Density Evolution Research Articles

Emergence of condensation patterns in kinetic equations for opinion dynamics

In this work, we define a class of models to understand the impact of population size on opinion formation dynamics, a phenomenon usually related to group conformity. To this end, we introduce a new kinetic model in which the interaction frequency is weighted by the kinetic density. In the quasi-invariant regime, this model reduces to a Kaniadakis–Quarati-type equation with nonlinear drift, originally introduced for the dynamics of bosons in a spatially homogeneous setting. From the obtained PDE for the evolution of the opinion density, we determine the regime of parameters for which a critical mass exists and triggers blow-up of the solution. Therefore, the model is capable of describing strong conformity phenomena in cases where the total density of individuals holding a given opinion exceeds a fixed critical size. In the final part, several numerical experiments demonstrate the features of the introduced class of models and the related consensus effects.

An improved solution of the probability density evolution equation for analyzing stochastic structural responses with adaptive time steps and initial conditions

The probability density evolution method (PDEM) offers an innovative approach for analyzing the stochastic vibration responses of structures. Given the complexities inherent in real-world challenges, the probability density evolution equations (PDEE) often require numerical methods for effective resolution. Consequently, improving computational efficiency and solution accuracy is of paramount importance. Currently, the impulse function discretization method (IFDM) faces several challenges, including limited differentiability in the spatial direction for initial value conditions. Furthermore, the probability density function produced by this method frequently deviates significantly from the true value, undermining the accuracy of the PDEE. Additionally, when addressing vibration responses characterized by rapid evolutionary velocities, the use of a globally fixed uniform time step size (FUTSS) results in a marked decrease in computational efficiency. To tackle these challenges, this study introduces an improved probability density evolution method (IPDEM), which integrates the Gaussian kernel density estimation discretization method (GKDEDM) and an adaptive non-uniform time step size (ANUTSS). The advantages of the IPDEM are illustrated through two numerical simulation examples. The findings indicate that the GKDEDM not only enhances spatial differentiability but also provides a more accurate estimation of the probability density at the initial moment, thereby improving the accuracy of the PDEE. Furthermore, the ANUTSS significantly reduces the number of iterations required while preserving precision, leading to a substantial optimization of computation time.

An efficient dynamic reliability method for maglev vehicle-bridge systems and its application in random controller parameters analysis

This article presents an efficient method for analyzing the dynamic reliability of maglev vehicle-bridge coupled systems by combining a theoretical model with an adaptive surrogate model and the probability density evolution method (PDEM). First, a refined theoretical model of a maglev vehicle-bridge coupling system is established. Next, an adaptive surrogate model of the equivalent extreme value of the system dynamic response is established by combining an adaptive sampling method with radial basis functions. Finally, the adaptive surrogate model and PDEM are combined to further improve the efficiency of the dynamic reliability analysis. In the numerical example, the theoretical model of the maglev vehicle-guideway system was first validated by comparing with the measured data from the Shanghai high-speed maglev line. Then, by treating the controller parameters as normally distributed random variables, the accuracy and efficiency of the proposed reliability method were verified through comparison with the Monte Carlo method and the one-stage sampling surrogate model. Additionally, the impact of the randomness of each controller parameter and the coefficient of variation of the controller parameters on the system’s dynamic reliability was discussed.

Subgrain Size Modeling and Substructure Evolution in an AA1050 Aluminum Alloy during High-Temperature Compression.

