Particle Systems Research Articles

Engineering Azeotropy to Optimize the Self-Assembly of Colloidal Mixtures.

The goal of inverse self-assembly is to design interparticle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new component increasing the thermodynamic degrees of freedom and, hence, the complexity of the self-assembly pathway. In this work we explore the possibility to use azeotropy, i.e., a special thermodynamic condition where the system behaves effectively as a one-component system, as a way to control the self-assembly of an arbitrary number of components. Exploiting the mass-balance equations, we show how to select patchy particle systems that exhibit azeotropic points along the desired self-assembly pathway. As an example we map the phase diagram of a binary mixture that, by design, fully assembles into cubic (and only cubic) diamond crystal via an azeotropic point. The ability to explicitly include azeotropic points in artificial designs reveals effective pathways for the self-assembly of complex structures.

On the ergodicity of interacting particle systems under number rigidity

In this paper, we provide relations among the following properties: the tail triviality of a probability measure mu on the configuration space {varvec{Upsilon }};the finiteness of a suitable L^2-transportation-type distance bar{textsf {d} }_{varvec{Upsilon }};the irreducibility of local {mu }-symmetric Dirichlet forms on {varvec{Upsilon }}. As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/permanental point processes including text {sine}_{2}, text {Airy}_{2}, text {Bessel}_{alpha , 2} (alpha ge 1), and text {Ginibre} point processes. In particular, the case of the unlabelled Dyson Brownian motion is covered. For the proof, the number rigidity of point processes in the sense of Ghosh–Peres plays a key role.

Transplantation and optimization of molecular dynamics simulation on MT-3000

Molecular dynamics (MD) simulation is a research method to simulate the change of particle systems with the help of the powerful calculating power of computers. As the number of atoms increases and the duration of the simulation system extends, current mainstream software for MD simulations has become increasingly strained. This is largely due to a surge in computing time, attributed to the architecture characteristics of the central processing unit (CPU), which executes instructions serially and accesses shared memory randomly. These features have resulted in an enormous overhead that these software applications can no longer efficiently manage. Recently, National University of Defense Technology proposed the MT-3000 processor, a multi-zone heterogeneous architecture with a double-precision peak performance of 11.5 TFLOPS. In this paper, we implement the heterogeneous transplantation and optimization of the massively parallel program for MD simulation on Tianhe new-generation supercomputer based on MT-3000. By porting the key computing hotspot module to the acceleration zones of MT-3000, we have greatly improved the efficiency and performance of the simulation of billion-metal-atom cascade collision. The experimental results show that the heterogeneous MD program on a single node can achieve about 6 times faster than the original version executed in a general purpose zone of MT-3000. On the basis of 250 thousand cores, the strong-scalability parallel efficiency of heterogeneous MD program using 4 million cores can reach 89.89%, and the weak-scalability parallel efficiency can reach 91.98%. It can be predicted that the heterogeneous MD implementation has excellent scaling ability to simulate large-scale atomic cascade collisions on ten million of cores.

Numerical simulation for the initial state of avalanche in polydisperse particle systems

Numerical simulation is employed to investigate the initial state of avalanche in polydisperse particle systems. Nucleation and propagation processes are illustrated for pentadisperse and triadisperse particle systems, respectively. In these processes, particles involved in the avalanche grow slowly in the early stage and explosively in the later stage, which is clearly different from the continuous and steady growth trend in the monodisperse system. By examining the avalanche propagation, the number growth of particles involved in the avalanche and the slope of the number growth, the initial state can be divided into three stages: T1 (nucleation stage), T2 (propagation stage), T3 (overall avalanche stage). We focus on the characteristics of the avalanche in the T2 stage, and find that propagation distances increase almost linearly in both axial and radial directions in polydisperse systems. We also consider the distribution characteristics of the average coordination number and average velocity for the moving particles. The results support that the polydisperse particle systems are more stable in the T2 stage.

