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Thermal energy storage and utilization has been widely concerned due to the intermittency, renewability, and economy of renewable energy. In this paper, the potential energy function of binary Na2CO3–K2CO3 salt was first constructed using the Deep Potential GENerator (DPGEN) enhanced sampling method. Deep potential molecular dynamics simulations were performed to calculate the thermal properties and structural evolution of binary carbonates. The results show that as the temperature increases from 1073 to 1273 K, the viscosity and thermal conductivity decrease from 5.011 mPa s and 0.502 W/(m K) to 2.526 mPa s and 0.481 W/(m K), respectively. The decrease in viscosity is related to the distance and interaction between the molten salt ions. In addition, the diffusion coefficients, energy barriers, ionic radius, angular distribution function, and coordination number of molten salt were calculated and analyzed. The CO32− exhibits a stable planar triangular structure. The ionic radius of Na+ is smaller than that of K+, which makes Na+ suffer less spatial hindrance during motion and has a higher diffusion coefficient. The energy barriers that Na+ needs to overcome to escape the Coulomb force is greater than that of K+ ions, so molten salt containing Na+ may possess greater heat storage potential. We believe that the potential function constructed with DPGEN enhanced sampling strategy can provide more convincing results for predicting the thermal properties of molten salts. This paper aims to provide a technical route to develop the novel complex molten salt phase change material for thermal energy storage. [ABSTRACT FROM AUTHOR]

A preceding paper [M. Dhar, J. A. Dickinson, and M. A. Berg, J. Chem. Phys. 159, 054110 (2023)] shows how to remove additive noise from an experimental time series, allowing both the equilibrium distribution of the system and its Green's function to be recovered. The approach is based on nonlinear-correlation functions and is fully nonparametric: no initial model of the system or of the noise is needed. However, single-molecule spectroscopy often produces time series with either photon or photon-counting noise. Unlike additive noise, photon noise is signal-size correlated and quantized. Photon counting adds the potential for bias. This paper extends noise-corrected-correlation methods to these cases and tests them on synthetic datasets. Neither signal-size correlation nor quantization is a significant complication. Analysis of the sampling error yields guidelines for the data quality needed to recover the properties of a system with a given complexity. We show that bias in photon-counting data can be corrected, even at the high count rates needed to optimize the time resolution. Using all these results, we discuss the factors that limit the time resolution of single-molecule spectroscopy and the conditions that would be needed to push measurements into the submicrosecond region. [ABSTRACT FROM AUTHOR]

This paper presents the design of a single-phase solid phononic crystal (PnC) structure featuring a regular hexagonal perforation pattern. The structure manifests three negative refraction bands, encompassing one for transverse waves and two for longitudinal waves, thereby enabling simultaneous control of shear and longitudinal waves. Due to the high symmetry of the triangular lattice, the equal frequency curves corresponding to the negative refraction band approach circular shapes, suggesting a nearly isotropic negative refraction effect. This negative refraction effect is achieved through specific mass resonance modes closely related to the porous structure designed in this paper. Initially, we analyze the band structure of the PnC, followed by designing the PnC plate structure to achieve negative refraction control for transverse waves at a frequency of 32.4 kHz, with a negative refraction index of −1. Additionally, negative refraction control for longitudinal waves is attained at frequencies of 44 and 64.54 kHz. Subsequently, we scrutinize the influence of various conditions on negative refraction, including different structural parameters, incident angles, and operating frequencies, while verifying the robustness of the designed phonon crystal structure. Leveraging the negative refraction characteristics of the structure, we construct an elastic wave lens to achieve perfect imaging of shear and longitudinal waves. Finally, employing finite element simulation and analyzing focusing imaging characteristics with different source positions, we validate that the results closely align with theoretical expectations. The solid PnC structure designed in this study holds significant potential for applications in the fields of elastic wave imaging. [ABSTRACT FROM AUTHOR]

The superadiabatic dynamical density functional theory (superadiabatic-DDFT) is a promising new method for the study of colloidal systems out-of-equilibrium. Within this approach, the viscous forces arising from interparticle interactions are accounted for in a natural way by explicitly treating the dynamics of the two-body correlations. For bulk systems subject to spatially homogeneous shear, we use the superadiabatic-DDFT framework to calculate the steady-state pair distribution function and the corresponding viscosity for low values of the shear-rate. We then consider a variant of the central approximation underlying this superadiabatic theory and obtain an inhomogeneous generalization of a rheological bulk theory due to Russel and Gast. This paper thus establishes for the first time a connection between DDFT approaches, formulated to treat inhomogeneous systems, and existing work addressing nonequilibrium microstructure and rheology in bulk colloidal suspensions. [ABSTRACT FROM AUTHOR]

