Field Model Research Articles

A lattice Boltzmann model with sharp interface tracking for the motion and growth of dendrites in non-equilibrium solidification of alloys

A lattice Boltzmann model (LBM) with sharp interface tracking is developed to simulate the motion and growth of dendrites in non-equilibrium solidification of alloys. The model is validated through comparative analysis with the drafting-kissing-tumbling (DKT) phenomena of two and three particles and the continuous growth model (CGM), and demonstrates its computational efficiency advantage without compromising accuracy by comparison with the multi-phase field (MPF) model. Subsequently, the model is utilized to investigate the dendrite morphology transition and primary dendritic arm spacing (PDAS). It is found that the velocity dependent solute partition and the resulting changes in constitutional undercooling strongly influence the estimated morphology region and PDAS. Moreover, the segregation and microstructure evolution during the rapid solidification were studied. And the results revealed that free dendrites lead to significant changes in microstructure and segregation under the influence of non-equilibrium effects. This work illustrates the great potential of the proposed model in simulating dendrites and microstructure evolution under a wide range of solidification conditions. Its suitability for extreme conditions and non-equilibrium solidification can contribute to the understanding of microstructure formation patterns and solute segregation in rapid solidification.

Effect of dark matter interaction on hybrid star in the light of the recent astrophysical observations

We have explored the effect of dark matter interaction on hybrid star (HS) in the light of recent astrophysical observational constraints. The presence of dark matter is assumed to be there in both the hadron as well as the quark sector. The dark matter particle interacts with both hadron and quark matter through the exchange of a scalar as well as a vector meson. The equation of state (EOS) of the hadron part is computed using the NL3 version of the relativistic mean field(RMF) model, whereas the quark part is taken care of using the well-known MIT Bag model with the vector interaction. We investigate the effect of the dark matter density and the mass of the dark matter particle on various observables like mass, radius, tidal deformability of the dark matter admixed hybrid star(DMAHS).In this study, we have noted an intriguing aspect that is the speed of sound in the DMAHS is insensitive to both the mass as well as the density of dark matter. We also observe a striking similarity in the variation of transition mass and its corresponding radius, as well as the maximum mass of neutron stars, with dark matter density and mass. We employ observational constraints from neutron stars to narrow down the allowed range of the parameters of dark matter.

Estimation and research of the temperature field models of large space spherical mesh shell structures under localized fire

This paper firstly investigated fire dynamics characteristics and the temperature field distributions of large space spherical mesh shell (SMS) structures under localized fire in FDS, and divided the temperature fields into plume region, smoke accumulation region and ceiling jet region. Based on the classical axisymmetric plume model, the predictive models for the steady-state and transient temperature fields in different fire regions for large space SMS structures were proposed in this paper. Thereafter, the proposed temperature models were compared with the simulated results and experimental test results by other scholars, and they were in good agreement. In order to further discover the realistic fire development progress and temperature distribution of large space fire, and validate the proposed temperature field models, this paper designed and conducted three full-scale large space fire tests (Test-1 ∼ Test-3) with different fire source powers in a large space building. Results showed that temperature fields of large space fires could be consisted of near-fire region (Flame region) and far-fire region (Plume region and Ceiling jet region). The steady-state fire source powers were tested for 443 kW, 886 kW, 1090 kW for Test-1, Test-2 and Test-3, respectively, while their maximum temperatures of the roof reached 75 °C, 105 °C and 120 °C. Based on McCaffrey plume model, we further proposed the transient temperature model in flame region for large space structures, and its accuracy was verified by the test results. Moreover, the proposed steady-state and transient temperature fields for large space SMS structures were compared with the tested temperature field data, and the tested and predicted temperature curves were generally in good agreement in plume and ceiling jet regions. Finally, the test results aimed to provide a scientific basis and reference for the fire safety and structural fire-resistant design of large space buildings.

