Density Discontinuity Research Articles

An Improved Single‐Layer Smoothed Particle Hydrodynamics Model for Water–Soil Two‐Phase Flow

ABSTRACTIn coastal and offshore engineering, the intense water–soil motion poses significant challenges to the safety of buildings and structures. The smoothed particle hydrodynamics (SPH) method, as a mesh‐free Lagrangian solver, has considerable advantages in the numerical resolution of such problems. SPH models for the water–soil two‐phase flow can be categorized into the multilayer type and the single‐layer type. Although the single‐layer model envisions a simpler algorithm and higher computational efficiency, its accuracy, stability, and recovery of interfacial details are far from satisfactory. In the present work, an improved single‐layer model is established to alleviate these limitations. First, the soakage function, which takes effect near the phase interface, is introduced to characterize the two‐phase coupling status. Additionally, the stress diffusion term and a modified density diffusion term applicable in density discontinuity scenario are introduced to ease the numerical oscillation. Finally, to remove the unphysical voids in the interfacial region, the particle shifting technique with special treatment tailored for free‐surface particles is implemented. Validations of the proposed model are carried out by a number of numerical tests, including the erodible dam‐break problem, the wall‐jet scouring, the flushing case, and the water jet excavation. Appealing agreements with either experimental data or published numerical results have been achieved, which verifies the accuracy, stability, and robustness of the proposed model for water–soil two‐phase flows.

Microplastic abundance in the surface water of tropical estuarine fronts.

Estuarine fronts are formed due to sharp density discontinuities resulting from the convergence of different water masses. This study, conducted in May and August of 2022 during the southwest monsoon season, focuses on assessing the role of estuarine fronts at Kuala Terengganu estuary in the accumulation of microplastics in surface seawater. The Terengganu River basin area covers approximately 4600 km2 and consists of two main tributaries that drain into the Kuala Terengganu estuary. Microplastic samples were collected from three areas, the plume, front, and shelf, utilizing two methods: manta net (> 350µm) and bucket-water sampling (> 20µm). Results indicate that the estuarine front consistently exhibited higher microplastic concentrations than the plume and shelf regions throughout the study period, with bucket-water sampling contributing significantly to the abundance. Specifically, peak concentrations occurred during the ebb tide at the frontal region in both months, reaching 5761.703 particles m-3 and 12,687.437 particles m-3, respectively. The microplastics, predominantly transparent fibers smaller than 1000µm, mostly showed signs of oxidative and mechanical weathering through SEM-EDS analysis, providing insights into their fate in estuarine surface waters. FTIR spectroscopy revealed polypropylene, polyethylene, and polyamide as the dominant polymers. These findings establish a baseline for microplastic abundance at the estuarine front of the Kuala Terengganu estuary and may inform future strategies for mitigating and recovering microplastic contamination in aquatic environments.

Diagnosis of the fragmentation of urban ecological network structure and its social-ecological responses.

The fragmentation of ecological network structures has become a common problem faced by cities. By establishing the urban ecological network under a specific socio-ecological system framework, we aimed to propose a quantitative index to diagnose the fragmentation of the network structure, and to construct detection model to explore the driving factors and mechanism of the network fragmentation. Using Shenzhen City as an example, we used the Floyd-Prim algorithm to generate the skeleton structure of the ecological network and construct a density discontinuity index to diagnose network fragmentation. Combined with the ecological network scenario, social-ecological system framework and a two-layer indicator system were constructed. The detection models were then established to explore the drivers of network disruption and their mode of impact. The models show that the average degree of network fragmentation in Shenzhen was 0.13, and the density of about 85% of corridor discontinuities was greater than 0.01, reflecting the serious state of structural fragmentation. Corridors with more severe structural fragmentation have poorer social-ecological coordination. The fragmentation in Shenzhen was mainly affected by the activities of actors (A) at the microlevel and the resource system (RS) at the macrolevel. The methods and the framework of socio-ecosystem analysis proposed in this paper can reveal the driving factors and influence modes of network fragmentation, providing decision-making reference for ecological restoration practice in urbanized areas.

