Mean Interparticle Distance Research Articles

Phenomenology of a Rydberg impurity in an ideal Bose-Einstein condensate

We investigate the absorption spectrum of a Rydberg impurity immersed in and interacting with an ideal Bose-Einstein condensate. Here, the impurity-bath interaction range can greatly exceed the mean interparticle distance; this discrepancy in length scales challenges the assumptions underlying the universal aspects of impurity atoms in dilute bosonic environments. Our analysis finds three distinct parameter regimes, each characterized by a unique spectral response. In the low-density regime, we find that the Rydberg impurity is dressed by the surrounding bath similarly to the known Bose polaron. Transitioning to intermediate densities, the impurity response, given by sharp quasiparticle peaks, fragments into an intricate pattern bearing the hallmarks of a diverse molecular structure. Finally, at high density, a universal Gaussian response emerges as the statistical nature of the bath dominates its quantum dynamics. We complement this analysis with a study of an ionic impurity, which behaves equivalently. Our exploration offers insights into the interplay between interaction range, density, and many-body behavior in impurity systems. Published by the American Physical Society 2024

Determining the absolute number density of a thermal vapor via photon correlations

We propose a technique to determine the absolute number density N of an alkali-metal vapor confined within a nanocell. This method is based on near-resonant driving of the vapor's constituent atoms and determining the mean interparticle distance (or equivalently the temperature) from the power spectrum associated with the offset photon intensity-intensity correlation function g(2)(τ)−1. In our investigation, we treat the atoms as an average of interacting and radiating dipole pairs randomly positioned within the nanocell. We observe that the power spectrum of the emitted light has a central dip for interparticle distances corresponding to ∼λ/5 and that this result is robust to variations in the driving Rabi frequency and the average detuning. With our proposed method, we can overcome the limitations in defining the absolute number density N, which is currently typically deduced from the temperature of heating elements applied externally to the cell. Published by the American Physical Society 2024

Benchmarking Data Assimilation Algorithms For 3D Lagrangian Particle Tracking

This paper reports a comparison of three state-of-the-art data assimilation (DA) algorithms for 3D Lagrangian particle tracking (LPT): Vortex-In-Cell sharp (VIC#), FlowFit3, and neural-implicit particle advection (NIPA). Particle trajectories, termed “tracks,” are spatially sparse, and a reconstruction algorithm is commonly employed to estimate dense Eulerian fields using position, velocity, and/or acceleration data from the tracks. DA algorithms for LPT combine the tracks with a set of governing equations (or constraints) to enhance the accuracy of the velocity field, relative to interpolation methods, and infer additional quantities like pressure. We compare the performance of VIC#, FlowFit3, and NIPA with respect to their accuracy and computational cost. Accuracy is assessed in terms of the mean inter-particle distance, frame rate, and magnitude of tracking errors, and costs are reported in wall time. Synthetic and experimental data sets for homogeneous isotropic turbulence and turbulent boundary layer flows are evaluated; direct numerical simulations are used for the synthetic tests, and realistic localization errors are added to the simulated tracks. All three DA methods perform well in cases with the highest spatio-temporal sampling of the flow, and all three methods are relatively robust to the frame rate and magnitude of localization errors. NIPA is more resilient to sparse seeding than FlowFit or VIC#, which exhibit similar performance, but NIPA is also the most expensive technique by some margin. DA reconstructions are superior to interpolation across the board, with a reduction of error up to 80% in the experimental demonstration.

Laser remelting of a novel carbide-reinforced Ni-Co-Cr-Hf-C alloy with ultra-fine HfC dispersion

The dispersion of stable nano-particles is essential for improving the high temperature creep properties of Ni-base alloys. Additive manufacturing by laser powder bed fusion (LPBF) offers novel means to tailor particle distributions taking advantage of the fast and directional solidification inside travelling melt pools. To benefit of this opportunity, a novel in-situ carbide reinforced alloy Ni − 32Co − 28Cr − 3.5Hf − 0.25C (wt. %) was developed. In a first rapid approach laser remelting of a cast alloy block was used to mimic LPBF solidification conditions. After a subsequent annealing treatment at 1150 °C for 6 h, an ultra-fine and intragranular dispersion of nano-sized HfC particles was obtained. The HfC particles have an average size of 54 nm and a mean inter-particle distance of 326 nm, which is an exceptional refinement compared to the as-cast microstructure. The number density of HfC particles ranges around 1 × 1012/m2 in 2D and is estimated to be 2 × 1019/m3 in 3D.