Characteristics and optimization strategy of microwave thermal regeneration of spent activated carbon based on a multi-physical field model

Microwave thermal regeneration is an efficient and low-consumption way to recycle spent activated carbon. However, traditional experimental approaches are difficult to analyze the electromagnetic field distribution in the microwave cavity, heat and mass transfer process of adsorbates, and optimization of the microwave reactor. Therefore, in this work, a multi-phase porous media model coupled with electromagnetism, heat and mass transfer is established to study the characteristics of microwave thermal regeneration procedure and to propose an optimization strategy for the microwave reactor. The results showed that the absorption of microwave by the sample can be strengthened by adjusting the width to height ratio of the waveguide. The optimal waveguide size (width: length = 80 mm: 10 mm) increased the microwave utilization efficiency from 65.4 % to 98.5 %. In addition, the combination of rotary and intermittent microwave heating significantly optimized the temperature uniformity in both lateral and vertical directions and reduced the microwave heating time. The combined microwave heating time was reduced from the initial 136 s to 80 s, saving 41 % of energy consumption. The temperature difference of the sample was also reduced from the initial 536 K to 191 K, and the covariance COVT decreased from 0.52 to 0.24. The results provide a valuable technical guideline for the optimization of the microwave reactor in order to improve the regeneration efficiency and the quality of the regenerated carbon.

Disentangling the Faraday rotation sky

Context. Magnetic fields permeate the diffuse interstellar medium (ISM) of the Milky Way, and are essential to explain the dynamical evolution and current shape of the Galaxy. Magnetic fields reveal themselves via their influence on the surrounding matter, and as such are notoriously hard to measure independently of other tracers. Aims. In this work, we attempt to disentangle an all-sky map of the line-of-sight (LoS)-parallel component of the Galactic magnetic field from the Faraday effect, utilizing several tracers of the Galactic electron density, ne. Additionally, we aim to produce a Galactic electron dispersion measure map and quantify several tracers of the structure of the ionized medium of the Milky Way. Methods. The method developed to reach these aims is based on information field theory, a Bayesian inference framework for fields, which performs well when handling noisy and incomplete data and constraining high-dimensional-parameter spaces. We rely on compiled catalogs of extragalactic Faraday rotation measures and Galactic pulsar dispersion measures, a well as data on bremsstrahlung and the hydrogen α spectral line to trace the ionized medium of the Milky Way. Results. We present the first full sky map of the LoS-averaged Galactic magnetic field. Within this map, we find LoS-parallel and LoS-averaged magnetic field strengths of up to 4 µG, with an all-sky root mean square of 1.1 µG, which is consistent with previous local measurements and global magnetic field models. Additionally, we produce a detailed electron dispersion measure map that agrees with existing parametric models at high latitudes but suffers from systematic effects in the disk. Further analysis of our results with regard to the 3D structure of ne reveals that it follows a Kolmogorov-type turbulence for most of the sky. From the reconstructed dispersion measure and emission measure maps, we construct several tracers of variability in ne along the LoS. Conclusions. This work demonstrates the power of consistent joint statistical analysis including multiple datasets and physical quantities and defines a road map toward a full three-dimensional joint reconstruction of the Galactic magnetic field and the ionized ISM.

Assessment of the Weimer Geomagnetic Perturbation Model for High‐Latitude Positioning and Navigation

AbstractThe Geomagnetism Group at the National Centers for Environmental Information (NCEI), in collaboration with the Cooperative Institute for Research in Environmental Sciences (CIRES), along with various government and industry partners, specializes in developing and providing access to Earth's internal magnetic field models. These models are crucial for applications such as compass navigation and wellbore positioning, offering reference values for the geomagnetic field (total field, dip or inclination, and declination) at any location across the Earth. This study assesses the Weimer geomagnetic perturbation model, proposed by Weimer in 2013, which is an empirical model of magnetic field variations at high latitudes driven by solar wind measurements, as a candidate for capturing geomagnetic field variations in high‐latitude areas. We compare the geomagnetic field variations predicted by the Weimer model against data from the INTERMAGNET and SuperMAG observatory networks. Our findings indicate that the Weimer model achieves a reduction in the standard deviations of high‐latitude magnetic field variations by approximately 20%–30% once quiet‐time baselines are removed from the data set. Furthermore, we compare the performance of the Weimer model against the Space Weather Modeling Framework's Geospace model during specific geomagnetic storms in 2017 and 2018, and we find that the Weimer model is more effective in predicting magnetic variations at high latitudes than the Geospace model during these storms. Additionally, comparisons to magnetometer data collected from high‐latitude directional‐drilling operations align with the trends observed in comparisons with INTERMAGNET and SuperMAG observatory data, confirming the Weimer model's reliability and effectiveness for such applications.