Application of SPH in rheology model for the submerged landslide

The seafloor environment is prone to rapid changes caused by landslides, which can result in significant human, financial, and environmental consequences. Previous research efforts have primarily focused on studying rigid submerged landslides using physical experiments and mesh-based numerical simulations. However, there is a need to investigate deformable soil masses due to their inherent complexity. In the current study, a smoothed particle hydrodynamics (SPH) method was developed to examine the behavior of submerged landslides. Three rheological models, namely Bingham, Herschel–Bulkley (H–B), and μ(I), were applied to characterize the properties of the sediment materials. The SPH governing equations were modified at the interface between the water and sediment phases to account for the density discontinuity between them. The viscosity term at this interface was determined using the Owens equation. The effective pressure, a crucial parameter in rheological models, was appropriately modified to reflect the influence of the water column on the sediment particles, utilizing a simple algorithm. For the μ(I) rheology, separate equations were applied to describe the behavior of dry and saturated conditions. Additionally, the Mohr–Coulomb criteria were utilized in the Bingham and H–B models to determine the yield stress. To validate the effectiveness of the proposed modeling approach, a column failure scenario was first simulated. Subsequently, a rigid submerged landslide was investigated to assess the capability and validity of the proposed framework in accurately capturing surge wave generation and calibrating the boundary friction factor. Finally, two deformable submerged landslides involving different materials, namely sand and glass beads, were simulated and compared with previous experimental and numerical studies at different time steps. Through these comprehensive investigations, the current understanding of the complex behavior exhibited by submerged landslides is enhanced, and valuable insight into landslide dynamics is provided.

Air‐gap field prediction in tubular doubly sided surface magnet machine using Bessel–Fourier series

Abstract2‐D air‐gap magnetic field distribution is the essential prerequisite of electrical machine analysis. Because of the natural periodicity of rotary machines, Fourier analysis is a suitable choice for air‐gap field prediction. However, due to the end‐effect, periodicity is not present in linear machines and the Fourier series is not appropriate. In engineering mathematics, a rigorous method of solving partial differential equations is the separation of the variables method (SVM) which is based on the hypothesis that the field solution is in the form of the product of two functions of orthogonal directions; for example, in an axisymmetric structure, a longitudinal harmonic function (LHF) and a radial harmonic function (RHF). A particular case of these functions is trigonometric functions, which result in the Fourier series. SVM is imposed in a different manner, where RHF is approximated by the Bessel–Fourier series and consequently LHF has a (piecewise) exponential behaviour. This choice of basis functions not only serves the purpose of modelling the end‐effect but also removes the Gibbs phenomenon, that is, it precisely models discontinuities of flux density at the surface of PMs. A numerical case‐study of a slotless double‐sided linear tubular surface‐PM machine shows that the piecewise exponential approximation can attain 1% error while utilising only three harmonics, whereas the trigonometric approximation, due to the Gibbs phenomenon, slowly arrives at 20% error with 100 harmonics for approximating flux density. Results of both methods were validated using the finite element method (FEM). Additionally, it was discovered that the computational complexity of the model is independent of varying position; therefore, the analytical method could yield the back electromotive force and electromagnetic thrust force for a number of 320 positions at merely 0.2 s while the FEM software required 5 min.

