Particle Motion Research Articles

Two complementary eigen-based geometric properties of a vortex

In our previous paper [V. Kolář and J. Šístek, “Orbitally compact and loose vortex regions,” Phys. Fluids 35, 121708 (2023)], the eigenvalue-based measure of orbital compactness of particle motion inside a vortex for compressible flows has been proposed. Here, a complementary eigenvector-based geometric property of cylindricity (three-dimensional /3D/ aspect) is introduced. This property is closely related to the local flow axisymmetry in the swirl plane (two-dimensional /2D/ aspect) which explains the positive response of the vortex-identification Δ-criterion, and closely related criteria swirling strength and Rortex (Liutex), for almost no vorticity and a large (without any limitation) rate-of-strain magnitude. A relatively high correlation between orbital compactness, cylindricity, and widely used vortex-identification criteria has been found for several flow examples.

Research on circulation control mechanisms based on Lagrangian dynamics

Circulation control technology greatly improves an aircraft's aerodynamic efficiency by employing high-speed jets at the wing's trailing edge, which generates the Coanda effect. This paper analyzes and reveals the mechanism of circulation control from the perspective of Lagrangian dynamics. First, simulate the circulation control airfoil using the shear stress transport turbulence model to obtain instantaneous flow field data under various jet momentum coefficients (Cμ) and angles of attack. Subsequently, from the perspective of Lagrangian dynamics, the mixing, material transport, and momentum transfer processes between the jet and the trailing-edge separation zone are analyzed using attracting Lagrangian Coherent Structures (aLCSs) under different jet momentum coefficients. Next, through the perspective of particle motion in the Lagrangian framework, the study reveals the accelerating effect of the Coanda jet on the low-speed fluid over the upper wing surface. Additionally, repelling Lagrangian Coherent Structures are used to characterize the downward movement of the leading-edge stagnation point after applying circulation control, and the impact of this movement on the flow state is analyzed. Finally, the analysis using aLCSs assesses the flow control effectiveness of Coanda jets as “virtual aerodynamic flaps.” This analysis helps to further understand the advantages of the “virtual rudder surface” formed by Coanda jet.

Experimental study on particle dispersion between particle-laden jet and supersonic crossflow in cavity-structured channel

Dispersion of Particle-laden Jet in Supersonic Crossflow (PJSC) is an essential process in many applications, experimental study on which, however, has rarely been reported. In order to gain physical insights into PJSC, a specialized experimental setup capable of producing a supersonic crossflow at Mach 2.6 and a particle-laden jet with particle mass loading up to 60% is developed. Visualization of the particles motion is achieved with the help of high-speed planar laser scattering technology. The dispersion characteristics of PJSC within a supersonic channel structured by cavity are systematically analyzed through six experimental cases. The results indicate that the vortices have a significant influence on particle dispersion, leading to preferential concentration of particles, i.e. particle clusters. The particle dispersion is summarized as the “scale dispersion” pattern. The primary pathways for particles entering the cavity are identified as the shear layer above the cavity and collisions at the cavity rear edge. Among the studied factors, the momentum flux ratio exerts the most substantial influence on the dispersion process. Importantly, a reduction in the injection distance is correlated with less particles entering the cavity. The insights gained from this research provide essential references for furthering understanding particle dispersion mechanisms in supersonic flows and developing highly accurate numerical models.

Numerical Optimization of Hall Effect Thruster with variation in Magnetic Field

In the present study, numerical analyses were conducted to enhance the strength of the magnetic field. While electromagnetic coils and permanent magnets have conventionally been used for this purpose, the study explores the utilization of superconducting magnets, known for their significantly stronger magnetic fields. Through analytical tests on a thruster powered by a 5-kW source at 400 V, and 12.5 A current, computer simulations are conducted using an open-source HallThruster.jl developed using Julia language which gave 1D simulation of plasma properties of Hall effect thruster (HET), along a thrust of 0.687 N was achieved representing a three times greater increase, and specific impulse increasing to 3097 sec which is 1.7 times more compared to conventional results, accompanied by improved plasma parameters. Furthermore, to study the particle behavior the Particle In cell (PIC) approach was utilized, from which particle motion due to the magnetic field was achieved. By enhancing the magnetic field, we can significantly boost thrust, unlocking new possibilities for exploring distant planets and conducting long-duration space missions. Utilizing superconducting materials ensures continuous, efficient operation with increased thrust and fewer operating payloads, ultimately enhancing overall spacecraft functionality. This advancement paves the way for future innovations in space exploration and applications.

