Particle Systems Research Articles

Lane formation of colloidal particles driven in parallel by gravity.

We investigate the lane formation in nonequilibrium systems of colloidal particles moving in parallel that are driven by the force of gravity. For this setup, an experimental implementation of a channel on a slope can be conceptualized. We employ the Brownian dynamics algorithm and confine the repulsive particles with hard walls based on the solution of the Smoluchowski equationin the half space. A difference of the driving force acting on the colloids could be achieved by using two spherical particle types with differing diameters but equal mass density. First, we investigate how a difference in the channel slope affects the lane formation of the systems, after which we analyze the lanes that formed. We find that the large particles push the small particles to the walls, resulting in exclusively small particle lanes at the walls. This contrasts the equilibrium state, where depletion forces push the larger particles to the walls. Additionally, we have a closer look at the mechanisms by which the lanes form. Finally, we find system parameter values that foster lane formation to lay the foundation for an experimental realization of our proposed setup. To round this off, we give an exemplary calculation of the slope angle needed to get the experimental system into a state of lane order. With the examination of lane order in systems that are driven in parallel, we hope to deepen our understanding of nonequilibrium order phenomena.

Remediation of charged organic pollutants—binding motifs for highly efficient water cleaning with nanoparticles

AbstractMany charged organic molecules behave as persistent and hazardous pollutants with harmful effects on human health and ecosystems. They are widely distributed related to their charged molecular structure that provides water solubility. In order to track the fate and behavior of such pollutants, charged dyes with specific absorption in the visible spectra serve as convenient model compounds. We provide a platform of smart adsorbers that efficiently remediate positively and negatively charged dyes (crystal violet and Amaranth) from water. Metal oxide nanoparticles serve as a core with an intrinsically large surface area. The surface potential was tuned towards positive or negative by decorating the cores with self‐assembled monolayers of dedicated long‐chained phosphonic acid derivatives. Selective remediation of the dyes was obtained with corresponding oppositely charged core‐shell nanoparticles. Mixed dye solution can be cleaned by a cascade approach or by applying both particle systems simultaneously. The removal efficiency was determined as a function of particle concentration via UV‐spectroscopy. The results of remediation experiments at different pH values and using superparamagnetic iron oxide nanoparticle cores lead to a simple process with recycling capability.

Asymptotics and criticality for a space-dependent branching process

We investigate a non-conservative semigroup determined by a branching process tracing the evolution of particles moving in a domain in . When a particle is killed at the boundary, a new generation of particles with mean number is born at a random point in the domain. Between branching, the particles are driven by a diffusion process with Dirichlet boundary conditions. According to the sign of , we distinguish super/sub-critical regimes and determine the exact exponential rate for the total number of particles , with depending explicitly on . We prove the Yaglom limit , where the quasi-stationary distribution ν is determined by the resolvent of the Dirichlet kernel at the point . The main application is in particle systems, where the normalization of the semigroup by its total mass gives the hydrodynamic limit of the Bak-Sneppen branching diffusions (BSBD). Since ν is the asymptotic profile under equilibrium, and the family of quasi-stationary distributions ν is indexed by , the model provides an explicit example of self-organized criticality.

Interpretasi Atom dalam Kajian Surat Aż-Żāriyāt

This research was conducted as an effort to obtain a reading material related to thermodynamics so that it can be more easily understood by students or other readers. In conducting research, a researcher needs to follow the rules and regulations that apply so that the results obtained can be said to be valid. This research was conducted using the literature review method, namely by looking for sources that lead to a literature review of the basic concepts of thermodynamics which in this search are very important and much needed. The results of this study are that there are implications or connectedness between the concept of a single particle system and thermodynamics. Single particle systems trapped in a potential well can be explained or understood from a thermodynamic perspective.

Approximation of distribution-independent and distribution-dependent stochastic differential equations with singular drifts

This work is concerned with convergence rate of Euler–Maruyama scheme for distribution-independent and distribution-dependent stochastic differential equations, where the drifts involved are Dini continuous and unbounded. Via introducing a new Zvonkin-type’s transformation, we investigate convergence rate of Euler–Maruyama scheme for stochastic differential equations with singular coefficients which allows the drifts to be unbounded. Moreover, via the analysis of interacting particle systems, we show an approximation issue on a class of distribution-dependent stochastic differential equations with singular drifts. More specifically, propagation of chaos and convergence rate of the Euler–Maruyama scheme associated with the interacting particle systems are investigated.