Effect of recycled brick powder with various particle features on early-age hydration, water state, and rheological properties of blended cement paste in the context of 3D Printing

Partially replacing cement with recycled brick powder (RBP) in 3D printing concrete (3DPC) is an effective way to reduce carbon footprint and resolve the construction and demolition waste disposal problems. Understanding the impact of RBP on the rheological parameters of 3DPC is of utmost importance, given its critical role in ensuring the requisite printability. Here, three types of RBPs with various particle features were prepared by mechanical grinding, and their effects on several rheological parameters of cement-RBP pastes were characterized by hydration kinetic and water state distribution. Results show that incorporating RBP increases the growth rate of static yield stress due to the nucleation effect in the first 2 h. The initial static yield stress and thixotropy of cement-RBP pastes are governed by morphology effect and Debye length, while the mean interparticle distance and water lubrication effect under shear process play the dominant role in dynamic yield stress. RBP can promote the evolution of structural build-up and thixotropy of cement paste, all of which have a significant positive impact on filament shape retention and structural stability of 3DPC.

Effects of Material Structure on Stress Relaxation Characteristics of Rapidly Solidified Al-Fe Alloy.

An Al-Fe alloy which was produced by hot extrusion of rapidly solidified powder is a possible solution to substitute copper-based electrical conductor material due to its high strength and high electrical conductivity. However, the stress relaxation characteristic-an essential parameter as a conductor material-and the effect of the material structure have not been reported, which was the aim of the present paper. An Al-5%Fe alloy was selected as the test material. The material structures were controlled by hot extrusion practice, annealing, and cold rolling. The Al-Fe intermetallic compound particles controlled the residual stress after the stress relaxation test via the Orowan mechanism. Decreasing the mean inter-particle distance reduces the electrical conductivity. The increase in the number of dislocations by the cold rolling increased strength at room temperature without changing electrical conductivity; however, it did not have a positive effect on the stress relaxation characteristics. The stress relaxation characteristics and the electrical conductivity of the Al-Fe alloy were superior to conventional C52100 H04 phosphor bronze when compared with the case of the same mass.

Measurements Of The Energy Dissipation Rate In Homogeneous Turbulence Using Dense 3D Lagrangian Particle Tracking And FlowFit

We present measurements of the full velocity gradient tensor and all volumetric dissipation rate elements based on dense fields of fluid particle trajectories in homogeneous turbulence at Re_λ~270 and ~370 in a Kármán flow between two counter-rotating disks with impellers. Applying the Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) algorithm, we are able to instantaneously track up to 80.000 particles in a volume of 40 x 40 x 15 mm³. The mean interparticle distance is lower than 7 Kolmogorov lengths for the Re_λ ~270 case. A data assimilation scheme (FlowFit) with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by a continuous 3D B-Spline representation, enabling to recover (locally) the smallest flow scales. In the presentation, we show Lagrangian velocity and acceleration statistics, as well as the Eulerian counterparts on velocity gradients and pressure fields. We compute the energy dissipation rate directly by making use of quadruples of particle trajectories in close proximity (r < 3η) and compare it to indirect approaches using second-order velocity- and velocityacceleration structure functions in the inertial subrange.

THEORETICAL-EXPERIMENTAL POSSIBILLITIES OF MICROSTRUCTURE QUANTIFICATION OF DISPERSION STRENGTHENED MATERIALS

The present paper is devoted to the possibilities to classify the spatial arrangement of the elements (features) of a stochastic process with geometrical objects. The fundamental quantities describing point processes were introduced. Experimental possibilities of structural objects determination, possibilities of evaluation of the size distribution of the secondary phases, testing of planar point structures (estimation of the process intensity, square method and characteristics of the second order) were estimated. Interparticle distances, namely mean interparticle distance, mean minimum distance, mean visibility and mean path of spherical contact were defined. Selected processes were described and demonstrated from simulated realizations on Al-Al4C3 dispersion strengthened material, prepared by a powder metallurgy method of reaction milling. Interparticle distances of Al4C3 particles were evaluated. Polygonal methods and quadrant counts method were used for characterization of the particle arrangement.