For materials with high stacking fault energy (SFE), such as aluminum alloys, dynamic recovery (DRV) and dynamic recrystallization (DRX) are essential softening mechanisms during plastic deformation, which lead to the continuous generation and refinement of newborn subgrains (2° ˂ misorientation angle ˂ 15°). The present work investigates the influence of compression parameters on the evolution of the substructures for a 1050 aluminum alloy at elevated temperatures. The alloy microstructure was investigated under deformation temperatures ranging from 300 °C to 500 °C and strain rates from 0.01 to 0.1 s-1, respectively. A well-defined substructure and subsequent subgrain refinement provided indication of the evolution laws of the substructure under high-temperature compression. Corresponding experimental data on the average subgrain size under various compression conditions were obtained. Two different independent average subgrain size evolution models (empirical and substructure-based) were used and applied with several internal state variables. The substructure model employed physical variables to simulate subgrain refinement and thermal coarsening during deformation, incorporating a corresponding dislocation density evolution model. The correlation coefficient (R) and root mean square error (RMSE) of the substructure-based model were calculated to be 0.98 and 5.7%, respectively. These models can provide good estimates of the average subgrain size, with both predictions and experiments reproducing the expected subgrain size evolution using physically meaningful variables during continuous deformation.

Forward J/ψ+J/ψ and J/ψ+ψ′ production with high-energy factorization

We calculate the cross sections of associated J/ψ+ψ′ and J/ψ+J/ψ production in pp collisions at s=13 TeV in the forward kinematic region. The high-energy factorization (kT-factorization) framework supplemented with the Catani-Ciafaloni-Fiorani-Marchesini evolution of gluon densities in a proton is applied. We demonstrate that the latest data on J/ψ+J/ψ production and first experimental data on J/ψ+ψ′ events taken very recently by the LHCb Collaboration can be described well by the color singlet terms and contributions from double parton scattering (DPS) with the standard choice for σeff parameter. The relative production rate σ(J/ψ+ψ′)/σ(J/ψ+J/ψ) is found to be sensitive to the DPS terms as well as to feeddown contributions. Published by the American Physical Society 2024

Exploring grain size influence on tensile behavior of 316 H austenitic stainless steel at high temperature: A phenomenological dislocation model

The high temperature mechanical behavior of 316 H austenitic stainless steel with different grain size was investigated in this study through the use of a novel phenomenological dislocation model finite element method. The study was conducted by producing steel specimens with varying grain sizes through adjustments in annealing temperature and time, followed by high temperature tensile tests at 550°C. The finite element method, when integrated with a phenomenological dislocation model that considers grain size parameters, effectively captured the mechanical response under different grain size conditions. Additionally, the two-variable Kocks-Mecking(KM) model accurately captured the grain size effect in 316 H austenitic steel and effectively depicted its tensile flow behavior. The model’s predictions were based on the evolution of forest dislocation density and mobile dislocation density, proving to be a reliable tool for analyzing the microstructural evolution of 316 H austenitic steel specimens with varying grain sizes. This study provides insight into the effect of grain size on the high temperature strength of austenitic stainless steels and demonstrates the utility of a novel phenomenological model finite element method for predicting the mechanical behavior of polycrystalline materials.

Electrosynthesis of adipic acid with high faradaic efficiency within a wide potential window

Electrosynthesis of adipic acid (a precursor for nylon-66) from KA oil (a mixture of cyclohexanone and cyclohexanol) represents a sustainable strategy to replace conventional method that requires harsh conditions. However, its industrial possibility is greatly restricted by the low current density and competitive oxygen evolution reaction. Herein, we modify nickel layered double hydroxide with vanadium to promote current density and maintain high faradaic efficiency (>80%) within a wide potential window (1.5 ~ 1.9 V vs. reversible hydrogen electrode). Experimental and theoretical studies reveal two key roles of V modification, including accelerating catalyst reconstruction and strengthening cyclohexanone adsorption. As a proof-of-the-concept, we construct a membrane electrode assembly, producing adipic acid with high faradaic efficiency (82%) and productivity (1536 μmol cm−2 h−1) at industrially relevant current density (300 mA cm−2), while achieving >50 hours stability. This work demonstrates an efficient catalyst for adipic acid electrosynthesis with high productivity that shows industrial potential.