Analysis of process parameter sensitivities of jet-based direct mixing gas phase hetero-agglomeration by DEM/CFD-modelling

A new approach to the formation of hetero-agglomerates, originating from mixtures of particles of different materials, has been proposed and analysed. The aim is to develop a process capable of producing hetero-agglomerates with a high relative number of contacts between particles of different materials. The proposed process is a jet based mixing gas phase hetero-agglomeration approach where the particle systems are dispersed into the gas phase and brought together by two particle laden jets. The process is analysed using Discrete Element Method (DEM) one-way coupled with Computational Fluid Dynamics (CFD), including models for adhesive contact forces, turbulence-induced fluctuating fluid forces and Coulomb forces for charged materials. Particle mass flow, particle surface energy, jets relative alignment, gas inflow velocity, particle size and electrical charge are varied to understand their effect on the hetero-agglomerate formation. This allows conclusions to be drawn about process intensification that can be used in subsequent experimental investigations.

Milstein schemes and antithetic multilevel Monte Carlo sampling for delay McKean–Vlasov equations and interacting particle systems

Abstract In this paper, we first derive Milstein schemes for an interacting particle system associated with point delay McKean–Vlasov stochastic differential equations, possibly with a drift term exhibiting super-linear growth in the state component. We prove strong convergence of order one and moment stability, making use of techniques from variational calculus on the space of probability measures with finite second-order moments. Then, we introduce an antithetic multilevel Milstein scheme, which leads to optimal complexity estimators for expected functionals of solutions to delay McKean–Vlasov equations without the need to simulate Lévy areas.

Phase transitions in systems of particles with only hard-core interactions

This article contains our comments and views on the status of the current understanding of phase transitions in systems in thermodynamic equilibrium with only hard-core interactions, based on our work in this area. The equation of state for the hard sphere gas in d-dimensions is discussed. The universal repulsive Lee-Yang singularity in the complex activity plane, and its relation to the directed and undirected polymer models are outlined. We also discuss orientationally disordered crystalline mesophases, and some of their models.

The cost-saving potential of next-generation particle technology CSP with steam cycles

The cost-saving potential of next-generation concentrating solar power plants based on particle technology with steam cycles is assessed. Techno-economic models were created to optimize three systems with different steam cycles, ranging from state of the art to future development, for levelized cost of electricity and to compare them to a state-of-the-art molten salt tower system. Results show that the minimum levelized cost for a particle system is almost identical to that of a molten salt system (+0.1%), however larger solar multiples and storage capacities are preferred. Cost advantages for the receiver and storage subsystems are compensated for by increased costs for a multi-tower setup and the particle heat exchanger. The choice of the three investigated power cycles has only a marginal impact on the overall levelized cost (¡2.3%). Finally, several potential improvements to particle systems are identified which could lead to further cost reductions and an increase in electric yield.

The regularised inertial Dean–Kawasaki equation: discontinuous Galerkin approximation and modelling for low-density regime

The Regularised Inertial Dean–Kawasaki model (RIDK) – introduced by the authors and J. Zimmer in earlier works – is a nonlinear stochastic PDE capturing fluctuations around the meanfield limit for large-scale particle systems in both particle density and momentum density. We focus on the following two aspects. Firstly, we set up a Discontinuous Galerkin (DG) discretisation scheme for the RIDK model: we provide suitable definitions of numerical fluxes at the interface of the mesh elements which are consistent with the wave-type nature of the RIDK model and grant stability of the simulations, and we quantify the rate of convergence in mean square to the continuous RIDK model. Secondly, we introduce modifications of the RIDK model in order to preserve positivity of the density (such a feature only holds in a “high-probability sense” for the original RIDK model). By means of numerical simulations, we show that the modifications lead to physically realistic and positive density profiles. In one case, subject to additional regularity constraints, we also prove positivity. Finally, we present an application of our methodology to a system of diffusing and reacting particles. Our Python code is available in open-source format.

