One-dimensional Model Research Articles

Disordered Heisenberg XYZ magnetic chains with exponential correlations: Localization and quantum state transfer

Our study investigates the Quantum State Transfer Protocol within a one-dimensional quantum Heisenberg spin chain model that features exponentially correlated disorder in the spin coupling distribution. We conducted extensive numerical simulations to explore how varying degrees of correlation impact the transfer of quantum states through this model of a quantum channel. Our results demonstrate that the extent of correlation significantly influences quantum communication along the channel. Specifically, we observed that in the strongly correlated regime, quantum communication remains largely unaffected even in large systems. These findings are interpreted in the context of the localization properties inherent to the disordered channel.

Full Stokes-vector Inversion of the Solar Mg ii h and k Lines

Abstract The polarization of the Mg ii h and k resonance lines is the result of the joint action of scattering processes and the magnetic field–induced Hanle, Zeeman, and magneto-optical effects, thus holding significant potential for the diagnostic of the magnetic field in the solar chromosphere. The Chromospheric LAyer Spectro-Polarimeter sounding-rocket experiment, carried out in 2019, successfully measured at each position along the 196″ spectrograph slit the wavelength variation of the four Stokes parameters in the spectral region of this doublet around 280 nm, both in an active-region plage and in a quiet region close to the limb. We consider some of these CLASP2 Stokes profiles and apply to them the recently developed HanleRT Tenerife Inversion Code, which assumes a one-dimensional model atmosphere for each spatial pixel under consideration (i.e., it neglects the effects of horizontal radiative transfer). We find that the nonmagnetic causes of symmetry breaking, due to the horizontal inhomogeneities and the gradients of the horizontal components of the macroscopic velocity in the solar atmosphere, have a significant impact on the linear polarization profiles. By introducing such nonmagnetic causes of symmetry breaking as parameters in our inversion code, we can successfully fit the Stokes profiles and provide an estimation of the magnetic field vector. For example, in the quiet region pixels, where no circular polarization signal is detected, we find that the magnetic field strength in the upper chromosphere varies between 1 and 20 G.

Simulation of Total Harmonic Distortion of Solid Oxide Fuel Cells for Carbon Deposition Detection

Abstract Identifying the degradation mechanisms at the early stage of operation is important for the long-term operation of solid oxide fuel cells (SOFCs). Compared to conventional methods, total harmonic distortion analysis (THDA) can significantly reduce the test time for identifying performance degradation during SOFC operation. In this study, a one-dimensional transient elementary reaction kinetic model of an SOFC fueled with syngas is developed. The model incorporates the coupling effect of elementary chemical and electrochemical reactions, the electrode microstructure, the charge and mass transport processes, and the detailed evolution reaction of surface adsorbed carbon. A THDA simulation calculation method was developed and applied to determine the failure mode of anode carbon deposition. The amplitude, duration, and harmonic number of the perturbation signal are determined to improve fault detection for THDs. The results show that the use of THD can not only detect carbon accumulation behavior at the early stage of SOFC operation but also distinguish the specific degradation mechanism caused by carbon deposition: the hindered SOFC charge transfer reaction can be detected in the frequency range of 100-4000 Hz, and the hindered gas diffusion process inside the anode can be detected in the frequency range of 0.01-10 Hz.

A One-Dimensional Model for Investigating Scale-separated Approaches to the Interaction of Oceanic Internal Waves