Vector Field Model of CKD Stage and Its Directional Derivative Mathematically Enable Accurate Kidney Prognosis Prediction

Vector Field Model of CKD Stage and Its Directional Derivative Mathematically Enable Accurate Kidney Prognosis Prediction

Unconditional Energy Stable Runge-Kutta Schemes for a Phase Field Model for Diblock Copolymers

Unconditional Energy Stable Runge-Kutta Schemes for a Phase Field Model for Diblock Copolymers

Far-field reactivation of natural fractures by stress shadow effect

Hydraulic fracturing is the most important means to achieve the reservoir stimulation of tight formations like shale, where the reservoir permeability is enhanced after the interaction between hydraulic fracture (HF) and natural fractures (NFs). Apart from the widely known direct intersection behaviors between HF and NFs (i.e., the HF meets the NFs), the NFs may also be reactivated by the stress shadow effect of HF, but the failure mechanism and reactivation modes are still unclear. To address this, the far-field reactivation of NFs under the stress shadow effect is described based on a hybrid phase field model (PFM) with the frictional contact criterion, where the open or slip conditions can be quantitatively calculated using the Mohr-Coulomb yield function along the contact interface of NFs. The zone with reactivated NFs is divided into mode II and mixed mode dominated sub-zones respectively, and the phase diagram of reactivation behaviors is summarized as variations of the location and angle of the NF. The NF reactivation modes are discussed under different geological conditions (strength of NFs, distribution angle of NFs, and initial stress difference). It could be found that the higher initial stress ratio leads to more mode II reactivated NFs, and NFs strengths and angles influence both mode II and mixed mode zones notably. The NF reactivation tends to take place with lower strength, higher injection rate, higher initial stress ratio, and special angle (e.g., HF are perpendicular to NFs), during which the permeability enhancement and reservoir stimulation are evaluated by the phase field model.

Characterization of hydromagnetic waves propagating over a steady, non-axisymmetric background magnetic field

Motivated by recent observations of rapid (interannual) signals in the geomagnetic data, and by advances in numerical simulations approaching the Earth’s outer core conditions, we present a study on the dynamics of hydromagnetic waves evolving over a static base state. Under the assumption of timescales separation between the rapid waves and the slow convection, we linearize the classical magneto-hydrodynamics equations over a steady non-axisymmetric background magnetic field and a zero velocity field. The initial perturbation is a super-rotating pulse of the inner core, which sets the amplitude and length scales of the waves in the system. The initial pulse triggers axisymmetric, outward propagating torsional Alfvén waves, with characteristic thickness scaling with the magnetic Ekman number as E k M 1 / 4 . Because the background state is non-axisymmetric, the pulse also triggers non-axisymmetric, quasi-geostrophic (QG) Alfvén waves. As these latter waves propagate outwards, they turn into QG, magneto-Coriolis (QG-MC) waves as the Coriolis force supersedes inertia in the force balance. The period of the initial wave packet is preserved across the shell but the QG-MC wavefront disperses and a westward drift is observed after this transformation. Upon reaching the core surface, the westward drift of the QG-MC waves presents an estimated phase speed of about 1100 k m y − 1 . This analysis confirms the QG-MC nature of the rapid magnetic signals observed in geomagnetic field models near the Equator.