Classical and quantum gravity from the axioms of relativistic quantum mechanics

It is common practice to describe elementary particles by irreducible unitary representations of the Poincaré group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincaré group. Representations of the Poincaré group are characterised by fixed eigenvalues of two Casimir operators corresponding to a fixed mass and a fixed angular momentum. In multi-particle systems (of massive spinless particles), fixing these eigenvalues leads to correlations between the particles. In the quasi-classical approximation of large quantum numbers, these correlations take on the structure of a gravitational interaction described by the field equations of conformal gravity. A theoretical value of the corresponding gravitational constant is calculated. It agrees with the empirical value used in the field equations of general relativity.

Dynamical Gibbs variational principles for irreversible interacting particle systems with applications to attractor properties

Dynamical Gibbs variational principles for irreversible interacting particle systems with applications to attractor properties

A review: Recent advancement in the formulation and evaluation of the nanoparticles and its application

Due to their unique or superior physical and chemical properties compared to bulk material, nanoparticles have become extremely popular in recent years. The pharmacokinetic and pharmacodynamic properties of many different types of pharmacological compounds have been altered and improved by using particle systems like nanoparticles. They were used in vivo to prevent the drug entity from leaving the systemic circulation, restrict drug access to the targeted areas, and deliver the drug at a steady and controlled rate to the site of action. To maximize therapeutic benefit while reducing adverse effects, a variety of polymers have been utilized in the nanoparticle drug delivery method. Because of its great selectivity towards the target region, nanotechnology use is significantly important in the field of medicine delivery since it can limit the potentially toxic effects of medication on normal cells. Nanoparticles (NP) play a crucial role and can conjugate with various medications using exact methods to deliver the drug to the target place. The nanoparticle surface is constructed with co-polymers to provide protection from immune cells and ligands to gain affinity inside the course of particular cells. The drug that is attached to nanoparticles can eventually recognize the location, join the target, and enter the cell by receptor-mediated endocytosis. Nanoparticles can then release medications under controlled conditions to treat disorders. Here, the review gives various aspects of the nanoparticle characterization, formulation, evaluation and application in delivery of drug molecules.

Rigid clumps in the MercuryDPM particle dynamics code

Discrete particle simulations have become the standard in science and industrial applications exploring the properties of particulate systems. Most of such simulations rely on the concept of interacting spherical particles to describe the properties of particulates, although, the correct representation of the nonspherical particle shape is crucial for a number of applications. In this work we describe the implementation of clumps, i.e. assemblies of rigidly connected spherical particles, which can approximate given nonspherical shapes, within the MercuryDPM particle dynamics code. MercuryDPM contact detection algorithm is particularly efficient for polydisperse particle systems, which is essential for multilevel clumps approximating complex surfaces. We employ the existing open-source CLUMP library to generate clump particles. We detail the pre-processing tools providing necessary initial data, as well as the necessary adjustments of the algorithms of contact detection, collision/migration and numerical time integration. The capabilities of our implementation are illustrated for a variety of examples.

Simulation of fast-firing densification by the discrete element method

The macroscopic behavior of powder compacts during the sintering process originates at the microscopic level. Despite the marked advance in analytical techniques, the characteristics of microscale densification, including heat transfer phenomena in particulate systems under fast firing, still need to be determined. Here, a numerical approach is used to explore macro and microscale densification gaps aiming to predict the behavior of parts consolidated by non-isothermal sintering. The model was built integrating concepts of heat transfer, transient temperature regime, sintering, and contact forces and implemented within the Discrete Element Method (DEM) framework. The scope of the article includes an alumina-based case study in which simulations were compared with the experimental investigation. The simulation results showed good agreement with the experimental data. Densification microkinetics depicted the evolution of densification gradients inside the sample. The model demonstrated its value for predicting high heating rate sintering features.