Detection of vortical structures in sparse Lagrangian data using coherent-structure colouring

In this study, vortical structures are detected on sparse Shake-The-Box data sets using the Coherent-Structure Colouring (CSC) algorithm. The performance of this Lagrangian approach is assessed by comparing the CSC-coloured tracks with the baseline vorticity field. The ability to extract vortical structures from sparse data is accessed on two Lagrangian particle tracking data sets: the flow past an Ahmed body and a swirling jet flow. The effects of two normalized parameters on the identification of vortical structures were defined and studied: the mean track length and the mean inter-particle distance. The accuracy of the vortical-structure detection problem through CSC is shown to improve with decreasing inter-particle distance values, whereas little dependence on the mean track length is observed at all. Overall, the CSC algorithm showed to yield accurate detection of coherent structures for inter-particle distances smaller than 15% of the characteristic dimension of the structure. However, the results quickly deteriorate for sparser Lagrangian data.

Addition to Structure and Dynamics of a Polymer–Nanoparticle Composite: Effect of Nanoparticle Size and Volume Fraction

In our previous publication (Ref. 1) we have shown that the data for the normalized diffusion coefficient of the polymers, $D_p/D_{p0}$, falls on a master curve when plotted as a function of $h/\lambda_d$, where $h$ is the mean interparticle distance and $\lambda_d$ is a dynamic length scale. In the present note we show that also the normalized diffusion coefficient of the nanoparticles, $D_N/D_{N0}$, collapses on a master curve when plotted as a function of $h/R_h$, where $R_h$ is the hydrodynamic radius of the nanoparticles.

Characterization of egg white gel microstructure and its relationship with pepsin diffusivity

Understanding the diffusion of digestive enzymes, particularly pepsin, in different food structures, is a key factor to better control protein digestion and absorption. This study aimed to investigate how protein-based food microstructure impacts pepsin diffusion. Two egg white gels (EWGs) of identical protein concentration (10%) but different structures were used as food models. The two different gel structures were prepared by heating liquid egg white at pH5 and pH9, respectively. Results showed that egg white proteins formed a compact and microstructurally homogeneous gel at pH9 (mean particle size of 0.32 ± 0.02 μm, with a mean interparticle distance of 0.76 ± 0.07 μm), which leads to a lower FITC-pepsin diffusion coefficient (Deff = 44.2 ± 6.1 μm2 s−1), compared to the pH5-EWG (Deff = 52.5 ± 5.3 μm2 s−1). The microstructure of the pH5-EWG was characterised by a spatially heterogeneous loose protein matrix made of larger aggregate particles (mean particle size of 0.76 ± 0.07 μm, with a mean interparticle distance of 1.79 ± 0.57 μm). In addition to the effects of the EWG microstructure, the environmental pH also affects the FITC-pepsin diffusion, likely because of the impact on electrostatic interactions between pepsin and the egg white proteins.

THEORETICAL-EXPERIMENTAL POSSIBILLITIES OF MICROSTRUCTURE QUANTIFICATION OF DISPERSION STRENGTHENED MATERIALS

<p>The present paper is devoted to the possibilities to classify the spatial arrangement of the elements (features) of a stochastic process with geometrical objects. The fundamental quantities describing point processes were introduced. Experimental possibilities of structural objects determination, possibilities of evaluation of the size distribution of the secondary phases, testing of planar point structures (estimation of the process intensity, square method and characteristics of the second order) were estimated. Interparticle distances, namely mean interparticle distance, mean minimum distance, mean visibility and mean path of spherical contact were defined. Selected processes were described and demonstrated from simulated realizations on Al-Al<sub>4</sub>C<sub>3 </sub> dispersion strengthened material, prepared by a powder metallurgy method of reaction milling. Interparticle distances of Al<sub>4</sub>C<sub>3</sub> particles were evaluated. Polygonal methods and quadrant counts method were used for characterization of the particle arrangement.</p>

Quantification of preferential concentration of colliding particles in a homogeneous isotropic turbulent flow

This paper addresses the effect of inter-particle collisions on the segregation of non-settling inertial particles in homogeneous isotropic turbulence. For this purpose, direct numerical simulations of particles in statistically steady homogeneous isotropic turbulence have been performed by the lattice Boltzmann method considering inter-particle collisions. The preferential concentration of suspended particles is quantified using several clustering measures: segregation parameter, correlation dimension, radial distribution function, Voronoï diagrams and the topological tool of Minkowski functionals. Effects of particle inertia, inter-particle collisions and increasing volume fraction in the aforementioned measures are discussed. The obtained results show that collisions between particles have a remarkable influence on the formation of clusters. In particular, under locally dilute conditions, increasing particle volume fraction implies a moderate clustering intensification, but for locally dense conditions an increase of the mean inter-particle distance inside clusters can be envisaged as a consequence of the re-dispersing effect of inter-particle collisions.