Abstract High-frequency wave propagation in near-inertial wave shear has, for four decades, been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave-breaking. We compare idealized ray tracing numerical results with metrics derived using a wave turbulence derivation for the kinetic equation and a path integral to study this specific process. Statistical metrics include the changing ensemble mean vertical wavenumber, referred to as a mean drift, dispersion about the mean drift, time lagged correlation estimates of wavenumber and phase locking of the wave packets with the background. The path integral permits us to identify the mean drift as a resonant process and dispersion about that mean drift as non-resonant. At small inertial wave amplitudes; ray tracing, wave turbulence and the path integral provide consistent descriptions for the mean drift of wavepackets in the spectral domain and dispersion about the mean drift. Extrapolating these results to the background internal wavefield over-predicts downscale energy transports by an order of magnitude. At oceanic amplitudes, however, the numerics support diminished transport and dispersion that coincide with the mean drift time scale becoming similar to the lagged correlation time scale. We parse this as the transition to a non-Markovian process. Despite this decrease, numerical estimates of downscale energy transfer are still too large. We argue that residual differences result from an unwarranted discard of Bragg scattering resonances. Our results support replacing the long standing interpretive paradigm of extreme scale-separated interactions with a more nuanced slate of ‘local’ interactions in the kinetic equation.

Quantum-coherence-assisted dynamical phase transition in the one-dimensional transverse-field Ising model

Quantum coherence will undoubtedly play a fundamental role in understanding the dynamics of quantum many-body systems; therefore, to be able to reveal its genuine contribution is of great importance. In this paper, we focus our discussions on the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state, and investigate the effects of quantum coherence on dynamical quantum phase transition (DQPT). After quenching the strength of the transverse field, the effects of quantum coherence are studied using Fisher zeros and the rate function of the Loschmidt echo. We find that quantum coherence not only recovers DQPT destroyed by thermal fluctuations, but also generates some entirely new DQPTs, which are independent of the equilibrium quantum critical point. We also find that the Fisher zero cutting the imaginary axis is not sufficient to generate DQPT because it also requires the Fisher zeros to be tightly bound close enough to the neighborhood of the imaginary axis. It can be manifested that DQPTs are rooted in quantum fluctuations. This work reveals new information on the fundamental connection between quantum critical phenomena and quantum coherence.

Does cabbeling shape the thermohaline structure of high-latitude oceans?

Abstract Vertical exchange of heat and carbon in the ocean regulates Earth’s climate. Convection, a driver of near surface exchange, occurs when dense water overlies light water. Fofonoff (1957) pointed out that when lighter overlying cold-fresh water mixes with denser underlying warm-salty water, the mixture can become denser than the underlying water due to a nonlinear process known as cabbeling. He suggested that such profiles, despite being gravitationally stable, could be classed as being unstable to cabbeling. Fofonoff (1957) hypothesised that, by mixing away such profiles, cabbeling may be shaping the thermohaline structure of polar oceans. We investigate this hypothesis here. In a one-dimensional model we find that convective mixing occurs in temperature inverted profiles that are unstable to cabbeling even when they are initially gravitationally stable. In data from an observationally constrained global circulation model, we find profiles with a temperature inversion larger than −0.5°C are unstable to cabbeling less than 0.02% of the time and in high quality in-situ observations they are unstable less than 12% of the time. We find that due to cabbeling larger temperature inversions, which should weaken stratification, make profiles more stable. Our results suggest that cabbeling limits the stability behaviour of temperature inverted profiles and influences the thermohaline structure in parts of the ocean where cold-fresh water overlays warm-salty water.

Predicting smoke temperature distribution beneath ceiling for a large subway station fire

Fire accident seriously threatens the stable operation and personnel security in the subway station, and clarifying the smoke temperature distribution is conducive to arranging reasonably fire alarm. In this study, model experiments and numerical simulations are conducted to investigate the ceiling temperature profiles, mainly altering the heat release rate (HRR) and fire locations in a large subway station. The repeatability of the experimental data is confirmed, and the numerical model is validated by the measurement data. During a fire happening in a large-wide space, the smoke movement beneath the ceiling can be divided into radial and one-dimensional flow, whose prediction models are proposed under fire source located at the center. On this basis, it can be found that the radial temperature profile is independent of fire source location. While, the one-dimensional temperature distribution model is modified by introducing the effects of transvers and longitudinal fire locations respectively. This work could provide data support and theoretical reference for clarifying the smoke movement for large subway station fire.