The basic resolvents of position and momentum operators form a total set in the resolvent algebra

Let Q and P be the position and momentum operators of a particle in one dimension. It is shown that all compact operators can be approximated in norm by linear combinations of the basic resolvents (aQ+bP-ir)-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(aQ + bP - i r)^{-1}$$\\end{document} for real constants a,b,r≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a,b,r \ e 0$$\\end{document}. This implies that the basic resolvents form a total set (norm dense span) in the C*-algebra R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {R}$$\\end{document} generated by the resolvents, termed resolvent algebra. So the basic resolvents share this property with the unitary Weyl operators, which span the Weyl algebra. These results are obtained for finite systems of particles in any number of dimensions. The resolvent algebra of infinite systems (quantum fields), being the inductive limit of its finitely generated subalgebras, is likewise spanned by its basic resolvents.

Orthogonal intertwiners for infinite particle systems in the continuum

This article focuses on a system of sticky Brownian motions, also known as Howitt–Warren martingale problem, and correlated Brownian motions and shows that infinite-dimensional orthogonal polynomials intertwine the dynamics of infinitely many particles and their n-particle evolution. The proof is based on two assumptions about the model: information about the reversible measures for the n-particle dynamics and consistency. Additionally, explicit formulas for the polynomials are used, including a new explicit formula for infinite-dimensional Meixner polynomials, the orthogonal polynomials with respect to the Pascal process. As an application of the intertwining relations, new reversible measures for the infinite-particle dynamics are obtained.

Construction of hypoallergenic microgel by soy major allergen β-conglycinin through enzymatic hydrolysis and lactic acid bacteria fermentation

Soy allergenicity is a public concern, and the combination of multiple processing methods may be a promising strategy for reducing soy allergenicity. In this study, a novel two-step enzymatic hydrolysis followed by lactic acid bacteria fermentation was proposed for the construction of hypoallergenic soybean protein microgel. β-Conglycinin was used as the main soy allergen. The effects of different enzymatic hydrolysis (Alcalase, Neutrase, and Protamex) and LAB fermentation on β-conglycinin microgel formation and its immunoreactivity were investigated. Results showed that the use of different enzymes and the attainment of different degrees of hydrolysis affected the particle distribution and zeta potential in the microgels and leads to differences in microstructure and immunoreactivity. All hydrolysates compared with intact protein accelerated the formation of gel during LAB fermentation. Among the three assayed enzymes, fermented Protamex hydrolysates at 60 min (PF-60) demonstrated a microgel with an overall reduced average particle size (741.20±7.18 nm), lower absolute values of zeta potential (10.43±0.65 mV), and regular gel network. The antigenicity and IgE-binding capacity decreased to the lowest value of 0.30 % and 6.93 %, respectively. Peptidomics and immunoinformatic analysis suggested that PF-60 disrupted 17/30, 16/44, and 23/75 epitopes in the α, α′, and β subunits, respectively. Unlike the LAB-fermented unhydrolyzed β-conglycinin disrupted epitopes mostly located at the loop domain, PF-60 primarily promoted the exposure and disruption of allergen epitopes with β-sheet structure located at the core barrel domain. These findings can provide new perspectives on the preparation of hypoallergenic soybean-gel products on edible particulate systems.

Investigation on permeability of filter cake with different particle sizes: Experimental and simulation study

Cake permeability is a crucial macroscopic physical property in characterizing filtration behavior for coal slurry. However, there is still no appropriate model derived to establish the essential relationship between the cake permeability and complex particle property. In this study, the three-dimensional microstructures with different particle gradation and porosity were generated using particle discrete element software. The permeability of each constructed model was calculated utilizing Lattice Boltzmann Method (LBM). Simulation result shows that the Kozeny–Carman (KC) model is proper to predict the permeability of porous media with different gradations. When the gradation parameters are not considered, it shows that d30 can best represent the particle size characteristics of the particle systems. When the porosity and average particle size remain unchanged, the permeability increases with the increasing of the non-uniformity coefficient (Cu) and the curvature coefficient (Cc). Moreover, we proposed an analytical expression for the permeability estimation with different gradation characteristics, which contains the parameters that can be easily measured in engineering. Then a set of coal slurry samples with different particle size distributions were selected to conduct the filtration test, the permeability of each sample was measured to compare with the predicted results of the gradation permeability model. It is clear that the KC equation in this case can not calculate the cake permeability effectively. Although the gradation model is relatively appropriate to estimate the cake permeability, its accuracy still needs to be improved by considering the pore structure property to eliminate the effect of constant terms.

