflectance data collected with a spectroradiometer at a field site in east-central Vermont. In this experiment, painted panels were inserted at various depths beneath the snow to emulate thin snow. The model compares remarkably well against the reflectance measured with a spectroradiometer, with an average RMSE of 0.03 in the 400–1600 nm range. Sensitivity simulations using this model indicate that snow transmittance is greatest in the visible wavelengths, limiting light penetration to the top 6 cm of the snowpack for fine-grain snow but increasing to 12 cm for coarse-grain snow. These results suggest that the 5 % transmission depth in snow can vary by over 6 cm according to the snow type.

Velocity field and pressure analysis of equatorial flows beneath solitary water waves

In this paper, we investigate steady equatorial flows beneath solitary water waves subject to the Coriolis effect, which propagate over a flat bed. In particular, we focus on irrotational flows and present some properties of velocity field, behavior of the pressure and the extrema of the dynamic pressure. In addition, we provide some estimates for the elevation of wave from pressure measurements at an arbitrary intermediate depth. The analysis is based on the maximum principles.

Emulation and modelling of semiconductor optical amplifier-based all-optical photonic integrated deep neural network with arbitrary depth

We experimentally demonstrate the emulation of scaling of the semiconductor optical amplifier (SOA) based integrated all-optical neural network in terms of number of input channels and layer cascade, with chromatic input at the neuron and monochromatic output conversion, obtained by exploiting cross-gain-modulation effect. We propose a noise model for investigating the signal degradation on the signal processing after cascades of SOAs, and we validate it via experimental results. Both experiments and simulations claim that the all-optical neuron (AON), with wavelength conversion as non-linear function, is able to compress noise for noisy optical inputs. This suggests that the use of SOA-based AON with wavelength conversion may allow for building neural networks with arbitrary depth. In fact, an arbitrarily deep neural network, built out of seven-channel input AONs, is shown to guarantee an error minor than 0.1 when operating at input power levels of −20 dBm/channel and with a 6 dB input dynamic range. Then the simulations results, extended to an arbitrary number of input channels and layers, suggest that by cascading and interconnecting multiple of these monolithically integrated AONs, it is possible to build a neural network with 12-inputs/neuron 12 neurons/layer and arbitrary depth scaling, or an 18-inputs/neuron 18-neurons/layer for single layer implementation, to maintain an output error <0.1. Further improvement in height scalability can be obtained by optimizing the input power.

Ultrafast laser inscription of efficient volume Bragg gratings deep in fused silica using active wavefront shaping

The maximum depth that photonic structures such as volume Bragg gratings (VBGs) can be precisely fabricated inside dielectric materials using ultrafast laser inscription (ULI) is limited by the aberration imparted on the laser beam by the air-substrate interface as it is focused into the substrate. Here, we use a computer-controlled spatial light modulator (SLM) to shape the wavefront of the ULI laser before it is focused into the substrate, such that the impact of this aberration on the manufacture of VBGs is minimized. We show that this technique allows us to inscribe efficient VBGs at depths in fused silica that would otherwise result in low efficiency VBGs. We find that an optimized “reference” grating fabricated at a mean depth of 200 µm without wavefront shaping exhibited a maximum relative first-order diffraction efficiency of 48%, whereas a grating fabricated at a mean depth of 900 µm using identical parameters exhibited an efficiency of 6.2% – both measured with 633 nm light polarized perpendicularly to the grating lines. Using the SLM to control the wavefront of the ULI laser beam, we were able to pre-compensate for the effect of the substrate surface aberration and fabricate gratings at a mean depth of 900 µm that increased the first-order relative diffraction efficiency to ∼42%. A further plasma study provided significant evidence to the effectiveness of Zernike polynomials for spherical aberration correction. Combing both plasma imaging and laser writing approaches, a set of polynomials for aberration correction at a range of depths was produced with scope for arbitrary depth correction.

Marchenko Green’s Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data

By solving a Marchenko equation, Green’s functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are collected at the top of the medium. To date, it has only been possible to obtain an exact solution if the medium obeyed stringent monotonicity conditions and if all forward-scattered (non-converted and converted) transmissions between the acquisition level and the inner depth level were known a priori. We introduce an alternative Marchenko equation by revising the window operators that are applied in its derivation. We also introduce an auxiliary equation for transmission data, which are collected at the bottom of the medium, and a coupled equation, which is based on both reflection and transmission data. We show that the joint system of the Marchenko equation, the auxiliary equation and the coupled equation can be succesfully inverted when broadband reflection and transmission data are available. This results in a novel methodology for elastodynamic Green’s function retrieval from two-sided data. Apart from these data, our approach requires P- and S-wave transmission times between the inner depth level and the top of the medium, as well as two angle-dependent amplitude scaling factors, which can be estimated from the data by enforcing energy conservation.