Two shell- and wing-shaped supernova remnants

Supernova remnants (SNRs) are profoundly affected by their ambient medium. In particular, SNRs with a mixed morphology (characterised by a shell-like radio morphology and centrally filled X-ray emission) are thought to be the result of the interaction of a supernova explosion with a dense environment. In this work, we present carbon monoxide (CO) observations around two mixed morphology SNRs, VRO 42.05.01 and G 350.0-2.0, that look remarkably similar in continuum radio emission, showing what we refer to as a shell and wing shape. It has been proposed that the shell and wing shape is the result of environmental effects, in the form of a sharp density gradient or discontinuity. Therefore, our motivation for studying these two sources jointly is that if the dense molecular environment causes the development of these sources’ shell and wing shape, then these two sources’ environments must be similar. This is contrary to what we observe. In the case of VRO 42.05.01, we have found direct evidence of an interaction with its molecular environment, in the form of broadened 12CO line profiles, high 12CO (J = 2−1) to 12CO (J = 1−0) line ratios, and arc features in position-velocity space. We interpret some of these features to be associated with the SNR shock, and some of them to be due to the presence of a pre-supernova stellar wind. We have found no such features in the abundant molecular gas surrounding G 350.02.0. In addition to the spectral line analysis, we have used radio continuum data to make a spectral index map of G 350.0-2.0, and we see that the radio spectrum of G 350.0-2.0 steepens significantly at frequencies <200 MHz, much like that of VRO 42.05.01. In spite of their spectral and morphological similarities, these two sources look substantially different in their observed optical and infrared emission. The lack of large-scale correspondence between the radio continuum and the molecular material, in either case, as well as the differences in the excitation and morphological properties of the molecular gas surrounding both sources, lead us to conclude that the shell and wing morphology of these two sources is not due to interactions with a similar ambient molecular interstellar medium.

Improved hybrid approach of monotonic upstream-centered scheme for conservation laws and discontinuity sharpening technique for steady and unsteady flows

In finite-volume methods, monotonic upstream-centered schemes for conservation laws (MUSCL) offer second-order spatial accuracy but tend to produce highly dissipative solutions for density discontinuity and weak shock waves. To address this limitation within a second-order framework, a novel strategy for hybridizing MUSCL with the tangent of the hyperbola interface capturing technique for both steady and unsteady compressible flows is presented. This hybridization optimizes the process based on the degree of nonlinearity and discontinuity around the target cells, providing a novel method to sharply resolve weak shock waves and robustly compute strong shock waves within the hybrid scheme. The proposed scheme sharply captures exceedingly weak shock waves that conventional MUSCL fails to resolve accurately due to excessive numerical dissipation. Furthermore, for resolving small vortices induced by instability at slip lines, computational results demonstrate high-resolution surpassing fifth-order spatial accuracy schemes within this second-order spatial accuracy framework with less computational cost. Moreover, the scheme exhibits commendable convergence and robustness when applied to steady-state problems featuring strong shock waves. This scheme offers a more precise and high-resolution alternative to conventional MUSCL for compressible flow computations, as it requires no additional stencil for reconstruction, unlike conventional fifth-order schemes.

The Populist Backlash Against Globalization: A Meta-Analysis of the Causal Evidence

AbstractThe literature on populism is divided on whether economic factors are significant and robust causes of populism. To clarify this, we performed the first systematic review and meta-analysis of the evidence of a causal association between economic insecurity and populism. We combined database searches with searching the citations of eligible studies and recently published reviews. We identified and reviewed thirty-six studies and presented a concise narrative summary and numerical synthesis of the key findings. Although we found significant heterogeneity in several dimensions, all studies reported a significant causal association. A recurrent magnitude was that economic insecurity explained around one-third of recent surges in populism. We tested for publication bias by conducting a funnel-plot asymmetry test and a density discontinuity test of the distribution of t-statistics. We found significant evidence of publication bias; however, the causal association between economic insecurity and populism remains significant after controlling for it.

“Beads-on-a-string” Star Formation Tied to One of the Most Powerful Active Galactic Nucleus Outbursts Observed in a Cool-core Galaxy Cluster