Dynamic visualization study of in situ cleaning of polystyrene microparticles off silicon wafer surface

With the improvement of chip performance, the requirements for cleaning the surface of silicon wafers are becoming higher. However, due to equipment and technology, it is difficult to observe the complex motion processes of particles at the microscopic scale. In this paper, an in situ dynamic visualization experiment on the cleaning of Polystyrene Latex (PSL) on the surface of silicon wafers is carried out by using a high-speed camera and image processing software. The mechanical behavior of PSL particles in fluid was investigated on a microscopic scale, and the trajectory and force of the polystyrene particles on the surface of the wafers were visualized, which provided a new perspective for understanding the complex cleaning process. Theoretical models were developed to explain the motion characteristics of the particles by calculating parameters such as van der Waals force, surface tension, and trailing force, and these models provide a theoretical basis for optimizing the cleaning process. There are four particle motion modes in the fluid: (1) interface capture, where the particles on the surface of silicon wafer are trapped by gas–liquid interface under surface tension; (2) particle collision, where the particles captured by the water film collide with the particles on the wafer surface to make the latter leave the silicon wafer; (3) jump attachment, where the particles jump and attach to the surface of the particle group under the action of lift; and (4) wall surface movement, where the particles start up under the action of water flow and then leave the silicon wafer quickly.

Circular motion and particle collisions in ergoregion of rotating and twisting charged black holes

The presence of clouds of strings, quintessential fields, and NUT charges has significant consequences for spacetime geometry, and their study is much more important from an observational and theoretical perspective. Hence, in this article, we aim to explore the rotating and twisting charged black holes with the cloud of strings and quintessential field through horizons, ergoregions, photon regions, circular motion, and energy efficiency. First, we derive the equation of motion and the expressions for studying the photon region. To investigate circular motion, we derive the mathematical expressions of energy and angular momentum. The cloud of stings reduces the stability of angular momentum and energy in prograde particle motions and shifts their minima from the black hole’s center to the right. Static black holes with clouds of strings have the greatest angular momentum in prograde orbital motion, while rotating ones without clouds of strings have the least. Furthermore, we examine the efficiency of energy extraction through the Penrose process. The known energy extraction efficiency of the Penrose process for an extreme Kerr black hole is about 21%, but in the presence of clouds of strings, it exceeds 100%.

Suppression of the coffee-ring effect by controlling the solid particle density

Previous studies show that the coffee-ring effect can be suppressed by altering the droplet's evaporation rate, surface tension, surface properties, and shape of particles. This experiment used five types of particles with different densities to analyze their behavior during the droplet evaporation process. The results showed that when the particle density is close to the fluid density, the particles move within the droplet and accumulate at the edges, forming a pronounced coffee-ring effect. Conversely, with the higher difference between the particle density and the fluid density increases, they tended to deposit uniformly at the bottom of the droplet and were less likely to be pushed to the edges by capillary effects, effectively suppressing the coffee-ring effect. We also observed that the movement speed of high-density particles relatively slowed down through particle image velocimetry tracking technology. By analyzing the Peclet number and the timescale between particle sinking speed and particle movement speed due to capillary flow, we explained how particle density influences the critical factors of particle sinking and suspension, thereby inhibiting the formation of the coffee-ring effect.

Surface Self-Diffusion Induced Sintering of Nanoparticles.

Despite the critical role of sintering phenomena in constraining the long-term durability of nanosized particles, a clear understanding of nanoparticle sintering has remained elusive due to the challenges in atomically tracking the neck initiation and discerning different mechanisms. Through the integration of in situ transmission electron microscopy and atomistic modeling, this study uncovers the atomic dynamics governing the neck initiation of Pt-Fe nanoparticles via a surface self-diffusion process, allowing for coalescence without significant particle movement. Real-time imaging reveals that thermally activated surface morphology changes in individual nanoparticles induce significant surface self-diffusion. The kinetic entrapment of self-diffusing atoms in the gaps between closely spaced nanoparticles leads to the nucleation and growth of atomic layers for neck formation. This surface self-diffusion-driven sintering process is activated at a relatively lower temperature compared to the classic Ostwald ripening and particle migration and coalescence processes. The fundamental insights have practical implications for manipulating the morphology, size distribution, and stability of nanostructures by leveraging surface self-diffusion processes.