Constructing group inclusions with arbitrary depth via wreath products

It was proved in a paper by Burciu, Kadison and Külshammer in 2011 that the ordinary depth d(S_n,S_{n+1}) of the symmetric group S_n in S_{n+1} is 2n-1, so arbitrarily large odd numbers can occur as subgroup depth. Lars Kadison in 2011 posed the question if subgroups of even ordinary depth bigger than 6 can occur. Recently in a paper with Breuer we constructed a series (G_n,H_n) of groups and subgroups where the depth d(H_n,G_n) was 2n, thus answering the question of Kadison. Here we generalize the method of that proof. The main result of this paper is that for every positive integer n there are infinitely many pairs (G, H) of finite groups such that d(H,G)=n. As a corollary of its proof we get that for every positive integer n there are infinitely many triples (H, N, G) of finite solvable groups Htriangleleft Ntriangleleft G such that G/N is cyclic of order lceil {n/2} rceil , N/H is cyclic of arbitrarily large prime order and d(H,G)=n. We investigate the series d(H_n,G_n) in the cases when the depth, d(H_1,G_1), is 1, 2 or 3, where H_n:=H_1times G^{n-1} and G_n:=G_1wr C_n. We also prove that if H_1=S_k and G_1=S_{k+1} then d(H_n,G_n)=2nk-1.

Designing Protein-Based Probes for Sensing Biological Analytes with Magnetic Resonance Imaging.

Genetically encoded sensors provide unique advantages for monitoring biological analytes with molecular and cellular-level specificity. While sensors derived from fluorescent proteins represent staple tools in biological imaging, these probes are limited to optically accessible preparations owing to physical curbs on light penetration. In contrast to optical methods, magnetic resonance imaging (MRI) may be used to noninvasively look inside intact organisms at any arbitrary depth and over large fields of view. These capabilities have spurred the development of innovative methods to connect MRI readouts with biological targets using protein-based probes that are in principle genetically encodable. Here, we highlight the state-of-the-art in MRI-based biomolecular sensors, focusing on their physical mechanisms, quantitative characteristics, and biological applications. We also describe how innovations in reporter gene technology are creating new opportunities to engineer MRI sensors that are sensitive to dilute biological targets.

Soft, bioresorbable coolers for reversible conduction block of peripheral nerves.

Implantable devices capable of targeted and reversible blocking of peripheral nerve activity may provide alternatives to opioids for treating pain. Local cooling represents an attractive means for on-demand elimination of pain signals, but traditional technologies are limited by rigid, bulky form factors; imprecise cooling; and requirements for extraction surgeries. Here, we introduce soft, bioresorbable, microfluidic devices that enable delivery of focused, minimally invasive cooling power at arbitrary depths in living tissues with real-time temperature feedback control. Construction with water-soluble, biocompatible materials leads to dissolution and bioresorption as a mechanism to eliminate unnecessary device load and risk to the patient without additional surgeries. Multiweek in vivo trials demonstrate the ability to rapidly and precisely cool peripheral nerves to provide local, on-demand analgesia in rat models for neuropathic pain.

A Novel Solution for Resonant Scattering Using Self-consistent Boundary Conditions

We present two novel additions to the semianalytic solution of Lyα radiative transfer in spherical geometry: (1) implementation of the correct boundary condition for a steady source, and (2) solution of the time-dependent problem for an impulsive source. For the steady-state problem, the solution can be represented as a sum of two terms: a previously known analytic solution of the equation with mean intensity J = 0 at the surface, and a novel, semianalytic solution which enforces the correct boundary condition of zero-ingoing intensity at the surface. This solution is compared to that of the Monte Carlo method, which is valid at arbitrary optical depth. It is shown that the size of the correction is of order unity when the spectral peaks approach the Doppler core and decreases slowly with line center optical depth, specifically as , which may explain discrepancies seen in previous studies. For the impulsive problem, the time, spatial, and frequency dependence of the solution are expressed using an eigenfunction expansion in order to characterize the escape time distribution and emergent spectra of photons. It is shown that the lowest-order eigenfrequency agrees well with the decay rate found in the Monte Carlo escape time distribution at sufficiently large line center optical depths. The characterization of the escape time distribution highlights the potential for a Monte Carlo acceleration method, which would sample photon escape properties from distributions rather than calculating every photon scattering, thereby reducing computational demand.