Monotonic and cyclic lateral loading of piles in low- to medium-density chalk

Offshore and other structures often rely on driven piles to carry lateral loads. However, there is currently no established design method to cover lateral loading at chalk sites, which are widespread across Northwest Europe. This paper reports monotonic and cyclic lateral load tests on highly instrumented 508 mm and 1220 mm diameter. open steel piles driven at a well-characterised chalk test site in Kent, UK, for a recent joint industry project that developed new benchmark datasets and analyses, supported by high-quality testing. The ultimate lateral pressures mobilised in the chalk are shown to be relatively low compared to its uniaxial compressive strengths (UCS) due to pile-driving damage, natural fracturing, local yielding and brittleness. Significant gaps opened between the piles and chalk during loading, that led to a substantially softer response on unloading and subsequent reloading, as well as marked axial capacity losses. Reaction curves extracted from the field measurements and applied in a one-dimensional numerical model perform well in reproducing the monotonic lateral tests. As with piles driven in other materials, one-way cyclic lateral loading led to permanent displacement accumulation and stiffness changes that were linked to the cyclic loading parameters. Both effects were more marked under biaxial cyclic lateral loading.

Impact of arterial system alterations due to amputation on arterial stiffness and hemodynamics: a numerical study

Subjects with amputation of the lower limbs are at increased risk of cardiovascular mortality and morbidity. We hypothesize that amputation-induced alterations in the arterial tree negatively impact arterial biomechanics, blood pressure and flow behavior. These changes may interact with other biological factors, potentially increasing cardiovascular risk. To evaluate this hypothesis regarding the purely mechanical impact of amputation on the arterial tree, we used a simulation computer model including a detailed one-dimensional (1D) arterial network model (143 arterial segments) coupled with a zero-dimensional (0D) model of the left ventricle. Our simulations included five settings of the arterial network: (1) 4-limbs control, (2) unilateral amputee (right lower limb), (3) bilateral amputee (both lower limbs), (4) trilateral amputee (lower-limbs and right upper-limb), and (5) quadrilateral amputee (lower and upper limbs). Analysis of regional stiffness, as calculated by pulse wave velocity (PWV) for large-, medium- and small-sized arteries, showed that, while aortic stiffness did not change with increasing degree of amputation, stiffness of medium and smaller-sized arteries increased with greater amputation severity. Despite a staged decrease in cardiac output, the systolic and diastolic blood pressure values increased, resulting in an increase in both central and peripheral pulse pressures but with an attenuation of pulse pressure amplification. The most significant increase in peak systolic pressure and decrease in peak systolic blood flow was observed at the site of the abdominal aorta. Wave separation analysis indicated no changes in the shape of the forward and backward wave components. However, the results from wave intensity analysis showed that with extended amputation, there was an increase in peak forward wave intensity and a rise in the inverse peak of the backward wave intensity, suggesting potential alterations in cardiac hemodynamic load. In conclusion, this simulation study showed that biomechanical and hemodynamic changes in the arterial network geometry could interact with additional risk factors to increase the cardiovascular risk in patients with amputations.

Electromechanical admittance-based automatic damage assessment in plate structures via one-dimensional CNN-based deep learning models

Electromechanical admittance-based automatic damage assessment in plate structures via one-dimensional CNN-based deep learning models

A novel explicit fast numerical scheme for the Cauchy problem for integro-differential equations with a difference kernel and its application

The present study focuses on designing a second-order novel explicit fast numerical scheme for the Cauchy problem incorporating memory associated with an evolutionary equation, where the integral term's kernel is a discrete difference operator. The Cauchy problem under consideration is related to a real finite-dimensional Hilbert space and includes a self-adjoint operator that is both positive and definite. We introduce a transformative technique for converting the Cauchy problem incorporating memory, into a local evolutionary system of equations by approximating the difference kernel using the sum of exponentials (SoE) approach. A second-order explicit scheme is then constructed to solve the local system. We thoroughly investigate the stability of this explicit scheme, and present the necessary conditions for the stability of the scheme. Moreover, we extended our investigation to encompass time-fractional diffusion-wave equations (TFDWEs) involving a fractional Caputo derivative with an order ranging between (1,2). Initially, we transform the main TFDWE model into a new model that incorporates the fractional Riemann-Liouville integral. Subsequently, we expand the applicability of our idea to develop an explicit fast numerical algorithm for approximating the model. The stability properties of this fast scheme for solving TFDWEs are assessed. Numerical simulations including a two-dimensional Cauchy problem as well as one-dimensional and two-dimensional TFDWE models are provided to validate the accuracy and experimental order of convergence of the schemes.