Dimensional measures of generalized entropy

Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond the additive definition pioneered by Boltzmann, Gibbs, and Shannon (applicable to thermodynamic equilibria). For generalized entropies to be applied rigorously to nonequilibrium statistical mechanics, we suggest that there is a need for a physically interpretable (dimensional) framework that can be connected to dynamical processes operating in phase space. In this work, we introduce dimensional measures of entropy that admit arbitrary invertible weight functions (subject to curvature and convergence requirements). These ‘dimensional entropies’ have physical dimensions of phase-space volume and represent the extent of level sets of the distribution function. Dimensional entropies with power-law weight functions (related to Rényi and Tsallis entropies) are particularly robust, as they do not require any internal dimensional parameters due to their scale invariance. We also point out the existence of composite entropy measures that can be constructed from functionals of dimensional entropies. We calculate the response of the dimensional entropies to perturbations, showing that for a structured distribution, perturbations have the largest impact on entropies weighted at a similar phase-space scale. This elucidates the link between dynamics (perturbations) and statistics (entropies). Finally, we derive corresponding generalized maximum-entropy distributions. Dimensional entropies may be useful as a diagnostic (for irreversibility) and for theoretical modeling (if the underlying irreversible processes in phase space are understood) in chaotic and complex systems, such as collisionless systems of particles with long-range interactions.

(Invited) Z-Scheme Water Splitting Using Dye-Sensitized Metal Oxide Nanosheets

Solar water splitting by a heterogeneous photocatalyst, producing H2 and O2, is a potential solution for realizing large-scale H2 production. While dye-sensitized metal oxides are good candidates as H2 evolution photocatalysts for solar-driven Z-scheme water splitting, their solar-to-hydrogen (STH) energy conversion efficiencies remains low because of uncontrolled charge recombination reactions. Here it is shown that modification of Ru dye-sensitized, Pt- intercalated HCa2Nb3O10 nanosheets (Ru/Pt/HCa2Nb3O10) with both amorphous Al2O3 and poly(styrenesulfonate) (PSS) improves the STH efficiency of Z-scheme overall water splitting by a factor of ~100, when the nanosheets are used in combination with a WO3-based O2 evolution photocatalyst and an I3 –/I– redox mediator, relative to an analogous system that uses unmodified Ru/Pt/HCa2Nb3O10. The Al2O3 and PSS modifiers, which have previously been shown to suppress back electron transfer reactions in a dye-sensitized H2 evolution photocatalyst, enabled operation of the Z-scheme system even at low intensity of simulated sunlight without a decrease in the STH values. By using the optimized photocatalyst, PSS/Ru/Al2O3/Pt/HCa2Nb3O10, a maximum STH of 0.12% and an apparent quantum yield of 4.1% at 420 nm were obtained, by far the highest among dye-sensitized water splitting systems and also comparable to conventional semiconductor-based suspended particulate photocatalyst systems.

A Monotone Discretization for the Fractional Obstacle Problem and Its Improved Policy Iteration

In recent years, the fractional Laplacian has attracted the attention of many researchers, the corresponding fractional obstacle problems have been widely applied in mathematical finance, particle systems, and elastic theory. Furthermore, the monotonicity of the numerical scheme is beneficial for numerical stability. The purpose of this work is to introduce a monotone discretization method for addressing obstacle problems involving the integral fractional Laplacian with homogeneous Dirichlet boundary conditions over bounded Lipschitz domains. Through successful monotone discretization of the fractional Laplacian, the monotonicity is preserved for the fractional obstacle problem and the uniform boundedness, existence, and uniqueness of the numerical solutions of the fractional obstacle problems are proved. A policy iteration is adopted to solve the discrete nonlinear problems, and the convergence after finite iterations can be proved through the monotonicity of the scheme. Our improved policy iteration, adapted to solution regularity, demonstrates superior performance by modifying discretization across different regions. Numerical examples underscore the efficacy of the proposed method.

Heterogeneous Dynamics of Sheared Particle-Laden Fluid Interfaces with Janus Particle Doping.