With two central galaxies engaged in a major merger and a remarkable chain of 19 young stellar superclusters wound around them in projection, the galaxy cluster SDSS J1531+3414 (z = 0.335) offers an excellent laboratory to study the interplay between mergers, active galactic nucleus (AGN) feedback, and star formation. New Chandra X-ray imaging reveals rapidly cooling hot (T ∼ 106 K) intracluster gas, with two “wings” forming a concave density discontinuity near the edge of the cool core. LOFAR 144 MHz observations uncover diffuse radio emission strikingly aligned with the “wings,” suggesting that the “wings” are actually the opening to a giant X-ray supercavity. The steep radio emission is likely an ancient relic of one of the most energetic AGN outbursts observed, with 4pV > 1061 erg. To the north of the supercavity, GMOS detects warm (T ∼ 104 K) ionized gas that enshrouds the stellar superclusters but is redshifted up to +800 km s−1 with respect to the southern central galaxy. The Atacama Large Millimeter/submillimeter Array detects a similarly redshifted ∼1010 M ⊙ reservoir of cold (T ∼ 102 K) molecular gas, but it is offset from the young stars by ∼1–3 kpc. We propose that the multiphase gas originated from low-entropy gas entrained by the X-ray supercavity, attribute the offset between the young stars and the molecular gas to turbulent intracluster gas motions, and suggest that tidal interactions stimulated the “beads-on-a-string” star formation morphology.

Nonlinear dynamics of large-amplitude, small-scale Alfvén waves

We study large-amplitude, very oblique Alfvén waves at low β, with small gradient length scales, comparable to the ion inertial scale di. Such waves have large density fluctuations and slight dispersion from finite-frequency and finite-ion sound radius effects. We derive a weakly nonlinear evolution equation governing the behavior of the waves in one dimension and categorize the different solitons appearing in different regimes: the regular solitons involve full rotations of the transverse magnetic field similar to modified Korteweg–de Vries (mKdV) solitons (our nonlinear equation reduces to the mKdV equation in the long-wavelength limit). However, for sufficiently small soliton widths, some become singular, small-amplitude solitons with density discontinuities and, are, thus expected to become strongly dissipative in a real plasma. These solutions may be useful in explaining some aspects of the sharp, ion-scale magnetic field rotations (switchbacks) observed in the near-Sun solar wind by Parker Solar Probe.

Pre-electoral coalitions and the distribution of political power

Pre-electoral coalitions (PECs) may increase parties’ chances of winning an election, but they may also distort electoral results and policies away from citizens’ preferences. To shed light on how PECs shape post-electoral power distribution, we study the causes and consequences of PECs in Finland where elections use an open-list proportional representation system, and parties may form joint lists. We present descriptive evidence showing that PECs are more common between parties of equal size and similar ideology, and when elections are more disproportional or involve more parties. Using difference-in-differences and density discontinuity designs, we illustrate that voters punish coalescing parties and target personal votes strategically within the coalitions, and that PECs are formed with the particular purpose of influencing the distribution of power. PECs increase small parties’ chances of acquiring leadership positions, lead to more dispersed seat distributions, and sometimes prevent absolute majorities. They can thus enable a broader representation of citizens’ policy preferences.

Lee–Yang Zeroes in the Baryon Fugacity Plane: The Role of High Densities

We compute the canonical partition functions and the Lee–Yang zeros in Nf=2 lattice QCD at temperature T=1.20Tc lying above the Roberge–Weiss phase transition temperature TRW. The phase transition is characterized by the discontinuities in the baryon number density at specific values of imaginary baryon chemical potential. We further develop our method to compute the canonical partition functions using the asymptotic expression for respective integral. Then, we compute the Lee–Yang zeros and study their behavior in the limit of high baryon density.

Probing phase transitions in neutron stars via the crust-core interfacial mode

Gravitational waves emitted from the binary neutron star (BNS) systems can carry information about the dense matter phase in these compact stars. The crust-core interfacial mode is an oscillation mode in a neutron star, and it depends mostly on the equation of state of the matter in the crust-core transition region. This mode can be resonantly excited by the tidal field of an inspiraling-in BNS system, thereby affecting the emitted gravitational waves and hence could be used to probe the equation of state in the crust-core transition region. In this work, we investigate, in detail, how the first-order phase transition inside the neutron star, if it exists, affects the properties of the crust-core interfacial mode using a Newtonian fluid perturbation theory on a general relativistic background solution of the stellar structure. Two possible types of phase transitions are considered: (1) the phase transitions happen in the fluid core but near the crust-core interface, which results in density discontinuities, and (2) the strong interaction phase transitions in the dense core (as in the conventional hybrid star case). We study how these phase transitions affect the properties of the neutron star oscillation mode excited at the interface, where there exists a shear modulus discontinuity (interfacial mode). In particular, the former phase transition has a minor effect on the mass-radius relation, and the adiabatic tidal deformability, but has the potential to significantly affect the interfacial mode frequency and thereby could be probed using gravitational waves. For the BNS systems, we discuss the possible observational signatures of these phase transitions in the gravitational waveforms and their detectability. Our work enriches the exploration of the physical properties of the crust-core interfacial mode and provides a promising method for probing the phase transition using the seismology of a compact star.