A Study on the Drift Characteristics of the Yellow Sea Using the Finite Element Model

This study investigates the drift characteristics of the Yellow Sea using a finite element model. A tidal model of the Yellow Sea was constructed, and its accuracy was verified by comparing the calculated tide levels and tidal current results with observed data. Six points with distinct tidal characteristics were selected across different areas of the Yellow Sea, and the drift paths due to tidal currents were analyzed. Additionally, the drift paths under the influence of increasing wind, in combination with tidal currents, were examined. At the point where a north-south reciprocating current occurs, the particle movement distance increases when a southwesterly wind blows, compared to the influence of the currents alone. On the other hand, at the point characterized by a counterclockwise elliptical current, the drift distance either increases or decreases depending on the location. The relationship between wind and water depth was analyzed, revealing that the shallower the water depth, the greater the wind's influence, leading to increased particle movement.

Fluctuating hydrodynamics of an autophoretic particle near a permeable interface

We study the autophoretic motion of a spherical active particle interacting chemically and hydrodynamically with its fluctuating environment in the limit of rapid diffusion and slow viscous flow. Then, the chemical and hydrodynamic fields can be expressed in terms of integrals. The resulting boundary-domain integral equations provide a direct way of obtaining the traction on the particle, requiring the solution of linear integral equations. An exact solution for the chemical and hydrodynamic problems is obtained for a particle in an unbounded domain. For motion near boundaries, we provide corrections to the unbounded solutions in terms of chemical and hydrodynamic Green's functions, preserving the dissipative nature of autophoresis in a viscous fluid for all physical configurations. Using this, we give the fully stochastic update equations for the Brownian trajectory of an autophoretic particle in a complex environment. First, we analyse the Brownian dynamics of particles capable of complex motion in the bulk. We then introduce a chemically permeable planar surface of two immiscible liquids in the vicinity of the particle and provide explicit solutions to the chemo-hydrodynamics of this system. Finally, we study the case of an isotropically phoretic particle hovering above an interface as a function of interfacial solute permeability and viscosity contrast.

Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to the S2 star orbit

This study provides a comprehensive analytical investigation of the bound and unbound motion of magnetized particles orbiting a Schwarzschild black hole immersed in an external asymptotically uniform magnetic field, which includes all conceivable types of bounded and unbounded orbits. In particular, for planetary orbits, we perform a comparative analysis of our findings with the observed position of the S2 star carrying magnetic dipole moment around Sagittarius A*. We found maximum and minimum values for the parameter of magnetic interaction between the magnetic dipole of the star and the external magnetic field, as well as the energy and angular momentum of the S2 star. As a result, we obtain estimations of the magnetic dipole of the star in the order of 106 G·cm3. Additionally, we explore deflecting trajectories akin to gravitational Rutherford scattering. In obtaining the solutions for the orbital equations, we articulate the elliptic integrals and Jacobi elliptic functions, and illustrative figures and simulations augment our study. Published by the American Physical Society 2024

Study of Flow Characteristics and Anti-Scour Protection Around Tandem Piers Under Ice Cover

The impact of an ice-covered environment on the local flow characteristics of a bridge pier was studied through a series of flume tests, and the dominant factors affecting the scour pattern were found to grasp the change laws of the local hydrodynamic characteristics of the bridge pier under the ice cover. At the same time, because the scour problem of the pier foundation is a technical problem throughout the life-cycle of the bridge, to determine the optimal anti-scour protection effect on the foundation of the bridge pier, active protection scour plate was used to carry out scour protection tests, and its structural shape was optimized to obtain better anti-scour performance. The test results show that the jumping movements of sediment particles in the scour hole around the pier are mainly caused by events Q2 and Q4, which are accompanied by events Q1 and Q3 and cause the particle rolling phenomenon, where Q1 and Q3 events are outward and inward interacting flow regimes, and Q2 and Q4 events are jet and sweeping flow regimes, respectively. The power spectral attenuation rate in front of the upstream pier is high without masking effects, while strong circulation at the remaining locations results in strong vorticity and high spectral density, in particular, when the sampling time series is 60 s (i.e., f = 1/60), the variance loss rates under ice-covered conditions at the front of the upstream pier, between the two piers, and at the tail end of the downstream pier are 0.5%, 4.6%, and 9.8%, respectively, suggesting a smaller contribution of ice cover to the variance loss.