Assessing field scale spatiotemporal heterogeneity in salinity dynamics using aerial data assimilation

Soil moisture and salinity shifts within the root zone can significantly alter crop yields. Thus, spatiotemporal dynamics of these parameters are essential for precision crop management. Airborne or spaceborne earth observation methods based on vegetation and soil observations have sometimes been used with limited success to indirectly understand parameters like soil salinity. These datasets lack spatiotemporal resolution to discern field-scale heterogeneities, and estimates’ accuracy is poor. A Metropolis-Hasting Markov Chain-Monte Carlo (MCMC) based method was developed to estimate field-scale soil salinity by assimilating estimated evapotranspiration (ET) data obtained from aerial canopy temperature sensing with ET outputs from a one-dimensional soil-water transport model. By aligning the two estimated ET values, we inferred anticipated soil salinity levels in a mature pecan orchard (28,951 m2). Our results aligned closely with in-situ measurements with a spatial cross-correlation more than 0.86 and highlighted the expected heterogeneities and nonlinearities. This research offers an approach to refine the current state-of-the-art crop models by accounting for field scale heterogeneities using remotely sensed data. This assimilation method will pave the way for a more inclusive agricultural system modeling that can infer critical but hard-to-measure soil properties from easier-to-obtain remotely sensed datasets. Though this paper concentrates on aerial observations, we anticipate similar methods can be used for satellite-based imagery, especially those with high spatial, temporal, and spectral resolutions.

Study on the source identification and migration and transformation characteristics of heavy metal pollution in sediments of Chaohu Lake Tongyang River Basin.

Heavy metal pollution in soil and groundwater is difficult to detect in time because of its long-term accumulation. This poses a severe hazard to the ecosystem security in polluted areas. Considering the Tongyang River Basin of the Chaohu Lake water system as the research object, various pollution evaluation methods, Geographic Information System (GIS) source analysis models, adsorption and desorption experiments, and mathematical models were used. Based on the data of the heavy metal content in the soil and river sediments in the study area, regional heavy metal pollution evaluation, spatial distribution characteristics, source identification, and lake loss analysis were conducted to evaluate the current situation of environmental pollution, pollution sources, and migration and transformation of heavy metals in the basin. The results show that the heavy metals in the soil of the basin are mainly distributed from the southwest to the northeast and the island distribution to the east of Tongyang Town. The Cd, Cu, Zn, and Pb concentrations are higher in the sediment than in the soil. The Unmix analytical model was established. The natural source of heavy metals in the Tongyang River Basin and the composite pollution source of traffic-production and life showed a high correlation. According to the one-dimensional steady-state model, the concentrations of the heavy metals are in the following descending order: Zn, Cr, Pb, Cu, Ni, and Cd. The amounts of these elements entering the lake annually are 1993.04, 1028.1, 372.47, 301.72, 308.80, and 19.46 kg, respectively (a total of 4023.6 kg).