The formation of particle clusters can substantially modify the dynamics and mechanical properties of suspensions in both two and three dimensions. While it has been well established that large network-spanning clusters increase the rigidity of particle systems, it is still unclear how the presence of localized nonpercolating clusters affects the dynamics and mechanical properties of particle suspensions. Here, we introduce self-assembled localized particle clusters at a fluid-fluid interface by mixing a fraction of Janus particles in a monolayer of homogeneous colloids. Each Janus particle binds to a few nearby homogeneous colloids, resulting in numerous small clusters uniformly distributed across the interface. Using a custom magnetic rod interfacial stress rheometer, we apply linear oscillatory shear to the particle-laden fluid interface. By analyzing the local affine deformation of particles from optical microscopy, we show that particles in localized clusters experience substantially lower shear-induced stretching than their neighbors outside clusters. We hypothesize that such heterogeneous dynamics induced by particle clusters increase the effective surface coverage of particles, which in turn enhances the shear moduli of the interface, as confirmed by direct interfacial rheological measurements. Our study illustrates the microscopic dynamics of small clusters in a shear flow and reveals their profound effects on the macroscopic rheology of particle-laden fluid interfaces. Our findings open an avenue for designing interfacial materials with improved mechanical properties via the control of formation of localized particle clusters.

Limit Solutions for a Lumped Parameter Model of Heat Transfer in a Diluted and Indirectly Heated Co-Current/Counter-Current Moving Bed Heat Exchanger with Heat Loss to Surroundings

Limit solutions and solutions by analogy play an important role in the interrelation of engineering problems. However, research with this approach is extremely rare in heat transfer in particulate systems. Given this scarcity, a series of limit solutions are developed for a lumped capacity (LP) model of a co/counter-current tubular moving bed heat exchanger (MBHE), vertically arranged, indirectly heated, diluted and with heat losses to the surroundings. In the solution methodology, the problem is formulated by analyzing the model parameters and the eigenvalues of the system operator, and by identifying indeterminate forms (INDs). Then, INDs are usually calculated by algebraic rearrangement and/or L'Hôpital's rule. Among the results, there are almost a dozen new solutions, the systematization of INDs in the counter-current flow and the verification of agreement between experimental data and the LP model for infinitely diluted bed - provided that the simplifying hypotheses are observed. Finally, the interconnection of LP models of MBHE in a decreasing order of complexity and in a historical perspective provides a broad understanding of the evolution of the LP modeling of this important industrial equipment.

Stochastic analysis of infinite particle systems—A new development in classical stochastic analysis and dynamical universality of random matrices

We examine the stochastic dynamics of infinite particle systems moving in R d \mathbb {R}^{d} . The classical stochastic analysis pursues the stochastic dynamics of a single particle. We explain how to extend the classical stochastic analysis when the object becomes an infinite particle system. The equilibrium states of a system of infinite number of particles resulting from random matrices have the logarithmic function as an interaction potential. Hence, we develop a theory that applies to interaction potentials having a dominating influence over long distances. As an application, we show that the universality of point processes related to random matrices holds for stochastic dynamics.

An insight into the interaction between fluid and granular soil based on a resolved CFD-DEM method

Fluid-solid interaction is an essential scientific issue interested many researchers in geological and geotechnical fields, which always holds the key to understanding the meso-mechanism underlying the water-induced geohazards of granular soils such as debris flow, piping erosion, and soil liquefaction. Therefore, this study utilized a resolved coupling method of computational fluid dynamics (CFD) and discrete element method (DEM) to investigate the fluid-solid interaction and its underlying meso mechanics within the granular soils. Three representative cases including single particle free setting, seepage in narrow tubes with dense-packed particles, and one-dimensional consolidation of particle column were implemented to validate the accuracy and efficiency of the resolved CFD-DEM in granular soils. Moreover, the influence of the mesh size and timestep were evaluated in dilute and dense particle systems, respectively. All the numerical results indicated well agreement with the experimental or analytical results reported in literatures. Furthermore, the nonlinear behaviours of the fluid-solid interaction (e.g., wake flow and wall effect) and authentic characteristics at pore scale level were fully depicted in this study. These novel findings provided a deep insight into the meso-mechanics of the complicated fluid-solid interaction within saturated granular soils.