Modeling the Swelling Behavior of Clayey Geomaterials Across Scales: Advances and Challenges

ABSTRACTMost soils and rocks contain varying fractions of clay minerals within their solid matrix. These geomaterials can exhibit a significant swelling potential toward chemo‐thermo‐hydromechanical loadings. Several multiscale modeling techniques have been developed to ascertain their swelling behavior across various scales, with molecular dynamics (MD), micromechanics‐based approaches, and double‐porosity models being the most common. MD simulation is a computational technique that applies Newton's second law of motion to depict the movement of particles within a granular system. Micromechanics‐based approaches upscale the poro‐elasticity law from the clay layer level to the sample scale through homogenization. Dual‐porosity models are generally based on elasto‐plasticity, incorporating different hydro‐mechanical laws at two distinct scales. These models have been extensively used, particularly for clayey soils and bentonites, though their application to clayey rocks has not been reported in the literature. Although their significant contribution to the understanding of clay swelling behavior, these techniques have been insufficiently reviewed, compared, and discussed mutually in the literature. This paper aims to provide a cross‐look on these multiscale approaches by presenting the theoretical background of existing formulations, highlighting breakthrough results, discussing major differences and current challenges, and proposing future perspectives.

Dirichlet Integral and Its Generalization by Different Methods

Dirichlet integral, as the integration of sine function over x from positive infinity to 0, or negative infinity, is known as one of the most important concepts in mathematical analysis. In probability and statistics, Dirichlet integral is used in calculating expectation and variance. In physics, Dirichlet integral is used in describing the movement of a charged particle in specific electromagnetic fields, and the wave function of particles in quantum physics. In computer science, Dirichlet integral is used in the optimization of neural network. In economics and management, Dirichlet integral is used in the optimization of production and distribution, the estimation of the risk and return in investment. In this paper, Dirichlet Integral and its generalization are studied. This paper provides several methods including residue theorem and Feynman’s trick to determine the value of Dirichlet integral. Meanwhile, this paper extends Dirichlet integral to the case of n -th power and deduces a general solution by gamma function for the integral.

A novel hybrid information-based PF-WOA algorithm for gas source localization in 3D space

Abstract In recent years, dangerous gas leakage events occur frequently. Rapid and accurate location of gas leakage sources by mobile robots is the key to avoid the expansion of disasters. In order to solve the problem of discontinuous gas concentration gradient and sparse gas environment in three-dimensional space, particle filter, and whale swarm optimization algorithm are integrated to locate gas source. Firstly, the Z-shape search and comb search are used to locate the plume, and then, the particle filter algorithm is combined with the whale optimization method to guide the particle movement, and the random inertial disturbance term is designed to improve the convergence speed and search accuracy of the algorithm. Experimental results in three-dimensional environment show that the proposed information-driven particle filter whale optimization hybrid algorithm effectively guides the robot in localizing gas source within a certain range, significantly enhancing both the efficiency and accuracy of localization compared to other algorithms.

Enhanced three-dimensional particle detection in microcirculation experiments with defocus particle tracking and ghost red blood cells