PPCon 1.0: Biogeochemical-Argo profile prediction with 1D convolutional networks

Abstract. Effective observation of the ocean is vital for studying and assessing the state and evolution of the marine ecosystem and for evaluating the impact of human activities. However, obtaining comprehensive oceanic measurements across temporal and spatial scales and for different biogeochemical variables remains challenging. Autonomous oceanographic instruments, such as Biogeochemical (BGC)-Argo profiling floats, have helped expand our ability to obtain subsurface and deep-ocean measurements, but measuring biogeochemical variables, such as nutrient concentration, still remains more demanding and expensive than measuring physical variables. Therefore, developing methods to estimate marine biogeochemical variables from high-frequency measurements is very much needed. Current neural network (NN) models developed for this task are based on a multilayer perceptron (MLP) architecture, trained over point-wise pairs of input–output features. Although MLPs can produce smooth outputs if the inputs change smoothly, convolutional neural networks (CNNs) are inherently designed to handle profile data effectively. In this study, we present a novel one-dimensional (1D) CNN model to predict profiles leveraging the typical shape of vertical profiles of a variable as a prior constraint during training. In particular, the Predict Profiles Convolutional (PPCon) model predicts nitrate, chlorophyll, and backscattering (bbp700) starting from the date and geolocation and from temperature, salinity, and oxygen profiles. Its effectiveness is demonstrated using a robust BGC-Argo dataset collected in the Mediterranean Sea for training and validation. Results, which include quantitative metrics and visual representations, prove the capability of PPCon to produce smooth and accurate profile predictions improving upon previous MLP applications.

Three-dimensional numerical modeling of soil-roots system based on X-ray computed tomography: Hydraulic effects study

Vegetation roots enhance soil stability by influencing saturation and pore structure, playing a pivotal role in stabilizing slopes, reducing erosion, and enhancing soil structure. However, current research on the hydraulic effects of roots on soil remains relatively limited. The micro-mechanisms of vegetation's impact on soil and the macro-level connections are not yet fully understood, which poses a challenge to the modeling of root-soil system. This study develops a three-dimensional (3D) finite element model of root-soil composites based on root computed tomography (CT) images and experimental results. Four different groups are modeled, including the rootless group, and those with Festuca arundinacea (FA) roots at various growth stages. The simulation results show that the saturation in the shallow layers significantly decreases in root-soil composite groups, and the rhizosphere water content is lower than that away from the roots, resulting in a net water flux toward the roots. The influence range of roots on suction is gradually amplified with increasing root growth process and root water uptake time. Higher levels of root development result in a stronger overall water uptake effect, leading to a more pronounced decrease in saturation. Closer proximity to the surface roots results in a more rapid increase in soil suction. Compared with one-dimensional root water uptake models, this model considers the effects of spatial heterogeneity of root structures on soil, which provides a comprehensive modeling basis for studying the effect of root system on soil.

Optimised use of interferometry, spectroscopy, and stellar atmosphere models for determining the fundamental parameters of stars

Thanks to recent progress in the field of optical interferometry, instrument sensitivities have now reached the level achieved in the domain of new space missions dedicated to exoplanet and stellar studies. Combining interferometry with other observational approaches enables the determination of stellar parameters and helps improve our understanding of stellar physics. In this paper, we aim to demonstrate a new way of using stellar atmosphere models for a joint interpretation of spectroscopic and interferometric observations. Starting from a discrete grid of one-dimensional (1D) stellar atmosphere models, we developed a training algorithm, based on an artificial neural network, capable of estimating the spectrum and intensity profile of a star over a range of wavelengths and viewing angles. A minimisation algorithm based on the trained function allowed for the simultaneous fitting of the observational spectrum and interferometric complex visibilities. As a result, coherent and precise stellar parameters can be extracted. We show the ability of the trained function to match the modelled intensity profiles of stars in the effective temperature range of $4500$ K to $7000$ K and surface gravity range of $3$ to $5$ dex, with a relative precision to the model that is better than $0.05<!PCT!>$. Using simulated interferometric data and actual spectroscopic measurements, we demonstrated the performance of our algorithm on a sample of five benchmark stars. Using this method, we achieved an accuracy within $0.5<!PCT!>$ for the angular diameter, radius, and surface gravity, and within $20$ K for the effective temperature. This paper demonstrates a new method of using interferometric data combined with spectroscopic observations. This approach offers an improved determination of the radius, effective temperature, and surface gravity of stars.