Phase diagram and thermoelastic property of iron oxyhydroxide across the spin crossover under extreme conditions

Spin transition and its effect on the physical properties of iron-bearing minerals at high pressure-temperature $(P\text{\ensuremath{-}}T)$ are of great importance for understanding the structural heterogeneity of Earth's mantle. Here, we investigate the phase diagram and thermoelastic properties of iron oxyhydroxide (FeOOH) across the spin crossover using dynamic high $P\text{\ensuremath{-}}T$ experiments and theoretical simulations. The Hugoniot equation of state in FeOOH has been measured up to $\ensuremath{\sim}90$ GPa and $\ensuremath{\sim}2100$ K in a two-stage light-gas gun and exhibits a density discontinuity between 47 GPa (\ensuremath{\sim}950 K) and 61 GPa (\ensuremath{\sim}1150 K) due to the high-low spin transition of ${\mathrm{Fe}}^{3+}$, which is consistent with our first-principles calculations. The $P\text{\ensuremath{-}}T$ phase diagram indicates that the shock-elevated temperature shifts the spin transition to a higher pressure and broadens the pressure range of mixed spins. The large volume collapse of FeOOH during its spin crossover leads to remarkable elastic anomalies, with \ensuremath{\sim}60% softening of adiabatic bulk modulus and a negative Poisson's ratio (\ensuremath{-}0.1) of abnormal auxeticity in the mixed-spin phase. Our results suggest that FeOOH undergoes an unselective spin transition of ferric iron at the corresponding $P\text{\ensuremath{-}}T$ conditions of the Earth's 1400--1800 km depth and exhibits drastic softening in sound velocities and elastic modulus which may be detected as seismic heterogeneities in subducting slabs of the lower mantle.

An improved multiphase SPH algorithm with kernel gradient correction for modelling fuel–coolant interaction

Fuel–coolant interaction (FCI) has a pivotal role in the development of core disruptive accident in a sodium-cooled fast reactor. The drastic deformation of multiphase interface in the FCI is hard to deal with in the traditional grid method. In this paper, an improved multiphase smoothed particle hydrodynamics (SPH) algorithm corrected with the kernel gradient correction (KGC) technique is presented for multiphase flow with a large density ratio and complex interfacial behaviors. The density discontinuity across the multiphase interface is described with the use of special volume, which only depends on the position information of adjacent particles. This multiphase SPH algorithm, which is troubled by an unstable and mixed-interface problem under a large density ratio, is significantly improved with the KGC technique. The accuracy and robustness of the improved method are demonstrated in the numerical simulations of the deformation of a square droplet, Rayleigh–Taylor instability, and bubble rising in water. The verified corrected multiphase SPH is applied to simulate the hydrodynamic behaviors of the general FCI and the interaction between fuels coated with stainless steel film and coolant. Boundary layer stripping, Rayleigh–Taylor instability, and Kelvin–Helmholtz instability are observed as important mechanisms of hydraulic fracturing. The fragments’ distribution and the influence of stainless steel film are analyzed. The existence of a stainless steel film has been shown to inhibit breakage.