Piezoelectric semiconductor (PS) materials have attracted much attention in recent years due to their unique properties. This paper explores the electromechanical coupling behavior of bent piezoelectric semiconductor fibers with non-uniform cross-sectional areas. The study uses the generalized differential quadrature method to numerically solve the field equations with variable coefficients derived from piezoelectric theory. The research examines the mechanical and electrical field distribution of bent variable cross-sectional fibers, comparing the performances of non-uniform fibers with different profiles. The study reveals that the variable cross-sectional profile of the fiber changes the characteristic of the uniform fiber's electrical distribution along the axis, and it exhibits a more sensitive and stronger electrical response to the same external force. The research also shows that the concavity and convexity of the radius distribution function of the non-uniform fibers determine whether there are extreme points of surface potential. Finally, the study suggests that by designing extreme points of the PS fiber profile, surface potential extreme points can be artificially created at the same location. These results offer a theoretical direction for creating advanced piezoelectric semiconductor nanodevices and present novel insights into designing higher-efficiency nanogenerators and mechanical strain sensors in the future. [ABSTRACT FROM AUTHOR]

Data-driven turbulence modeling has been extensively studied in recent years. To date, only high-fidelity data from the mean flow field have been used for Reynolds-averaged Navier–Stokes (RANS) modeling, while the instantaneous turbulence fields from direct numerical simulation and large eddy simulation simulations have not been utilized. In this paper, a new framework is proposed to augment machine learning RANS modeling with features extracted from instantaneous turbulence flow data. A conditional generative model is trained to model the probability distribution of the local instantaneous turbulence field given local mean flow features. Then, the generative model is transferred to machine learning RANS modeling. The present work is mainly focused on generating a local instantaneous turbulence field using conditional generative adversarial networks (CGANs). Several GANs are trained first on the turbulence data from channel flow and periodic hill flow to generate complete one-dimensional and two-dimensional turbulence fields. Then, a CGAN is trained on the periodic hill flow data to generate local turbulence fields. Statistical analysis is performed on the generated samples from the GAN models. The first and second moments, the two-point correlation, and the energy spectra conform well to those of real turbulence. Finally, the information learned by the CGAN is used for machine learning RANS modeling by multitask learning, and the feasibility of the framework proposed in this paper is initially verified. [ABSTRACT FROM AUTHOR]

The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. For filaments in the low-temperature limit and under a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed state to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression. We determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates this transition. We find that the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble, the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show that the theory is highly sensitive to fluctuations in length in two dimensions and the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts. [ABSTRACT FROM AUTHOR]

Sets of saddle equilibria connected by trajectories are known as heteroclinic networks. Trajectories near a heteroclinic network typically spend a long period of time near one of the saddles before rapidly transitioning to the neighborhood of a different saddle. The sequence of saddles visited by a trajectory can be considered a stochastic sequence of states. In the presence of small-amplitude noise, this sequence may be either Markovian or non-Markovian, depending on the appearance of a phenomenon called lift-off at one or more saddles of the network. In this paper, we investigate how lift-off occurring at one saddle affects the dynamics near the next saddle visited, how we might determine the order of the associated Markov chain of states, and how we might calculate the transition probabilities of that Markov chain. We first review methods developed by Bakhtin to determine the map describing the dynamics near a linear saddle in the presence of noise and extend the results to include three different initial probability distributions. Using Bakhtin's map, we determine conditions under which the effect of lift-off persists as the trajectory moves past a subsequent saddle. We then propose a method for finding a lower bound for the order of this Markov chain. Many of the theoretical results in this paper are only valid in the limit of small noise, and we numerically investigate how close simulated results get to the theoretical predictions over a range of noise amplitudes and parameter values. [ABSTRACT FROM AUTHOR]

This paper investigates the optimization of the inner thermal layout in nanofluid-filled horizontal annular pipes under natural convection conditions. Two-dimensional models of annular pipes are established using a numerical simulation approach. Then, using this as the simulation tool, the layouts of single-, triple-, and quadruple-heat-source annular pipes are optimized. The coordinates of the inner cylinders are defined as the decision variables, and the average Nusselt number (Nu) on the cold wall surface as the objective function. For the single-cylinder model, both the Bayesian optimization algorithm (BOA) and the genetic algorithm (GA) derive the same results: an axisymmetric layout where the single heat source is positioned slightly above the axis of the annulus. However, the BOA takes much less computational time than the GA and, consequently, is chosen for cases with more complex geometry. The optimization layout of the three-cylinder model also shows an axisymmetric distribution, while the result for the four-cylinder model presents a centrally symmetric distribution. Compared to the original average Nu, the optimized ones are enhanced by 17.83%, 8.36%, and 6.18% for single-, triple-, and quadruple-heat-source annular pipes, respectively. The results of this study can be used for guiding the layout design and optimization of the nanofluid-filled exchangers with multi-inner heat sources. [ABSTRACT FROM AUTHOR]