Effect of Solid Particles in Polymer Waste Liquid on Grinding Tool Wall Erosion

Abstract With the continuous accumulation of polymer waste liquid in the third oil recovery process, the treatment of wellhead return waste liquid has become a key issue in oilfield exploitation and environmental protection. In this paper, the erosion failure of the cutter caused by sand-containing particles in the waste liquid during the shear grinding process is studied. The influence of the main structural parameters of the grinding tool and the erosion failure is studied by using the comprehensive numerical simulation method to reduce the erosion rate of the polymer flooding waste liquid on the cutter. Firstly, the flow field model of the solid-liquid fluid is established, and the erosion phenomenon on the tool wall is studied by combining the model with field experiments. In addition, the relationship between the different cutters structure and erosion rate of the grinding tool is studied, and the mathematical model is established. The optimized structural parameters are given to enhance the erosion resistance of the grinding tool in the process of polymer flooding wellhead waste liquid treatment and prolong its service life.

Investigation on Wax Deposition Risk in Shale Oil Well During Production Test

Abstract During production test of the shale oil well, the low temperature environment in the wellbore is likely to cause wax precipitation of shale oil, and in turn disrupt the normal production test, increase the operating costs and risks. In view of this problem, by considering the gas-liquid flow, radial heat transfer and temperature gradient etc, a temperature and pressure field model of shale oil wellbore was established, and a prediction method of wax deposition zone in the shale oil wellbore during production test was proposed. Furthermore, by using the production data of a shale oil well with wax deposition in the South China Sea during production test, the accuracy of the model in calculating the fluid temperature and pressure of the wellbore with wax deposition was verified. The wellhead temperatures calculated by the model had a maximum error of 9.31%, and the bottom-hole pressures calculated by the model had a maximum error of 7.52%, indicating the model has high calculation accuracy. The model was used to analyze the sensitivities of wax deposition to the time and rate of production, water content and the ratio of gas to oil. It is found that the wax deposited in wellbore increases in thickness with the production time, is more strongly affected by production rate and water content, but less affected by the ratio of gas to oil. The research results can provide support for preventing wax deposition during production test of shale oil wells.

A microstructural defect-orientation informed phase field model

Micro-cracks, micro-voids and other such defects, which typically coalesce to form macroscopic cracks, could be represented through incompatible, local rotations of material points, i.e. micro-regions. Specifically, based on a micropolar or Cosserat continuum-like hypothesis that requires attaching directors to material points, we track the evolving frame rotation and hence the microstructural orientation during quasi-brittle damage. We introduce a critical energy release rate incorporating the wryness tensor, which in turn is a function of the micro-rotation field and its gradient within the damaged region. The (pseudo) rotation field appears as additional degrees of freedom to describe a frame field, whose evolution is particularly significant within a diffused region of evolving damage as obtained through a phase-field formulation of brittle fracture. We emphasize that, unlike micropolar continua where it contributes to elastic energy, the wryness tensor appears only in the fracture energy in our approach. Thus, without damage, the solid conforms to the classical continuum. By making suitable modifications to the terms within the elastic energy and applying the principle of virtual work, we arrive at the governing partial differential equations (PDEs). For assessing the proposed framework, we choose a specific form of energy density and demonstrate, through numerical examples, the effect of the newly introduced parameters. The classical phase-field model is readily recovered by switching off the micro-rotation. Additionally, we explore a potential application of this model in representing and propagating initial defects.

Total Solar Eclipse White-light Images as a Benchmark for Potential Field Source Surface Coronal Magnetic Field Models: An In-depth Analysis over a Solar Cycle

Potential field source surface (PFSS) models are widely used to simulate coronal magnetic fields. PFSS models use the observed photospheric magnetic field as the inner boundary condition and assume a perfectly radial field beyond a “source surface” (R ss). At present, total solar eclipse (TSE) white-light images are the only data that delineate the coronal magnetic field from the photosphere out to several solar radii (R ⊙). We utilize a complete solar cycle span of these images between 2008 and 2020 as a benchmark to assess the reliability of PFSS models. For a quantitative assessment, we apply the Rolling Hough Transform to the eclipse data and corresponding PFFS models to measure the difference, Δθ, between the data and model magnetic field lines throughout the corona. We find that the average Δθ, 〈Δθ〉, can be minimized for a given choice of R ss depending on the phase within a solar cycle. In particular, R ss ≈ 1.3 R ⊙ is found to be optimal for solar maximum, while R ss ≈ 3 R ⊙ yields a better match at solar minimum. Regardless, large (〈Δθ〉 > 10°) discrepancies between TSE data and PFSS-generated coronal field lines remain regardless of the choice of source surface. However, implementation of solar-cycle-dependent R ss optimal values does yield more reliable PFSS-generated coronal field lines for use in models and for tracing in situ measurements back to their sources at the Sun.