Numerical investigation of the flow characteristics inside a supersonic vapor ejector

Integrating a vapor ejector with an air-cooled absorption cooling system (ACS) requires understanding how the ejector responds to varying condenser conditions and how the geometrical parameters affect the system's performance. This study provides a numerical investigation of the flow characteristics inside supersonic vapor ejectors. The primary objectives were identifying the best nozzle design for ACS and explaining how the secondary flow responds to different back pressures. The developed model was validated against experimental data and a one-dimensional model. Despite exhibiting increased flow fluctuations, the convex nozzle achieved an entrainment ratio of 0.4. This value was 4.9 % and 7 % higher than the values obtained by the straight and the concave nozzles, respectively. In contrast, the concave nozzle exhibits better flow stability and pressure recovery, which are considered appealing for the air-cooled ACS. The straight nozzle emerged as a balanced alternative, offering moderate entrainment alongside favorable flow stability. Moreover, secondary flow behavior at different operating modes was elaborated. Secondary flow choked at back pressures between 60–70 kPa, indicating optimal entrainment. However, at 75–80 kPa, while the secondary flow was entrained, it failed to reach sonic speed due to high-pressure waves, resulting in the sub-critical condition. Further increases in back pressure to 85–90 kPa induced back-flow due to elevated local static pressure. Mach number profiles at the mixing tube entrance remained consistent under critical operation but deviated post-critical back pressure, reflecting altered flow characteristics downstream of the mixing tube. Such elaboration of flow dynamics within ejectors paves the way for innovative designs of vapor ejectors, potentially developing ACS.

Gas jet target with controllable density via throat diameter of conical nozzle

A supersonic gas jet has been a special target in the ultraintense laser interaction field due to its controllable atomic density distribution. This work investigates the spatial atomic density distribution in argon gas jets ejected from conical nozzles with different throat diameters. Both experiment and simulation results show that the atomic density and its distribution can be controlled by changing the throat diameter of the conical nozzle. The quantitative dependence of atomic density on the throat diameter under different backing pressures is obtained. It also agrees with that from the one-dimensional gas dynamics model. However, it is noted that for a large throat diameter at a high gas backing pressure, a radial saddle-shaped atomic density profile is demonstrated experimentally within a few millimeters away from the nozzle outlet. The results are helpful to optimize the density profile in gas-jet targets and to understand the effect of the throat diameter of the conical nozzle on cluster size in Hagena scaling law.

An iterative technique for a class of highly nonlinear BVP arising in a one-dimensional corneal shape model

An iterative technique for a class of highly nonlinear BVP arising in a one-dimensional corneal shape model

Resonant transport in a double-barrier heterostructure AlxGa1−xAs/GaAs and mass discontinuity: a semiclassical path integral approach

In this paper, we investigate the dependence of the resonant carrier transport in an AlGaAs/GaAs double-barrier heterostructure on the electron’s effective mass discontinuity between the well and the barrier layer. We use a one-dimensional model for the effective potential and consider the activation of the resonant tunneling mechanism when a bias is applied between the emitter and the collector. We calculate the system’s Green’s function through semiclassical path integration to obtain the complex spectrum. Electron’s effective mass discontinuity affects our calculations through the contributions of the various propagations inside the heterostructure and the multiple reflections from the turning points. Our findings show that the lowest resonance energy decreases linearly with increasing bias, while the real energy shift of the resonance decreases in a non-linear manner with the mass discontinuity. We also observe that the resonant transport time increases nearly linearly with the mass discontinuity. These results demonstrate the impact of the carrier’s inertia enhancement on the resonance characteristics and are consistent with established concepts in quantum mechanics and previously published works. Furthermore, we identify a critical bias value that distinguishes the behavior of the symmetric and asymmetric heterostructure. Additionally, the derivative of the transport time with respect to mass discontinuity is found to be independent of the applied bias. Our results provide concise analytical relationships involving parameters such as barrier and well thickness and shape, enabling the prediction and optimization of various nanoscale devices’ performance.