Impedance spectroscopy experiments are able to reveal the fundamental charge transport properties of a wide variety of complex disordered and nano-structured materials provided that appropriate modeling tools are used. In this paper, we present a numerical simulation-based approach to model the dynamical conductivity of networks formed by self-assembled metal nanoparticles. Inter-particle nano-resistance and nano-capacitance are implemented at the nano-scale assuming inter-particle charge transfer and accumulation mechanisms that can be adapted depending on the nature of the nano-particles and the surrounding medium. The actual positions and spatial arrangements of the nanoparticles within the network are taken into consideration, allowing the attributes of percolating conducting routes to be extracted, classified, and compared in terms of path conductance and statistical distribution of path lengths. Our findings are contrasted to those obtained using analytic models, which are commonly used, but rely on strong assumptions about the electric properties of the conducting paths. We address these assumptions and show that in the case of weakly disordered systems, there is a general agreement between numerical simulations and analytic modeling-based approaches. In the case of disordered networks where the nano-particle size and position fluctuations are included, we show that the path length distribution is frequency-dependent and can differ significantly from the lognormal distribution usually assumed in the analytic models. The impedance of individual pathways may be extracted from the numerical simulations; we discovered that the conductance and susceptance of a specific path are frequency-dependent and inversely proportional to the path length only in ordered networks. Strong scattering of conductance values is caused by disorder effects. The developed numerical approach is generic and applies to most nano-devices where charge transport relies on percolation; it allows to bridge the gap between the nano-scale and micro-scale electric characteristics and, thus, permits a deeper understanding of the charge transport properties of nano-structured materials. [ABSTRACT FROM AUTHOR]

In underwater acoustic target parameter estimation, the cross-spectrum method estimates the velocity of the target by the interference structure of the cross-correlated fields in two ranges. However, with the increase in interference in the marine environment, the performance of conventional cross-spectrum target velocity estimation methods gradually declines or even fails. To solve this problem, a cross-spectrum histogram method that combines the multi-line spectrum characteristics of the target is proposed in this paper. First, each frequency point of all line spectra is compensated by the cross-spectrum compensation method. Then the target velocity estimation value is obtained by performing probability distribution statistics on the velocity estimation results for all frequency points. Under different signal-to-noise ratios, simulations and experiments are carried out to verify the effectiveness of the proposed method. The results show that the proposed method is still effective in estimating the target velocity when the conventional method fails. [ABSTRACT FROM AUTHOR]

In traditional cesium beam clocks, cesium atoms are deflected by strong inhomogeneous magnetic fields. The distribution of the detectable atoms, which is critical to the short-term frequency stability, is hard to describe with analytical functions. In this paper, we numerically analyze the beam optics performance of cesium beam tubes based on the magnetic-state-selected and fluorescence detection scheme. To accurately model the cesium beam tube, we apply the Monte Carlo sampling directly inside the collimator. The finite element method is also applied to model the magnetic field. Upon the high dimensional distribution space, two key parameters are selected as indicators of the short-term performance of the cesium beam tube, the effective velocity distribution, and the normalized density difference of atoms in | F = 3 , m F = 0 ⟩ and | F = 4 , m F = 0 ⟩. The influence of the configuration of the collimator is analyzed. Experiments are carried out with two manufactured beam tubes. The results show good agreement with the simulation model. We also discuss limitations of the simulation method when applied to designing cesium beam tubes. [ABSTRACT FROM AUTHOR]