Experimental investigations on the motion of rigid particles in microcirculation environments are still scarce owing to the three-dimensional (3D) motion of the particles and to the particle image masking due to the presence of the red blood cells (RBCs). Despite the recent progress on the 3D tracking of rigid particles in RBC flows with defocus particle tracking (DPT) methods, the problem of particle image masking remains to be solved. Here, we propose, test, and evaluate the use hemoglobin-free RBCs, also known as ghost RBCs, as a replacement for normal RBCs in experiments with rigid particles in microcirculation environments. We performed DPT measurements of a pressure-driven flow of normal and ghost RBC suspensions seeded with rigid particles at three different flow rates. We show that the quasi-transparent appearance of ghost RBCs, as a result of the lack of hemoglobin, eliminates the RBC-induced masking of the defocused particle images and allows to achieve the particle matching standards found in cell-free experiments. In fact, ghost RBC suspensions enable the tracking of the rigid particles across the entire height of the microchannel, which was not possible in normal RBC flows. On a fluid dynamic level, we show that ghost RBC suspensions provide similar conditions to normal RBCs in terms of the velocity of the rigid particles and the rigid particles exhibit similar lateral dynamics in both types of cell suspensions. In essence, the findings from this work demonstrate that ghost RBCs are a well-suited replacement for normal RBCs in experiments aiming at deciphering the motion of rigid particles in microcirculation environments.Graphical abstract

Motion of charged particles in an electromagnetic swirling universe: The complete set of solutions

Motion of charged particles in an electromagnetic swirling universe: The complete set of solutions

Motility-Induced Pinning in Flocking System with Discrete Symmetry.

We report a motility-induced pinning transition in the active Ising model for a self-propelled particle system with discrete symmetry. This model was known to exhibit a liquid-gas type flocking phase transition, but a recent study reveals that the polar order is metastable due to droplet excitation. Using extensive MonteCarlo simulations, we demonstrate that, for an intermediate alignment interaction strength, the steady state is characterized by traveling local domains, which renders the polar order short-ranged in both space and time. We further demonstrate that interfaces between colliding domains become pinned as the alignment interaction strength increases. A resonating back-and-forth motion of individual self-propelled particles across interfaces is identified as a mechanism for the pinning. We present a numerical phase diagram for the motility-induced pinning transition, and an approximate analytic theory for the growth and shrink dynamics of pinned interfaces. Our results show that pinned interfaces grow to a macroscopic size preventing the polar order in the regime where the particle diffusion rate is sufficiently smaller than the self-propulsion rate. The growth behavior in the opposite regime and its implications on the polar order remain unresolved and require further investigation.

Epicyclic oscillations and particle collision with trajectories around quantum corrected black holes

The present study deals with the orbital, oscillatory motion, and trajectories of test particles around quantum-corrected black holes. The angular momentum within specific energy is calculated to discuss stable circular orbits. The effective potential through Hamiltonian is calculated around quantum-corrected black holes. The trajectories scenario around particles of considered black hole solutions are discussed. Further, we provide the mathematical formulas for both latitudinal and radial frequencies. The primary properties of test particle quasi-periodic oscillations in stable circular orbits in the black hole’s equatorial plane are investigated. We provide a Markov Chain Monte Carlo analysis of the restrictions on quantum-corrected black hole attributes. We analyze QPOs detected in X-ray binaries, namely the cores of the galaxies Sgr A∗, M82 X-1, microquasars XTE J1550-564, GRS 1915+105 and GRO J1655-40. Additionally, the process of Periastron precession is examined. We show that the velocity of particles around black holes is strongly dependent on the parameters of the model. Notably, the pictorial behavior that describes our results feasibility.

Complex stochastic optimal control foundation of quantum mechanics

Abstract Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB equation directly to complex numbers, an approach that overlooks the fundamental problem of comparing complex numbers when finding optimal controls. This paper explores the application of the HJB equation in the context of complex variables. It provides an in-depth investigation of the stochastic movement of quantum particles within the framework of stochastic optimal control theory. We obtain the complex diffusion coefficient in the stochastic equation of motion using the Cauchy-Riemann theorem, considering that the particle’s stochastic movement is described by two perfectly correlated real and imaginary stochastic processes. During the development of the covariant form of the HJB equation, we demonstrate that if the temporal stochastic increments of the two processes are perfectly correlated, then the spatial stochastic increments must be perfectly anti-correlated, and vice versa. The diffusion coefficient we derive has a form that enables the linearization of the HJB equation. The method for linearizing the HJB equation, along with the subsequent derivation of the Dirac equation, was developed in our previous work [V. Yordanov, Scientific Reports 14, 6507 (2024)]. These insights deepen our understanding of quantum dynamics and enhance the application of stochastic optimal control theory to quantum mechanics.