Effect of temperature anisotropy formed by fast electron beams moving in the flare loop on its excited electron-cyclotron maser instability

Context. The electron-cyclotron maser instability (ECMI) is a significant coherent radio emission mechanism widely utilized in various astrophysical radio phenomena. It is well known that the velocity anisotropic distribution of energetic electrons, which leads to an inverted perpendicular population in the vertical direction with ∂fb/∂v⊥ > 0, can provide the free energy necessary for the ECMI. Aims. The initial velocity distribution of energetic electrons leaving the acceleration region is typically isotropic or beam-like. However, as these energetic electrons travel along the magnetic field as fast electron beams (FEBs) in magnetic plasma, various velocity anisotropic distributions can emerge. In this paper, we examine the impact of temperature anisotropy formed by beam electrons traveling along a flare loop on the ECMI. Methods. By neglecting the energy loss of energetic electrons as they traverse the corona and invoking the conservation of energy and magnetic moments, we established the relationship between momentum dispersion and the magnetic field. Utilizing the magnetic field model of the flare loop, we calculated the evolution of momentum dispersion and the growth rates of the ECMI as FEBs precipitate along the flare loop. Results. The results demonstrate that the temperature anisotropy arising as FEBs descend along the flare loop significantly impacts the ECMI. The maximum growth rates of the excited modes exhibit a gradual increase initially and then decline rapidly after reaching a critical height for β0 = 0.2c and 0.15c. The results also show that the growth rates of the O2 mode are one order of magnitude smaller than those of the O1 and X2 modes. This indicates that the harmonic radiation is X-mode polarized. Notably, the temperature anisotropy of FEBs as they precipitate along the flare loop with different magnetic field models or at different heights has similar effects on the ECMI.

Nonlinear soliton spiral induces coupled multimode dynamics in multi-stable dissipative metamaterials

With the robust and self-trapped properties, recent advances about soliton dynamics in multi-stable mechanical metamaterials have led to many innovative techniques from signal processing to robotics. This work proposes a multi-stable mechanical metamaterial driven by nonlinear dissipative solitons, in which the coupling and decoupling of multiple locomotion modes can be achieved. Based on a cylinder network with asymmetric energy landscape, the uniform field model of Landau theory is developed. During the theoretical calculation, the analytical solutions of several dissipative solitons are derived, which allow multiple special behaviors of solitary waves, such as wave velocity gaps, directional propagation and spiral phase transition. By incorporating such effects into robotic designs, a variety of complex movements can be achieved by a single structure, including hopping, rolling, rotating, swinging, bending and translational components. In particular, as excitation positions change, the mechanical metamaterial can flexibly switch multiple locomotion modes without changing configurations, e.g., spinning and spin-less, straight and oblique as well as coupled multimode movements. This work wishes to provide some new inspirations for the applications of nonlinear elastic wave metamaterials and phase transition theory in robotics.

Effect of porosity gradient on fracture mechanics of bi-directional FGM structures: Phase field approach

This research aims to develop a computational model that can accurately predict the fracture behavior of porous bi-directional Functionally Graded Materials (FGMs). The Voigt model for homogenization, is established to account the effects of porosity fraction and gradient distribution within the FGMs, providing valuable insights about the brittle crack propagation. The study employs the UMAT subroutine in ABAQUS software and establishes an analogy between the phase field evolution law and the heat transfer equation, enabling efficient analysis of complex fracture problems. To validate the model, 2D fracture benchmark cases are analyzed, demonstrating its ability to capture different failure modes and the intricate material behavior of porous FGMs under fracture conditions. Furthermore, newly parametric analyses, that highlights the impact of various values of porosity’s volume fraction and FGM’s power law indexes on the brittle fracture path, are conducted to further validate the effectiveness of the newly developed phase field model in predicting the fracture behavior of bi-directional porous FGMs.