Surfactants play a critical role in the physics of paint and coating formulations, affecting key rheological properties such as viscosity, yield stress, and thixotropy. This paper proposes a new three-dimensional phase-field model that uses the cumulant lattice Boltzmann method (LBM) to simulate soluble surfactants. Although current phase-field models commonly use Langmuir's relationship, they cannot calculate interfacial tension analytically, or the LBM models used are unstable when viscosities are low. However, the proposed method overcomes these limitations through two main features. First, the main parameters for modeling and controlling the surfactant's strength and interaction with other phases are directly obtained from a given initial interfacial tension and bulk surfactant, eliminating the need for trial-and-error simulations. Second, a new equilibrium distribution function in the moment space that includes diagonal and off diagonal elements of the pressure tensor is used to minimize Galilean invariance violation. Additionally, there is no need to use an external force to recover multiphase flows, which could break mass conservation. Furthermore, this method has significant potential for parallelization since only one neighbor's cell is used for discretization. The method shows Langmuir relation behavior and is validated with analytical solutions for various interfacial tensions and surfactant concentrations. Moreover, the paper demonstrates the influence of interfacial tension and surfactants on spurious velocities, indicating the method's stability at low viscosities. The dynamics of droplets in the presence of the surfactants is studied in spinodal decomposition and under various external forces. The method accurately simulates the breaking-up and coalescence for these cases. Furthermore, the method successfully simulates the breakage of a liquid thread at a high viscosity ratio. [ABSTRACT FROM AUTHOR]

The motivation of this paper is to examine the evaluation of local surface stresses and hydrodynamic forces acting on a stationary or moving body using a diffuse interface immersed boundary method (IBM). This task is not trivial for the diffuse IBM because it uses a smoothed regularized delta function in the transfer steps between Lagrangian and Eulerian locations. In our earlier work [D. Xu et al., Phys. Rev. E 105, 035306 (2022)], a particle distribution function (PDF) discontinuity-based kinetic immersed boundary method (KIBM) was proposed based on the Boltzmann equation. This paper is a continuation of our work on the improvement of the KIBM in the framework of the diffuse interface IBM. In the present study, the concept of the immersed boundary layer (IBL) is brought forward, and the dynamic effects of particle advection and collision in the IBL are coupled and evaluated within a numerical time step scale in a kinetic manner. Consequently, the PDFs on both sides of the IBL are reconstructed, and the general immersed boundary force density can be obtained accurately and efficiently. Meantime, the local surface stress distribution acting on the body wall from the actual fluid can be conveniently and accurately calculated by the moment of the PDFs. Finally, some commonly used problems involving incompressible fluid flows in the continuum flow regime with stationary and moving boundaries are simulated by the present KIBM, and the results show that the present KIBM can significantly accelerate the rate of convergence and has a good agreement with other numerical and experimental results. [ABSTRACT FROM AUTHOR]

Shannon entropy is used to measure information uncertainty, while the information dimension is used to measure information complexity. Given two probability distributions, the difference can be measured by relative entropy. However, the existing relative entropy does not consider the effect of information dimension. To improve the existing entropy, a new relative entropy is presented in this paper. The information fractal dimension is considered in the proposed relative entropy. The new relative entropy is more generalized than the initial relative entropy. When dimension is not considered, it will degenerate to the initial relative entropy. Another interesting point is that the new relative entropy may have negative values when calculating. The physical meaning is still under exploration. Finally, some application examples are provided to exemplify the utilization of the proposed relative entropy. [ABSTRACT FROM AUTHOR]

The advent of NdFeB bonded magnets with freedom of shape design is effective in achieving motor size and weight reductions. In this paper, the NdFeB bonded magnets were produced through calendaring molding, and the effect of powder shape on degree of alignment (DOA) of NdFeB bonded magnets was investigated. The magnetic measurement results demonstrate that platelet-shaped anisotropic Master Quality Authenticated (MQA) powders exhibit a significantly higher DOA compared to sphere-shaped anisotropic HDDR powders. Microstructural analysis reveals the presence of an oriented structure induced by mechanical stress in MQA bonded magnets, resulting in magnetic anisotropy. This observation is consistent with the difference in X-ray diffraction (XRD) patterns between the cross-section and surface of MQA bonded magnets. Conversely, spherical HDDR particles display minimal orientation and maintain a random distribution, resulting in magnetic isotropy. The XRD pattern of the cross-section of HDDR bonded magnets closely resembles that of its surface. In summary, our findings highlight the superior potential of platelet-shaped anisotropic MQA powders for achieving enhancing magnetic properties during the calendaring molding process, in contrast to sphere-shaped anisotropic HDDR powders. This study provides valuable insights into the determinants of mechanical particle orientation during the fabrication of anisotropic NdFeB bonded magnets, with implications for the development of high-performance bonded magnets. [ABSTRACT FROM AUTHOR]