Effect of Glow Discharge Parameters on the Mean Interparticle Distance in Dusty Plasma Structures in the Cryogenic–Room Temperature Range

The molecular dynamics method is used for studying the effect of forces acting in a dusty plasma and discharge parameters on the mean interparticle distance in structures in a dc glow discharge in the temperature range 50–300 K. We report on the results of the dependence of the mean interparticle distance on the neutral gas temperature in simplified and modified models of the dusty plasma. The simplified model includes the screened Coulomb potential and the ambipolar trap; in the modified model, the thermophoretic force, the ion shading force, and the neutral shading force are accounted for additionally. All these forces are calculated from the experimental values of the discharge parameters (current, pressure, temperature, and type of gas). The modified model of the dusty plasma system makes it possible to explain the experimental form of the dependence of the mean interparticle distance in dusty structures on the discharge gas temperature. We propose a method for estimating the ion concentration in the discharge gas from the mean interparticle distance in dusty plasma structures.

Phase Transition in the Boltzmann\u2013Vlasov Equation

In this paper we revisit the problem of explaining phase transition by a study of a form of the Boltzmann equation, where inter-molecular attraction is included by means of a Vlasov term in the evolution equation for the one particle distribution function. We are able to show that for typical gas densities, a uniform state is unstable if the inter-molecular attraction is large enough. Our analysis relies strongly on the assumption, essential to the derivation of the Boltzmann equation, that nu ll 1, where nu =d/l is the ratio of the molecular diameter to the mean inter-particle distance; in this case, for fluctuations on the scale of the molecular spacing, the collision term is small, and an explicit approximate solution is possible. We give reasons why we think the resulting approximation is valid, and in conclusion offer some possibilities for extension of the results to finite amplitude.

Nanoscale resetting of the Th/Pb system in an isotopically-closed monazite grain: A combined atom probe and transmission electron microscopy study

Understanding the mechanisms of parent-daughter isotopic mobility at the nanoscale is key to rigorous interpretation of U–Th–Pb data and associated dating. Until now, all nanoscale geochronological studies on geological samples have relied on either Transmission Electron Microscope (TEM) or Atom Probe Microscopy (APM) characterizations alone, thus suffering from the respective weaknesses of each technique. Here we focus on monazite crystals from a ∼1 Ga, ultrahigh temperature granulite from Rogaland (Norway). This sample has recorded concordant U–Pb dates (measured by LA-ICP-MS) that range over 100 My, with the three domains yielding distinct isotopic U–Pb ages of 1034 ± 6 Ma (D1; S-rich core), 1005 ± 7 Ma (D2), and 935 ± 7 Ma (D3), respectively. Combined APM and TEM characterization of these monazite crystals reveal phase separation that led to the isolation of two different radiogenic Pb (Pb*) reservoirs at the nanoscale. The S-rich core of these monazite crystals contains Ca–S-rich clusters, 5–10 nm in size, homogenously distributed within the monazite matrix with a mean inter-particle distance of 40–60 nm. The clusters acted as a sink for radiogenic Pb (Pb*) produced in the monazite matrix, which was reset at the nanoscale via Pb diffusion while the grain remained closed at the micro-scale. Compared to the concordant ages given by conventional micro-scale dating of the grain, the apparent nano-scale age of the monazite matrix in between clusters is about 100 Myr younger, which compares remarkably well to the duration of the metamorphic event. This study highlights the capabilities of combined APM-TEM nano-structural and nano-isotopic characterizations in dating and timing of geological events, allowing the detection of processes untraceable with conventional dating methods.

Particle size-dependent viscosity behavior of a suspension using image processing

In this work, interparticle distances for different powder particle sizes were determined using an image-processing method. Considering the theoretical model only available under several assumptions, this method enables calculation of the interparticle distance regardless of those assumptions. The method is based on the intensity difference between a powder and binder system, and enables the distinction of powder particles from the binder system. A mixed suspension composed of 17-4PH stainless steel powder and a wax-based polymeric binder system was polished with acetone to observe the powder distribution. The boundaries and centroids for the powder particles in the binder system detected by the image-processing method were employed to calculate the mean interparticle distance of a randomly selected particle. To obtain a representative value of interparticle distance for a given feedstock, the Monte Carlo method was used. Although the interparticle variation converged to 0 with repetitive iteration, outlier points satisfied the limitations to determine the iteration number. To overcome this problem induced by the outlier points, the summation of five points of interparticle variation as the limitation was considered. As the iteration number was based on the defined limitation, the interparticle distances for suspensions of the different-size-distribution powders were naturally obtained. With these obtained interparticle distances, the relationship between viscosity and powder particle size was analyzed. The powder characteristics in the viscosity model were analyzed in terms of the interparticle distance. The developed image-processing method to quantify the interparticle distances for powder particle sizes can enhance understanding of physical phenomena in various industrial applications, because the interparticle distance enables quantitative analysis of rheological characteristics such as viscosity or powder agglomeration.