Redshift-dependent galaxy formation efficiency at z = 5 − 13 in the FirstLight Simulations

Context. Some models of the formation of first galaxies predict low masses and faint objects at extremely high redshifts, z ≃ 9 − 15. However, the first observations of this epoch indicate a higher-than-expected number of bright (sometimes massive) galaxies. Aims. Numerical simulations can help to elucidate the mild evolution of the bright end of the UV luminosity function and they can provide the link between the evolution of bright galaxies and variations of the galaxy formation efficiency across different redshifts. Methods. We use the FirstLight database of 377 zoom-in cosmological simulations of a volume- and mass-complete sample of galaxies. Mock luminosities are estimated by a dust model constrained by observations of the β–MUV relation at z = 6 − 9. Results. FirstLight contains a high number of bright galaxies, MUV ≤ −20, consistent with current data at z = 6 − 13. The evolution of the UV cosmic density is driven by the evolution of the galaxy efficiency and the relation between MUV and halo mass. The efficiency of galaxy formation increases significantly with mass and redshift. At a fixed mass, galactic halos at extremely high redshifts convert gas into stars at a higher rate than at lower redshifts. The high gas densities in these galaxies enable high efficiencies. Our simulations predict higher number densities of massive galaxies, M* ≃ 109 M⊙, than other models with constant efficiency. Conclusions. Cosmological simulations of galaxy formation with detailed models of star formation and feedback can reproduce the different regimes of galaxy formation across cosmic history.

Reconciling cosmological tensions with inelastic dark matter and dark radiation in a U(1) D framework

We propose a novel and comprehensive particle physics framework that addresses multiple cosmological tensions observed in recent measurements of the Hubble parameter, S 8, and Lyman-α forest data. Our model, termed `SIDR+z t ' (Self Interacting Dark Radiation with transition redshift), is based on an inelastic dark matter (IDM) scenario coupled with dark radiation, governed by a U(1) D gauge symmetry. This framework naturally incorporates cold dark matter (DM), strongly interacting dark radiation (SIDR), and the interactions between these components. The fluid-like behavior of the dark radiation component which originates from the self-quartic coupling of the U(1) D breaking scalar can suppress the free-streaming effects. Simultaneously, the interacting DM-DR system can attenuate the matter power spectrum at small scales. The inelastic nature of DM provides a distinct temperature dependence for the DM-DR interaction rate determined by the mass-splitting between the inelastic dark fermions which is crucial for resolving the Ly-α discrepancies. We present a cosmologically consistent analysis of the model by solving the relevant Boltzmann equations to obtain the energy density and number density evolution of different species of the model. The DR undergoes two “steps” of increased energy density when the heavier dark species freeze out and become non-relativistic, transferring their entropy to the dark radiation and enhancing ΔN eff. The analysis showcases the model's potential to uphold the Big Bang Nucleosynthesis (BBN) prediction of ΔN eff but dominantly producing additional contributions prior to recombination, while simultaneously achieving correct relic density of DM though an hybrid of freeze-in and non-thermal production.

A local fractional modified Crank–Nicolson scheme for fractal LWR model of traffic flow

This research proposes a modified Crank–Nicolson finite difference scheme with local fractional derivatives to approximate the solutions of local fractional LWR traffic flow model. The stability and consistency of the scheme are examined. Further, convergence of the scheme is assured by using Lax’s equivalence theorem. Some exemplary instances are discussed along with their simulations to validate the proposed method. The obtained numerical solutions show the dynamical evolution of traffic density with respect to time and space. The results derived using the proposed numerical scheme establish that they are quite effective in obtaining the numerical solution to the fractal vehicular traffic flow problem.

An approximate decoupled reliability-based design optimization method for efficient design exploration of linear structures under random loads

Reliability-based design optimization (RBDO) provides a promising approach for achieving effective structural designs while explicitly accounting for the effects of uncertainty. However, the computational demands associated with RBDO, often due to its nested loop nature, pose significant challenges, thereby impeding the application of RBDO for decision-making in real-world structural design. To alleviate this issue, an approximate decoupled approach is introduced for a class of RBDO problems involving linear truss structures subjected to random excitations, with the failure event defined by compliance. This contribution aims to provide an approximate but efficient way for design exploration to facilitate decision-making during the initial design phase. Specifically, the proposed approach converts the original RBDO problem into a deterministic optimization problem through a modest number of reliability analyses by the probability density evolution method (PDEM). Once the deterministic optimization problem is obtained, the solution of the whole RBDO problem can be obtained by solving this equivalent problem without further reliability analysis, resulting in notable enhancement in terms of computational efficiency. In this way, this contribution expands the frontier of application of the operator norm theory within the RBDO framework. Numerical examples are conducted to illustrate the effectiveness and capabilities of the proposed approach.