Probability distributions have prominent applications in different sectors. Among these sectors, probability models are mostly used to analyze datasets in engineering. Among the existing probability distributions, the two-parameter Weibull model plays an important role in providing the best fit for engineering and other related datasets. This paper introduces a new method called a novel updated-W (denoted by "NU-W") family of distributions that is used to develop a new updated form of the Weibull distribution. The proposed updated extension of the Weibull model is referred to as a novel updated Weibull (denoted as NU-Weibull) distribution. Distributional properties such as identifiability, heavy-tailed characteristic, and rth moment of the NU-W family are derived. The residual life analysis of the NU-Weibull distribution is provided. Finally, two physical applications from civil engineering and reliability sectors are analyzed to demonstrate the application and effectiveness of the NU-Weibull distribution. The data fitting results show that the NU-Weibull distribution is a more suitable and best fit for engineering datasets. [ABSTRACT FROM AUTHOR]

We investigate the behavior of self-propelled particles in infinite space dimensions by comparing two powerful approaches in many-body dynamics: the Fokker–Planck equation and dynamical mean-field theory. The dynamics of the particles at low densities and infinite persistence time is solved in the steady state with both methods, thereby proving the consistency of the two approaches in a paradigmatic out-of-equilibrium system. We obtain the analytic expression for the pair distribution function and the effective self-propulsion to first-order in the density, confirming the results obtained in a previous paper [T. Arnoulx de Pirey et al., Phys. Rev. Lett. 123, 260602 (2019)] and extending them to the case of a non-monotonous interaction potential. Furthermore, we obtain the transient behavior of active hard spheres when relaxing from the equilibrium to the nonequilibrium steady state. Our results show how collective dynamics is affected by interactions to first-order in the density and point out future directions for further analytical and numerical solutions of this problem. [ABSTRACT FROM AUTHOR]

In recent decades, a paradigm shift in macroscopic methods has favored the use of non-primitive variables, such as velocity and vorticity (V–V), over traditional primitive variables. This shift eliminates the need for solving a Poisson equation for pressure, aligning numerical treatments more closely with physical reality. However, the lattice Boltzmann method (LBM), renowned for its efficacy in studying fluid flow phenomena, continues to rely on the conventional pressure–velocity (P–V) approach. This conventional approach necessitates a pressure–density relation, posing challenges in maintaining the incompressible condition. This study pioneers a novel application of the LBM to three-dimensional velocity–vorticity equations, expanding upon our suggested recent method for two-dimensional cases [Kefayati, Phys. Fluids. 36, 013128 (2024)]. To address the complexities introduced by the vortex stretching term in three dimensions, a new equilibrium distribution function is formulated and introduced to the three-dimensional nature of the vorticity vector. The paper details the derivation of the three-dimensional LBM and substantiates its effectiveness through numerical examples, showcasing its applicability in fluid dynamics. By bridging the gap between traditional P–V formulations and the benefits of non-primitive V–V variables, this work contributes to the ongoing exploration of LBM applications in fluid dynamics. The focus on three-dimensional scenarios involving velocity–vorticity equations marks a significant advancement, offering insights into the nuanced dynamics of fluid flow and paving the way for more accurate and realistic simulations in complex environments. [ABSTRACT FROM AUTHOR]

This article reports the first measurements of high-energy photons produced with the high-intensity PETawatt Aquitaine Laser (PETAL) laser. The experiments were performed during the commissioning of the laser. The laser had an energy of about 400 J, an intensity of 8 × 1018 W cm−2, and a pulse duration of 660 fs (FWHM). It was shot at a 2 mm-thick solid tungsten target. The high-energy photons were produced mainly from the bremsstrahlung process for relativistic electrons accelerated inside a plasma generated on the front side of the target. This paper reports measurements of electrons, protons and photons. Hot electrons up to ≈35 MeV with a few-MeV temperature were recorded by a spectrometer, called SESAME (Spectre ÉlectronS Angulaire Moyenne Énergie). K- and L-shells were clearly detected by a photon spectrometer called SPECTIX (Spectromètre Petal à Cristal en TransmIssion pour le rayonnnement X). High-energy photons were diagnosed by CRACC-X (Cassette de RAdiographie Centre Chambre-rayonnement X), a bremsstrahlung cannon. Bremsstrahlung cannon analysis is strongly dependent on the hypothesis adopted for the spectral shape. Different shapes can exhibit similar reproductions of the experimental data. To eliminate dependence on the shape hypothesis and to facilitate analysis of the data, simulations of the interaction were performed. To model the mechanisms involved, a simulation chain including hydrodynamic, particle-in-cell, and Monte Carlo simulations was used. The simulations model the preplasma generated at the front of the target by the PETAL laser prepulse, the acceleration of electrons inside the plasma, the generation of MeV-range photons from these electrons, and the response of the detector impacted by the energetic photon beam. All this work enabled reproduction of the experimental data. The high-energy photons produced have a large emission angle and an exponential distribution shape. In addition to the analysis of the photon spectra, positron production was also investigated. Indeed, if high-energy photons are generated inside the solid target, some positron/electron pairs may be produced by the Bethe–Heitler process. Therefore, the positron production achievable within the PETAL laser facility was quantified. To conclude the study, the possibility of creating electron/positron pairs through the linear Breit–Wheeler process with PETAL was investigated. [ABSTRACT FROM AUTHOR]