Application of immersed boundary methods to non-Newtonian yield-pseudoplastic flows

The interaction force between fluid and particles in particulate flows is highly dependent on the rheology of fluid. In some engineering applications, like mineral processing, the rheological behaviour of the carrier fluid is characterized by a yield-pseudoplastic non-Newtonian model. The immersed boundary method (IBM) is a numerical strategy to simulate the interaction between phases in the particulate systems using a Cartesian fixed grid. It imposes the solid boundary condition in the computational domain through a modification (e.g. a forcing term) in the governing equations. However, there is still little study in the literature discussing the applicability of different IBMs to yield-pseudoplastic flows. In this paper, the numerical methodology in several versions of immersed boundary methods, including the Volume Penalization IBM (VP-IBM), Indirect Imposition of Discrete Forcing IBM (ID-IBM), and Direct Imposition of Discrete Forcing (DD-IBM), is described. The numerical implementation of the methods is first validated using Newtonian benchmark cases. Then the solvers are utilized for the simulation of yield-pseudoplastic cases with stationary or moving particles. The investigation shows that in the explicit forcing methods, like VP-IBM and ID-IBM, the forcing procedure is conducted using an intermediate solution over the entire computational domain. The dependence of viscosity to strain rate in non-Newtonian cases leads to an inevitable sharp change in viscosity near the solid surface, giving rise to stiffness of the intermediate solution in the interface region. This makes the explicit forcing approaches based on intermediate solution incompatible with the flows with non-Newtonian yield-pseudoplastic rheology. On the other hand, the implicit forcing used in DD-IBM directly implements the boundary conditions on the boundary cells, making this method free from the perturbations related to the highly viscous solid region. In this regard, the simulation with the Direct Imposition IBMs like ghost-cell shows a good agreement between the predicted results and the experimental measurements for the stationary/moving cases. Therefore, it is shown that the DD-IBM is a reliable approach to modelling non-Newtonian flows.

The Use of Particulate Systems for Tuberculosis Prophylaxis and Treatment: Opportunities and Challenges.

The use of particles to develop vaccines and treatments for a wide variety of diseases has increased, and their success has been demonstrated in preclinical investigations. Accurately targeting cells and minimizing doses and adverse side effects, while inducing an adequate biological response, are important advantages that particulate systems offer. The most used particulate systems are liposomes and their derivatives, immunostimulatory complexes, virus-like particles, and organic or inorganic nano- and microparticles. Most of these systems have been proven using therapeutic or prophylactic approaches to control tuberculosis, one of the most important infectious diseases worldwide. This article reviews the progress and current state of the use of particles for the administration of TB vaccines and treatments in vitro and in vivo, with a special emphasis on polymeric particles. In addition, we discuss the challenges and benefits of using these particulate systems to provide researchers with an overview of the most promising strategies in current preclinical trials, offering a perspective on their progress to clinical trials.

Turbulent Diffusion of the Particles within Pulsar Wind Nebulae

A turbulent diffusion model is presented to account for the energy and spatial diffusion of the particles within pulsar wind nebulae (PWNe), with the assumption that the energy injected from the pulsar into the nebula is split between the turbulence waves and electrons/positrons. In the model, the mutual interactions between the turbulence waves and particles are taken into account, representing the damping effect of the turbulence waves and the stochastic acceleration and spatial diffusion of the particles, respectively. The evolutions of the turbulence waves and particles are described with the coupled kinetic equations, in which the Kolmogorov- and Kraichnan-type turbulence are, respectively, considered. The model is applied to the Crab Nebula and shows that the spectral energy distribution of the PWN can be naturally explained. Our modeling results indicate that, for the Crab Nebula, the stochastic acceleration and spatial diffusion processes play a role in modifying the electron spectrum at the low energies of E e ≲ 1 TeV. The damping process seems more effective for modulating the turbulent spectrum in the Kraichnan-type turbulence, resulting in the nonlinear variations of the current energy and spatial diffusion coefficients with energy generated in the wave–particle systems. In the Kolmogorov-type turbulence, the diffusion coefficients are more consistent with the quasi-linear distributions, due to the energy cascade dominating over the damping effect.