JWST PRIMER: a new multifield determination of the evolving galaxy UV luminosity function at redshifts z ≃ 9 – 15

ABSTRACT We present a new determination of the evolving galaxy ultraviolet (UV) luminosity function (LF) over the redshift range $8.5< z< 15.5$ using a combination of several major Cycle-1 JWST imaging programmes – Public Release IMaging for Extragalactic Research, JWST Advanced Deep Extragalactic Survey, and Next Generation Deep Extragalactic Exploratory Public Survey. This multifield approach yields a total of $\simeq 370$ arcmin2 of JWST/NIRCam imaging, reaching (5-$\sigma$) depths of $\simeq 30$ AB mag in the deepest regions. We select a sample of 2548 galaxies with a significant probability of lying at high redshift ($p(z> 8.5)> 0.05$) to undertake a statistical calculation of the UV LF. Our new measurements span $\simeq 4$ mag in UV luminosity at $z=9-12.5$, placing new constraints on both the shape and evolution of the LF at early times. Our measurements yield a new estimate of the early evolution of cosmic star-formation rate density ($\rho _{\rm {SFR}}$) confirming the gradual decline deduced from early JWST studies, at least out to $z \simeq 12$. Finally we show that the observed early evolution of the galaxy UV LF (and $\rho _{\rm {SFR}}$) can be reproduced in a ${\rm \Lambda }$cold dark matter Universe, with no change in dust properties or star-formation efficiency required out to $z \simeq 12$. Instead, a progressive trend towards younger stellar population ages can reproduce the observations, and the typical ages required at $z \simeq$ 8, 9, 10, and 11 all converge on $\simeq 380-330$ Myr after the big bang, indicative of a rapid emergence of early galaxies at $z \simeq 12 - 13$. This is consistent with the first indications of a steeper drop-off in $\rho _{\rm {SFR}}$ we find beyond $z \simeq 13$, possibly reflecting the rapid evolution of the halo mass function at earlier times.

Microstructure-Based Flow Stress Model to Predict Machinability of Inconel 718.

Due to its exceptional mechanical and chemical properties at high temperatures, Inconel 718 is extensively utilized in industries such as aerospace, aviation, and marine. Investigating the flow behavior of Inconel 718 under high strain rates and high temperatures is vital for comprehending the dynamic characteristics of the material in manufacturing processes. This paper introduces a physics-based constitutive model that accounts for dislocation motion and its density evolution, capable of simulating the plastic behavior of Inconel 718 during large strain deformations caused by machining processes. Utilizing a microstructure-based flow stress model, the machinability of Inconel 718 in terms of cutting forces and temperatures is quantitatively predicted and compared with results from orthogonal cutting experiments. The model's predictive precision, with a margin of error between 5 and 8%, ensures reliable consistency and enhances our comprehension of the high-speed machining dynamics of Inconel 718 components.

Modeling the thermo-oxidative aging effects on fatigue life of natural rubber using a continuum damage mechanics approach