Statistical modeling and forecasting are crucial to understanding the depth of information in data from all sources. For precision purposes, researchers are always in search of ways to improve the quality of modeling and forecasting, whatever the complexity of the situation. To this end, new (probability) distributions and suitable forecasting methods are demanded. The first part of this paper contributes to this direction. Indeed, we introduce a modified version of the flexible Weibull distribution, called the modified flexible Weibull distribution. It is constructed by mixing the flexible Weibull distribution with the exponential T-X scheme. This strategy is winning; the new distribution has a larger panel of functionalities in comparison to those of the classical Weibull distribution, among other things. To check the quality of the fitting of the modified flexible Weibull distribution, two different datasets are analyzed. After analyzing these datasets, it is observed that the modified flexible Weibull distribution has improved fitting power compared to other similar distributions. Apart from this, the conventional time series model, namely, the autoregressive integrated moving average (ARIMA) model, and the modern artificial neural network (ANN) model are considered for forecasting results. Utilizing the two datasets discussed earlier, it was discovered that the ANN model is more effective than the traditional ARIMA model. [ABSTRACT FROM AUTHOR]

The physics of macromolecular orientation has been used to explain the elasticity of polymeric liquids. Specifically, by first sculpting a rigid bead–rod likeness of the macromolecule, we can then derive its hydrodynamic resistance to orientation. The solution for the orientation distribution function has then been used, by integration in phase space, to get rheological material functions in both (i) small- and (ii) large-amplitude oscillatory shear flow, including its limiting case, and (iii) steady shear flow. However, rheological material functions in steady homogeneous extension from rigid bead–rod theory remain elusive. In this paper, we derive the orientation distribution function, and the rheological material functions, for suspensions of general rigid bead–rod structures. We focus on the time-steady viscosities in extension, and we first do so for general extensional kinematics. We then obtain the viscosities in steady extension for (iv) uniaxial extension, (v) planar extension, and (vi) biaxial extension. We close with a worked example, in which we use our new result for the steady uniaxial extensional viscosity to build a bridge between the macromolecular theory and the Oldroyd framework for rheological constitutive models. We, thus, arrive at a constitutive equation whose parameters are deducible from the moments of inertia of the macromolecule, and thus, deducible from macromolecular architecture alone. Our model is accurate up to third order for time-independent flows and is accurate to second order for time-dependent ones. [ABSTRACT FROM AUTHOR]

This article introduces a new statistical distribution called the power unit Burr-XII distribution, which is an extension of the Burr XII distribution obtained through a power transform. This paper investigates several statistical properties of this new model, including mode, moments, moment generating and characteristic functions, entropy, and Bonferroni and Lorenz curves. In addition, various classical estimators for the parameters of the power unit Burr-XII distribution are evaluated, including maximum likelihood estimates, ordinary least squares estimates, maximum product of interval estimates, Anderson–Darling, right and left tail Anderson–Darling, and Cramer–von Mises estimators. This study provides tables and graphs to illustrate the performance of these methods under different scenarios and sample sizes. The results of the proposed distribution in different fields of application are shown using the mortality rates of COVID-19 patients in Spain and flood data from 20 observations. As a result of both applications, it was observed that the proposed distribution gave better results compared to other well-known distributions, such as the beta distribution, transformed gamma distribution, log-weighted power distribution, transmuted power distribution, Kumaraswamy distribution, Topp–Leone distribution, exponentiated reduce Kies distribution, and exponentiated Topp–Leone distribution. [ABSTRACT FROM AUTHOR]