Numerical study of the Roberge-Weiss transition

We study the Roberge-Weiss phase transition numerically. The phase transition is associated with the discontinuities in the quark-number density at specific values of imaginary quark chemical potential. We parameterize the quark number density $\rho_q$ by the polynomial fit function to compute the canonical partition functions. We demonstrate that this approach provides a good framework for analyzing lattice QCD data at finite density and a high temperature. We show numerically that at high temperature, the Lee-Yang zeros lie on the negative real semi-axis provided that the high-quark-number contributions to the grand canonical partition function are taken into account. These Lee-Yang zeros have nonzero linear density, which signals the Roberge-Weiss phase transition. We demonstrate that this density agrees with the quark density discontinuity at the transition line.

Interacting moving bottlenecks in traffic flow

<abstract><p>We present a general multi-scale approach for modeling the interaction of controlled autonomous vehicles (AVs) with the surrounding traffic flow. The model consists of a scalar conservation law for the bulk traffic, coupled with ordinary differential equations describing the possibly interacting AV trajectories. The coupling is realized through flux constraints at the moving bottleneck positions, inducing the formation of non-classical jump discontinuities in the traffic density. In turn, AVs are forced to adapt their speed to the downstream traffic average velocity in congested situations. We analyze the model solutions in a Riemann-type setting, and propose an adapted finite volume scheme to compute approximate solutions for general initial data. The work paves the way to the study of general optimal control strategies for AV velocities, aiming at improving the overall traffic flow by reducing congestion phenomena and the associated externalities.</p></abstract>

A new cylindrical detector for borehole muon radiography

Muons of cosmic origin have a great capability to penetrate through matter. This property is exploited in muon radiography, also known as muography, a technique which allows to highlight the presence of discontinuities of the mass density in the subsoil such as cavities, tunnels or rock masses. A detector of cylindrical geometry, optimized for borehole studies and with a diameter of 24 cm, was developed and tested . The scintillation light is read out by 384 Silicon Photomultipliers, directly coupled to the bars. The front-end and acquisition electronics, entirely housed inside the detector, are based on the EASIROC chip and are characterized by limited energy consumption (about 30 W for the entire detector). The detector has been designed in such a way as to simplify its construction as much as possible for its eventual mass production. In this article some details concerning the construction and preliminary results of measurements conducted in the Mt Echia (Naples, Italy) underground are presented.

On a Guiding of Whistler‐Mode Waves by Density Gradients

AbstractObservations from satellites demonstrate that in the magnetosphere, VLF whistler‐mode waves are frequently detected in the narrow transition regions, where the plasma density changes its magnitude over a short distance across the ambient magnetic field. These observations suggest that the small‐scale, isolated density gradients can guide the VLF whistler‐mode waves along the field. We investigate the guiding of the whistler‐mode waves by the transverse density gradients with a size much less than the characteristic perpendicular size of the wave. We found analytical solutions describing these waves in the plasma with a sharp density discontinuity between two homogeneous regions, and confirm with time‐dependent, two‐dimensional simulations that these waves are indeed guided by the discontinuity. Simulations also reveal that the parameters of the guided waves (the frequency and parallel wavelength) relate to the parameters of the plasma.

MPS-based axisymmetric particle method for bubble rising with density and pressure discontinuity

Numerical simulation of gas bubble rising in liquid is challenging due to high density and viscosity ratios. This study proposes to model the liquid and gas phases separately by the incompressible and Weakly Compressible Moving Particle Semi-implicit (MPS) methods with the aim of preserving the interfacial discontinuity. The liquid-gas interface is explicitly represented by a series of discrete nodes. By adequately enforcing the stress conditions on these moving interface nodes, the MPS and WC-MPS methods are coupled. The surface tension is considered as a pressure jump rather than the volume force. Without applying any smoothing or averaging scheme, the density, viscosity and pressure are discontinuous across the interface. The axisymmetric formulation is directly introduced based on the least squares method to save computational cost. In addition, a multi-time step algorithm is proposed so that independent time increments can be adopted for different phases. Furthermore, the particle shifting technique is extended to control the multi-spatial resolution dynamically. Several numerical tests, including hydrostatic pressure problems, droplet deformation and bubble rising benchmark are conducted to show the accuracy, efficiency and stability. Finally, validations are performed using experimental results with wide ranges of Reynolds number and Bond number, which dominate the bubble shape.