Thermo-oxidative aging (TOA) significantly impacts the fatigue life of rubbers by reducing the fatigue strength and modifying the slope of the Wöhler curve, rendering traditional time-temperature superposition methods inadequate. In this work, we aim to develop a model capable of predicting the effect of TOA on the fatigue properties of rubbers. For this purpose, dumbbell specimens of natural rubber (NR) were subjected to aging in an air-vented oven at different temperatures prior to mechanical testing. Tensile tests were conducted to quantify the aging effects on a microscale network parameter known as elastically active chains (EAC) density, along with determining ultimate properties such as the stress and strain at break. By using a time-temperature equivalence and the Arrhenius shift factor, master curves were constructed for both EAC density and ultimate properties. Subsequently, the fracture properties of the aged material were predicted using an energy limiter approach whose evolution follows that of EAC density. Furthermore, a relationship between the parameters of the continuum damage mechanics (CDM) approach (specifically, the power law parameters of the Wöhler curve) and the fracture properties was proposed, resulting in accurate estimates of the fatigue life regardless of the aging conditions. Satisfactory agreement was observed between the model predictions and the data for nine aging conditions encompassing four different temperatures. The CDM approach also allows assessing the evolution of mechanical damage within the material influenced by TOA. The novelty of this approach lies in establishing a direct relationship between fatigue and fracture properties. Moreover, this is the first time to the best of our knowledge that TOA has been explicitly incorporated into a fatigue life prediction model via the evolution of the EAC density.

Electronic structure, absorption spectra and oxidation dynamics in polyynes and dicyanopolyynes.

The advent of femtosecond to attosecond experimental tools has made now possible to study such ultrafast carrier dynamics, e.g., the spatial and temporal charge density evolution, after an initial oxidation or reduction in molecules, candidates for atomic wires like polyynes and dicyanopolyynes. Here, we study the electronic structure and hole transfer in symmetric molecules containing carbon, nitrogen and hydrogen, the first members in the series of polyynic carbynes and dicyanopolyynes, using methods based on density functional theory (DFT): constrained DFT (CDFT), time-dependent DFT (TDDFT) and real-time TDDFT (RT-TDDFT), with Löwdin population analysis, comparing many levels of theory and obtaining convergence of the results. For the same purposes, we develop a tight binding (TB) variant using all valence orbitals of all atoms. This TB variant is applied here in linear molecules, but it is also adequate for electronic structure, charge transfer and charge transport of non-linear molecules and clusters of molecules. We calculate the electronic structure, the time-dependent dipole moment and the probabilities of finding the hole at each site, their mean over time values, the mean transfer rates from the oxidation site to other sites and the frequency content (using charge as well as dipole moment oscillations). We take into account zero-point motion. The initial conditions for RT-TDDFT are obtained by CDFT. For TB, we explore different initial conditions: we place the hole at a particular orbital or distribute it among a number of orbitals; it is also possible to include phase differences between orbitals. Finally, we compare with available experimental data.

Dynamic reliability and seismic fragility analysis for high concrete-faced rockfill dam slopes subjected to stochastic earthquake and parameter excitation via PDEM

The randomness of material parameters and earthquake excitation greatly impacts the seismic stability of high concrete-faced rockfill dam (CFRD) slopes. However, no research has comprehensively analyzed the impacts of stochastic earthquake excitations, random parameters and their coupled effects on seismic stability of CFRD slopes and selected a multi-indicator evaluation criterion to carry out performance-based safety assessment. This paper develops a novel and comprehensive framework for evaluating the seismic stability of CFRD slopes based on the generalized probability density evolution method (GPDEM) with high efficiency and accuracy. The effects of three kinds of randomness on seismic stability of CFRD slopes were comprehensively compared and analyzed on the basis of multi-indices (safety factor (FS), cumulative slip displacement and cumulative time with FS < 1.0). Firstly, the nonlinear shear strength parameters of 40 high CFRDs were statistically collected to obtain the statistical characteristics of rockfill material strength parameters of actual CFRD projects. Secondly, three kinds of random samples were generated using generalized F-discrepancy (GF-discrepancy) method and Spectral expression-Random function (SERF) method. Then, the GPDEM was introduced to combine with three indices to perform the stochastic analysis and reliability evaluation. Finally, the fragility analysis of the CFRD slope was conducted. The results reveal that FS is more sensitive to the ground motions randomness, while cumulative slip displacement and cumulative time with FS < 1.0 are more sensitive to the material parameters randomness. The seismic safety evaluation of CFRD slopes based on multiple indices with full consideration of coupled randomness effects is necessary.