In the negative hydrogen ion sources, the positive bias of the plasma grid with respect to the discharge chamber is often used to suppress co-extracted electrons. Because most of the co-extracted electrons are magnetically deflected onto the extraction grid, the difference between the extraction and acceleration current (i.e., Iext − Iacc) is commonly used to represent the number of co-extracted electrons. In the single-driver RF negative ion source at ASIPP, the variation of Iext − Iacc with the plasma grid bias voltage was accidentally found to have different trends with and without the Cs seeding. When the current density of Iacc (regarded as JH-) was larger than 120 A/m2 during Cs conditioning, the Iext − Iacc fell first and then rose with the increasing bias voltage. The previous research results from NIFS that the beam optics were changed by the bias voltage can be used to explain the phenomenon. In this paper, the electron temperature (Te) in front of the plasma grid was found to increase from the Langmuir probe measurement, when the bias voltage was higher than a threshold of 4.5 V to the float potential. Interestingly, the bias voltage corresponding to the trough of Iext − Iacc was higher than the float potential—a similar value of 4.1 V to the threshold of Te increasing. Since the negative hydrogen ions are easily destroyed by the high-energy electrons, the increasing of Te may also cause the change of beam optics and the increase in co-extracted electrons. The electron energy distribution function was used to explain the change of plasma parameters in front of the plasma grid. [ABSTRACT FROM AUTHOR]

When the hypersonic vehicle is flying, the plasma in the area near the stagnation point of the front end of the vehicle can be approximately seen as the fully ionized dusty plasma. Due to the existence of dust particles, dusty plasma affects the communication quality of the hypersonic vehicle. In this paper, the general Boltzmann equation applicable to dusty plasmas containing electrons and the Fokker–Planck–Landau collision model are combined to derive a general formula for the electron distribution function of fully ionized dusty plasmas. Considering the contribution of the collision effect and charging effect to the dispersion relationship of fully ionized dusty plasma, the dielectric constant of fully ionized dusty plasma under an external magnetic field is solved. The Wentzel–Kramers–Brillouin method is used to calculate the attenuation coefficient (α) of the THz wave in fully ionized dusty plasma, and the influence of the external magnetic field strength and other dusty plasma parameters on the attenuation characteristics of the THz circularly polarized wave is analyzed. The research results show that the α of the THz left-hand circularly polarized wave decreases with the increase in the external magnetic field strength, while the α of the THz right-hand circularly polarized wave increases. In addition, increasing the dust particle radius, dust particle density, and electron density in a certain frequency range can increase the α of the THz circularly polarized waves. These research results provide theoretical guidance for the exploration of the interaction mechanism between the THz waves and fully ionized dusty plasma. [ABSTRACT FROM AUTHOR]

We present a mesoscopic numerical solver for the constitutive equation of dilute polymer solutions, as described by the Fokker–Planck equation of bead-spring dumbbell models with linear spring forces, such as Oldroyd-B, FENE-P (finitely extensible nonlinear elastic with Peterlin closure), and C-FENE-P (charged FENE-P). The configuration density function of the Fokker–Planck equation is expanded into a series of Hermite polynomials, and we show that only a second order in the expansion is needed to describe the evolution of the polymer-induced stresses. The polymer-induced stress tensor is given exactly through a discrete representation of the configuration distribution function, which is obtained from a finite set of Gauss–Hermite quadrature points. In addition, we derive the conformation tensor equation, which serves as a mathematical quality check for the method. We solve the time evolution of the extra stress tensor for homogeneous flows of dilute polyelectrolyte solutions, conceptualized by the C-FENE-P model, which is a generalization of the FENE-P dumbbell model. The results are shown to be in excellent agreement with analytical and semi-analytical reference results for simple shear and extensional flows. While in this paper the focus is on linear connector forces, we believe that the principles of the derivation are extendable to other force laws. [ABSTRACT FROM AUTHOR]

In micro- and nanoscale channels, where the characteristic scale approaches or falls below the mean free path between gas molecules, flow characteristics exhibit pronounced discontinuity. In such scenarios, continuum-based models are inadequate, and adopting kinetic models based on statistical mechanics becomes imperative for accurately describing the gas transport phenomenon. This paper presents a novel steady-state discrete Boltzmann model (DBM) that is specifically tailored for non-equilibrium flows at the micro–nanoscale. Unlike the conventional DBM, the new model focuses on the evolution equation of the non-equilibrium component of the molecular velocity distribution function in the Lagrangian coordinate system, which follows the fluid micro-element. Through numerous numerical simulations, we demonstrate the effectiveness of our model in capturing gas flow characteristics across a wide spectrum of rarefaction parameters, ranging from slip flow to free molecular flow. Utilizing this new model, we initially examine the Onsager reciprocal relationship between heat flux generated by pressure gradients and mass flux resulting from temperature gradients in micro/nanochannels. Subsequently, we calculate higher-order non-equilibrium quantities up to the 10th order and make a comparison of their characteristics. Finally, we present and discuss the features of the non-equilibrium component of the molecular velocity distribution function. [ABSTRACT FROM AUTHOR]