Cyperus rotundus L. drives arable soil infertile by changing the structure of soil bacteria in the rhizosphere, using a maize field as an example

Rhizosphere microorganisms can greatly affect plant growth, especially the plant growth-promoting rhizobacteria (PGPR), which can improve plant root development and growth because they contain various biological functions including nitrogen fixation, phosphate solubilization, and phytosiderophore production. This study demonstrates that Cyperus rotundus L. is capable of developing and forming complex underground reproductive systems at arbitrary burial depths and cutting modes due to its extremely strong multiplication and regeneration ability. With the densities of C. rotundus increasing, the abundance of PGPR, soil enzymes invertase and urease, the nutrient contents of the field soil, and maize quality were impacted. Notably, more abundance of PGPR-most notably, the nitrogen-fixing microorganisms (NFMs) such as Azospirillum, Burkholderia, Mycobacterium, and Rhizobium-enriches in the rhizosphere of C. rotundus than in that of maize. In addition, the activities of soil enzymes invertase (S_SC) and urease (S_SU) were significantly higher in its rhizosphere than in maize, further proving that more NFMs enrich the C. rotundus rhizosphere. The nutrient contents of the field soil of TN, SOM, and SOC were reduced, indicating that the presence of C. rotundus made the soil infertile. Hence, these pieces of evidence indicate that C. rotundus may drive the field soil infertile as reflected by reduced soil nutrients via altering rhizosphere bacteria community structure.

Efficient phase shift migration for ultrasonic full-matrix imaging of multilayer composite structures

Multilayer composite structures are essential for various fields but void defects inside will greatly reduce its mechanical properties. Ultrasonic full-matrix capture (FMC) is a useful imaging modality to detect defects in multilayer structures, but it also brings heavy computational burden. Though great progress has been made in the full-matrix imaging for homogeneous medium, most of these methods are invalid or inefficient for the cases of multilayer structures. To amend it, an efficient phase shift migration for ultrasonic full-matrix imaging of multilayer structures is proposed in this paper. The method regards FMC as data in three dimensions: receiver position, transmitter position and time, and transforms it into frequency-wavenumber (f-k) space by a three-dimensional fast Fourier transform. By downward extrapolating the wavefield on the surface, the wavefield at arbitrary depth in the measuring region is reconstructed, with a firstly introduced double-square-root vertical wavenumber. Then the imaging condition t = 0 is directly applied in the f-k space to produce the defect image. Computational complexity was reduced greatly, and the calculation time of the proposed method was only 1/6 of that of the well-established extended phase shift migration, in the case of the same resolution. Therefore, the proposed method has great potential in on-line ultrasound defect detection, especially for cases of large multilayer structures.

Disnht: Modeling X-ray absorption from distributed column densities

Collecting and analyzing X-ray photons over either spatial or temporal scales encompassing varying optical depth values requires knowledge about the optical depth distribution. For a sufficiently broad optical depth distribution, assuming a single column density value leads to a misleading interpretation of the source emission properties, nominally its spectral model. We present a model description for the interstellar medium absorption in X-ray spectra at moderate energy resolution, extracted over spatial or temporal regions encompassing a set of independent column densities. The absorption model (called disnht) approximates the distribution with a lognormal distribution and is presented in table format. The solution table and source code are made available and can be further generalized or tailored for arbitrary optical depth distributions encompassed by the extraction region. The disnht absorption model and its generalized solution are expected to be relevant for current and upcoming large angular scale analyses of diffuse X-ray emission, such as those from the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) and the future Athena missions.

High-frequency instabilities of Stokes waves

Euler's equations govern the behaviour of gravity waves on the surface of an incompressible, inviscid and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes waves, i.e. periodic gravity waves of permanent form and constant velocity, in both finite and infinite depth. We develop a perturbation method to describe the first few high-frequency instabilities away from the origin, present in the spectrum of the linearization about the small-amplitude Stokes waves. Asymptotic and numerical computations of these instabilities are compared for the first time, with excellent agreement.

Enhanced settling and dispersion of inertial particles in surface waves

Particulate matter in the environment, such as sediment, marine debris and plankton, is transported by surface waves. The transport of these inertial particles is different from that of fluid parcels described by Stokes drift. In this study, we consider the transport of negatively buoyant particles that settle in flow induced by surface waves as described by linear wave theory in arbitrary depth. We consider particles that fall under both a linear drag regime in the low Reynolds number limit and in a nonlinear drag regime in the transitional Reynolds number range. Based on an analysis of typical applications, we find that the nonlinear regime is the most widely applicable. From an expansion in the particle Stokes number, we find kinematic expressions for inertial particle motion in waves, and from a multiscale expansion in the dimensionless wave amplitude, we find expressions for the wave-averaged drift velocities. These drift velocities are analogous to Stokes drift and can be used in large-scale models that do not resolve surface waves. We find that the horizontal drift velocity is reduced relative to the Stokes drift of fluid parcels and that the vertical drift velocity is enhanced relative to the particle terminal settling velocity. We also demonstrate that a cloud of settling particles released simultaneously will disperse in the horizontal direction. Finally, we discuss the accuracy of our expressions by comparing against numerical simulations, which show excellent agreement, and against experimental data, which show the same trends.