Evolutionary distribution and mode transition in medium frequency from 50 kHz to 5 MHz of argon atmospheric pressure dielectric barrier discharge plasma

Dielectric barrier discharges (DBDs) provide a promising technology for generating non-equilibrium cold plasmas at atmospheric pressure. For both application-focused and fundamental research, it is important to explore the discharge mode transition and electron heating mechanism to enable effective independent tuning of key plasma parameters in a DBD system. In this work, we report numerical studies of the effects of single-frequency excitation on atmospheric argon DBDs, which are carried out in the medium driving frequency (MF) range from 50 kHz to 5 MHz by using a one-dimensional hydrodynamics coupling model. The spatio-temporal evolution of particle density associated with the discharge mode transition and electron dynamic behavior has been investigated. By tuning different components of a single frequency, we observe the electron heating behaviors of the individual modes and mode transitions from the Townsend discharge to the glow discharge in the low frequency to the Ω mode and the hybrid mode in the medium frequency to the α-mode and the γ-mode in the radio frequency. The physical analysis is understood based on these fundamental insights into the plasma physics.

Investigation on the propagation of uncertainties of a timber floor under human excitation

Due to the characteristics of high stiffness-weight ratio, timber floors are prone to annoying vibrations under human excitation. Given the natural origin of timber, its mechanical properties exhibit significant variability. The randomness inherent in human excitation cannot be overlooked during structural dynamic analysis. Consequently, the adoption of a stochastic approach is imperative for attaining reliable serviceability evaluation results. However, current research on human-induced vibrations in the timber floor, accounting for this randomness, remains inadequate. In this paper, an experimental investigation is conducted on the dynamic properties and human-induced responses of a timber floor composed of glued laminated timber and oriented strand board. A finite element model is developed and subsequently validated for accuracy in terms of modal properties and dynamic responses. The probability density evolution method is introduced for stochastic analysis, which demonstrates that both the natural frequency and dynamic responses of the floor exhibit considerable variability when uncertainty factors are considered. The Kullback–Leibler divergence indices are used to assess the impact of each uncertain variable quantitatively. The results indicate that the longitudinal elastic modulus has the greatest influence on the natural frequency, while the first dynamic load factor, αz1, exerts the most significant impact on dynamic responses. Notably, both material mechanical properties and load model parameters contribute to the uncertainty of dynamic responses, with the influence of the load model parameters being significantly greater than that of material mechanical properties.

Cover Image, Volume 62, Issue 16

The cover image is based on the Article Sintering evolution monitoring of ultra‐highmolecular‐weight polyethylene by Ying Zhou et al., https://doi.org/10.1002/pol.20230156. The cover image by Ying Zhou shows a density evolution analysis utilized to monitor the volume change during the sintering process of UHMWPE nascent powder. The analysis reveals substantial densification of the powder under pressure during heating, followed by notable density drops known as the melt explosion phenomenon. Subsequent crystallization leads to the formation of a contiguous solid UHMWPE structure within a relatively short timeframe and at moderate temperatures. image

Tracking surface charge dynamics on single nanoparticles.

Surface charges play a fundamental role in physics and chemistry, in particular in shaping the catalytic properties of nanomaterials. However, tracking nanoscale surface charge dynamics remains challenging due to the involved length and time scales. Here, we demonstrate time-resolved access to the nanoscale charge dynamics on dielectric nanoparticles using reaction nanoscopy. We present a four-dimensional visualization of the spatiotemporal evolution of the charge density on individual SiO2 nanoparticles under strong-field irradiation with femtosecond-nanometer resolution. The initially localized surface charges exhibit a biexponential redistribution over time. Our findings reveal the influence of surface charges on surface molecular bonding through quantum dynamical simulations. We performed semi-classical simulations to uncover the roles of diffusion and charge loss in the surface charge redistribution process. Understanding nanoscale surface charge dynamics and its influence on chemical bonding on a single-nanoparticle level unlocks an increased ability to address global needs in renewable energy and advanced health care.