Statistical batch-aware embedded integration, dimension reduction, and alignment for spatial transcriptomics.

Spatial transcriptomics (ST) technologies provide richer insights into the molecular characteristics of cells by simultaneously measuring gene expression profiles and their relative locations. However, each slice can only contain limited biological variation, and since there are almost always non-negligible batch effects across different slices, integrating numerous slices to account for batch effects and locations is not straightforward. Performing multi-slice integration, dimensionality reduction, and other downstream analyses separately often results in suboptimal embeddings for technical artifacts and biological variations. Joint modeling integrating these steps can enhance our understanding of the complex interplay between technical artifacts and biological signals, leading to more accurate and insightful results. In this context, we propose a hierarchical hidden Markov random field model STADIA to reduce batch effects, extract common biological patterns across multiple ST slices, and simultaneously identify spatial domains. We demonstrate the effectiveness of STADIA using five datasets from different species (human and mouse), various organs (brain, skin, and liver), and diverse platforms (10x Visium, ST, and Slice-seqV2). STADIA can capture common tissue structures across multiple slices and preserve slice-specific biological signals. In addition, STADIA outperforms the other three competing methods (PRECAST, fastMNN, and Harmony) in terms of the balance between batch mixing and spatial domain identification, and it demonstrates the advantage of joint modeling when compared to STAGATE and GraphST. The source code implemented by R is available at https://github.com/zhanglabtools/STADIA and archived with version 1.01 on Zenodo https://zenodo.org/records/13637744.

Study on micro electrochemical milling with programmable dynamic eccentric rotating electrode

Micro electrochemical machining (ECM) has the advantages of non-contact machining, no tool loss and no residual stress, and has great development potential in the field of microstructure manufacturing. However, the micron-scale machining gap is difficult to renew and discharge the electrolyte and electrolytic products in time. In this paper, a novel micro ECM with programmable dynamic eccentric rotating electrode (DER-ECM) is proposed, which can effectively improve the discharge of electrolytic products in the machining area. According to the process characteristics, a disc flexure hinge structure with one-stage amplification was designed, which was driven by a piezo-ceramic actuator, and the programmable eccentricity ranging from 0 to 20 μm. The multi-physics model of flow field and electric field of DER-ECM, micro ECM with eccentric rotating electrode (ER-ECM) and micro ECM with rotating electrode (R-ECM) were established. The theoretical simulation results showed that the flow rate generated by DER-ECM at the bottom of the electrode is 97 times that of ER-ECM. The current density generated by DER-ECM showed periodic pulsation, and the pulsation period was determined by the driving frequency of the piezo-ceramic actuator. The experimental results showed that DER-ECM could effectively eliminate the surface spike of the workpiece in the bottom machining area and effectively improve the machining accuracy. The micro-groove widths obtained under DER-ECM, ER-ECM and R-ECM were 418 μm, 446 μm and 468 μm, respectively. In addition, the influence of three types of dynamic eccentric rotation electrode trajectories on DER-ECM was studied. The experimental results showed that the sawtooth dynamic eccentric rotation electrode had better machining accuracy. Theoretical simulation and experimental results showed that DER-ECM could improve the flow field and achieve higher machining efficiency and machining localization.

Groundwater for urban water supply in Ukraine: a case study of Mykolaiv (Military challenges and lessons for the future)

The paper discusses the possibility of using groundwater as a source of water supply for Mykolaiv during emergencies or military operations. A hydrogeological model of the Mykolaiv groundwater field was developed to investigate the water exchange pattern and sources of operational groundwater reserves in the Upper Sarmatian aquifer, which is a primary source of drinking groundwater in the Mykolaiv area. The influence of various factors on water-bearing capacity of the Upper Sarmatian sediments was assessed, including the vulnerability of the fresh groundwater to the intrusion of brackish water from the Bug Estuary. The study also examined the feasibility of operating the aquifer under forced conditions, depending on the duration of emergency periods or military operations.