Zeta-like multiple zeta values in positive characteristic

We study multiple zeta values (MZV’s) over the rational function field over \({\mathbb {F}}_q\) which were introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we affirmatively solve a conjecture of Lara Rodriguez and Thakur which gives a full list of zeta-like MZV’s of weight at most \(q^2\) and depth 2. Further, we completely determine all zeta-like MZV’s of weight at most \(q^2\) and arbitrary depth. Our method is based on a criterion which is derived from the Anderson–Thakur motivic interpretation of MZV’s and the Anderson–Brownawell–Papanikolas criterion for linear independence in positive characteristic.

An attention-enhanced cross-task network to analyse lung nodule attributes in CT images

Accurate characterization of visual attributes such as spiculation, lobulation, and calcification of lung nodules in computed tomography (CT) images is critical in cancer management. The characterization of these attributes is often subjective, which may lead to high inter- and intra-observer variability. Furthermore, lung nodules are often heterogeneous in the cross-sectional image slices of a 3D volume. Current state-of-the-art methods that score multiple attributes rely on deep learning-based multi-task learning (MTL) schemes. These methods, however, extract shared visual features across attributes and then examine each attribute without explicitly leveraging their inherent intercorrelations. Furthermore, current methods treat each slice with equal importance without considering their relevance or heterogeneity, which limits performance. In this study, we address these challenges with a new convolutional neural network (CNN)-based MTL model that incorporates multiple attention-based learning modules to simultaneously score 9 visual attributes of lung nodules in CT image volumes. Our model processes entire nodule volumes of arbitrary depth and uses a slice attention module to filter out irrelevant slices. We also introduce cross-attribute and attribute specialization attention modules that learn an optimal amalgamation of meaningful representations to leverage relationships between attributes. We demonstrate that our model outperforms previous state-of-the-art methods at scoring attributes using the well-known public LIDC-IDRI dataset of pulmonary nodules from over 1,000 patients. Our model also performs competitively when repurposed for benign-malignant classification. Our attention modules provide easy-to-interpret weights that offer insights into the predictions of the model.

Modulational instability and statistical properties of irregular waves in finite water depth

Modulational instability is one of the possible basic mechanisms for the generation of rogue waves in deep water. Under the condition of finite depth, this instability is reduced and disappears as k1h<1.363 (k1 is the wavenumber of the carrier wave and h is the water depth). In this study, we addressed this phenomenon through three approaches, theoretical analysis of the Zakharov’s equation and the nonlinear Schrödinger equation and direct numerical simulations of the Euler equation. Their results on the modulational instability over arbitrary depths, particularly the growth rates of sidebands, are analysed and compared. In addition, the consequences of the suppression of modulational instability for realistic ocean waves are illustrated by direct simulations of long-crested, irregular waves at finite water depth. The results show that many phenomena related to the third-order nonlinearity (i.e. the downshift of the spectral peak frequency, the enhancement of kurtosis of surface elevations and rouge wave occurrence probability) are suppressed with decreasing depth k1h and eventually cease to exist as k1h<1.363. Considering the dependence of wave evolution on water depth, two Benjamin–Feir indices for arbitrary depths derived from Zakharov’s equation and nonlinear Schrödinger equation are used as indicators to estimate the modulational instability effect on nonlinear wave fields. Our results confirm that both parameters provide reasonable predictions of the modulational instability and probability of rogue wave occurrence.

Fully nonlinear hydroelastic modeling and analytic solution of large-scale floating photovoltaics in waves

This paper concerns the fully nonlinear fluid–structure interaction (FSI) of Large-scale floating photovoltaics (LFPV) in waves. The Euler Bernoulli–von Kármán beam models the structure while potential flow represents the fluid. A set of coupled dynamical equations is established. The fully analytic solution is sought with the unified Stokes perturbation method. The characteristic equation is derived up to third order, which has not been reported in literature before. The expressions obtained from the solution are applied to two typical cases of a pontoon LFPV and a membrane LFPV, with physical parameters from literature. The comparison with literature demonstrates our methodology for the membrane-type in waters of arbitrary depth and pontoon-type in relatively deep waters.