The validity of local thermodynamic equilibrium (LTE) in plasma is a long-term concern for laser-induced breakdown spectroscopy applications. In this paper, the spatial and temporal dependence of LTE deviation in picosecond laser-induced plasmas has been proved. A picosecond (∼20 ps) laser operated at 532 nm was used to ablate a silicon target to produce plasma at a pressure of 10−5 mbar. A general electron energy distribution function was used to provide access to the insight into population ratios of different energy levels for the spatially and temporally resolved optical emission intensity of laser-induced plasma. A precise temporal and spatial LTE boundary of plasma generated in picosecond laser ablation was obtained, and the results showed that only at delay times of 180–300 ns, the plasma away from the surface (>4 mm) is in LTE. [ABSTRACT FROM AUTHOR]

When simulating a charged particle trajectory in plasmas with Monte Carlo methods, the traditional single-scattering model is accurate but computationally expensive. The traditional multiple-scattering model reduces the computation cost but assumes an exponential distribution of the scattering angle, which overestimates the cumulative scattering angle. In this paper, we develop a new Monte Carlo method for the charged particle transport simulations. The scattering angle is naturally sampled from a modified screened Rutherford scattering cross section, in which a greatly amplified minimum deflection angle is used. With this model, the simulations give the same scattering angle distribution with the single-scattering model but only take a comparable computation cost with the multiple-scattering model when the small scattering angle and Markovian approximations can be fulfilled. This model would be especially useful for the study of inertial-confinement-fusion, which is sensitive to the alpha-particle energy deposition. [ABSTRACT FROM AUTHOR]

This paper introduces a new model to find the velocity-space location of energetic ions generating ion cyclotron emission (ICE) in plasmas. ICE is thought to be generated due to inverted gradients in the v ⊥ direction of the velocity distribution function or due to anisotropies, i.e., strong gradients in the pitch direction. Here, we invert synthetic ICE spectra generated from first principles PIC-hybrid computations to find the locations of these ICE-generating ions in velocity space in terms of a probability distribution function. To this end, we compute 2D ICE weight functions based on the magnetoacoustic cyclotron instability, which reveals the velocity-space sensitivity of ICE measurements. As an example, we analyze the velocity-space sensitivity of synthetic ICE measurements near the first 15 harmonics for plasma parameters typical for the Large Helical Device. Furthermore, we investigate the applicability of a least-square subset search, Tikhonov regularization, and Lasso regularization to obtain the locations in velocity space of the ions generating the ICE. [ABSTRACT FROM AUTHOR]

In this paper, expressions of number densities for electron trapping for generalized (r, q), kappa, and Cairns distribution functions, respectively, are reported using the approach adopted by Landau and Lifshitz for Maxwellian trapping of electrons. For illustrative purposes, dispersive and dissipative equations for ion-acoustic waves are obtained in the presence of non-Maxwellian trapped electrons in the small amplitude limit. The solutions of the modified dispersive and dissipative nonlinear equations are reported, and a graphical analysis is given to present a detailed comparison of non-Maxwellian and Maxwellian trapping. The results presented here, to the best of authors' knowledge, are a first attempt of this kind. It is expected that the present investigation will unravel new horizons for future research and encourage the researchers to search for the nonlinear structures presented in this paper in the satellite data. [ABSTRACT FROM AUTHOR]

The gas–solid flow state of the high-speed combustion system varies with the propellant combustion and the movement of the projectile. In this paper, to accurately obtain the motion characteristics and flow field distribution in the chamber, a mixed calculation model of interior ballistic two-phase flow combined with the particle element method and the two-fluid method was established. First, considering the different states of the combustion system in different periods, the particle element method was used to describe the initial charging state, while the two-fluid method was used to calculate the subsequent homogeneous flow. Next, the coupling and transformation of the two methods were realized by the boundary mapping. Finally, the mixed modeling method was validated by comparing the classic code results. Based on the novel approach, parameter distributions in the high-speed combustion chamber are obtained, and the particle movement and the development of the flow field in the chamber are described accurately. In the initial stage of ignition and flame-spreading, the flame front and heat transfer process appear completely. With the movement of the projectile, the flow field in the chamber changes drastically, and the particles gather toward the bottom of the projectile. When the propellant is burned out, the uniform distribution in the chamber is presented. The results indicate that the proposed method may be promising for a novel idea to obtain accurate parameter distributions in interior ballistic. [ABSTRACT FROM AUTHOR]