Low-temperature laser-stimulated controllable generation of micro-bubbles in a water suspension of absorptive colloid particles.

A method is described for the generation of micrometer-sized vapor-gas bubbles in a water suspension containing absorptive pigment nanoparticles. The diluted suspension (mean interparticle distance 20 μm) absorbs the continuous laser radiation (wavelength 808 nm), and each particle in the best illuminated volume (~10 × 10 × 200 μm3) serves as a bubble-nucleation center. The suspension heating is inessential (several degrees above the room temperature) and the bubbles are formed mainly of the air gases dissolved in water. The bubbles can stably exist within or near the illuminated area where their location is governed by the competition between thermal and optical forces and can be controlled via the laser beam parameters. The method enables controllable creation, support, prescribed transportation, and destruction of the bubbles. This can be useful in applications aimed at precise sorting, transportation, and delivery of species in nano- and micro-engineering as well as for biomedical studies.

Supersonic flows past an obstacle in Yukawa liquids

Shock formation, when a supersonic flow passes a stationary obstacle, is ubiquitous in nature. Considering particles mediating via a Yukawa-type interaction as a prototype for a strongly coupled complex plasma, characterized by coupling strength (Γ, ratio of the average potential to kinetic energy per particle) and screening parameter (κ, ratio of the mean inter-particle distance to the shielding length), we address the fundamental problem of supersonic fluid flow U0, past a stationary obstacle immersed in this strongly coupled system. We here report the results on the bow shocks formed in Yukawa liquids when the liquid flows at speeds larger than the speed of sound in the system. Depending on the values of Mach number MCL=U0CL, where CL is the longitudinal speed of sound in the system, the bow shocks are found to be either traveling or localized. We find that for the transonic flows (0.8 ≲MCL≲ 1.2), the bow shocks travel in the upstream direction opposite to the incoming fluid. The phase velocity of the traveling bow shocks is found to be a non-monotonous function of κ, varying as ∝1/k1.11 at a fixed value of Γ, and is found to be independent of Γ at a fixed value of κ. It is observed that for the flow values with MCL>1.5, the shock waves do not travel in the upstream direction but instead form a stationary arc like structure around the obstacle. For the fluid flows with 1≲MCL≲2.6, secondary bow shocks are seen to emerge behind the stationary obstacle which travel in the downstream direction, and the phase velocity of these secondary bow shocks is found to be equal to that of the primary bow shocks.

Formation and relaxation of quasistationary states in particle systems with power-law interactions.

We explore the formation and relaxation of the so-called quasistationary states (QSS) for particle distributions in three dimensions interacting via an attractive radial pair potential V(r→∞)∼1/r^{γ} with γ>0, and either a soft core or hard core regularization at small r. In the first part of the paper, we generalize, for any spatial dimension d≥2, Chandrasekhar's approach for the case of gravity to obtain analytic estimates of the rate of collisional relaxation due to two-body collisions. The resultant relaxation rates indicate an essential qualitative difference depending on the integrability of the pair force at large distances: for γ>d-1, the rate diverges in the large particle number N (mean-field) limit, unless a sufficiently large soft core is present; for γ<d-1, on the other hand, the rate vanishes in the same limit even in the absence of any regularization. In the second part of the paper we compare our analytical predictions with the results of extensive parallel numerical simulations in d=3 performed with an appropriate modification of the gadget code, for a range of different exponents γ and soft cores leading to the formation of QSS. We find, just as for the previously well studied case of gravity (which we also revisit), excellent agreement between the parametric dependence of the observed relaxation times and our analytic predictions. Further, as in the case of gravity, we find that the results indicate that, when large impact factors dominate, the appropriate cutoff is the size of the system (rather than, for example, the mean interparticle distance). Our results provide strong evidence that the existence of QSS is robust only for long-range interactions with a large distance behavior γ<d-1; for γ≥d-1, the existence of such states will be conditioned strongly on the short-range properties of the interaction.