Upper bound efficiencies for work generation from the energy of confined systems of quantum particles

The maximum amount of work extraction from confined particles energy is treated for a larger class of particles than the usual case of boltzons and photons. The treatment does not restrict to exergy evaluation since real-world processes take place in finite time. Both reversible and endoreversible work extraction is considered. The maximum extractable work is estimated in case that the equilibrium of the particle system with the environment is not reached during work extraction. This result is different for bosons or fermions having non-zero rest mass in the non-relativistic limit and for zero rest mass or non-zero rest mass particles in the extreme relativistic limit, respectively. For particles obeying spontaneous creation and annihilation the exergy content cannot be properly defined. The exergy concept makes sense for confined particles for which very slow (flowing) filling and emptying processes may be imagined. The Carnot efficiency is not a proper upper bound for the conversion of confined thermal radiation into work but it may be used as a safe superior (but less accurate) limit in this case.

A comparative study of the fixed pivot technique and finite volume schemes for multi-dimensional breakage population balances

When modeling particle breakage, the use of a single dimension to characterize particulate systems becomes intractable when multiple dimensions (e.g., size and shape) are important. Amongst many potential numerical techniques, the Fixed Pivot Technique (FPT) and Finite Volume Schemes (FVS) are popular choices to resolve multi-dimensional breakage population balance equations (PBEs). However, whether there exists a general multi-purpose technique between the two remains unclear. Across all test cases with identical size domain and mesh, while both techniques demonstrate comparable accuracy in resolving the moments and number densities (with maximum difference in average relative errors of ∼O(100) and ∼O(102), respectively), and exhibit similar computational efficiency (time taken by FPT relative to FVS is of ∼O(100)), the choice of numerical technique is contingent upon the properties where accurate prediction is critical. To this end, FVS is the preferred choice when precise estimation of up to two properties is required owing to its simplicity, albeit requiring distinct schemes for different properties. Conversely, when more than two properties are crucial, the FPT is more suited as it preserves up to four properties in the internal 2D space. Overall, this work offers rational guidance for efficient and accurate modeling of multi-dimensional breakages.

Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems

We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2D Navier–Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically smoothing by means of the Neumann heat semigroup on the space domain, allows to establish uniform convergence of regularized empirical measures to (weak solutions of) Navier–Stokes equations.

Investigation of a Jet-Based Direct Mixing Process for Improved Structuring of Conductive Battery Hetero-Agglomerates

A jet-based direct mixing process is used to effectively mix heterogeneous materials. In this work, its application in the structuring, coating and agglomeration of cathode materials for all-solid-state battery (ASSB) production is investigated, with the aim of increasing the homogeneity and conductivity of the composites and ultimately improving battery performance. In this process, different particle systems consisting of lithium iron phosphate (LFP), carbon black (CB) and sodium chloride (NaCl) are dispersed in the gas phase and brought together in a mixing zone as particle-laden aerosol jets. The cathode material’s structure is studied through scanning electron microscopy combined with a focussed ion beam (SEM–FIB). Electrical conductivity measurements of the resulting composites assess the degree of mixing and the changes in tortuosity, while a laser light diffractor and a cascade impactor analyse the particle size distribution (PSD). The jet-based process effectively produces hetero-agglomerates with the possibility of creating different composite structures by adjusting the process parameters. The mass concentration influences not only the structure, but also the PSD in the flow and the electrical conductivity of the composite. The results serve as a basis for future experiments with solid electrolytes to comprehensively evaluate the process and the resulting battery materials.

Evolution of force networks during stick-slip motion of an intruder in a granular material: Topological measures extracted from experimental data.

In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of the granular medium to the driven intruder, focusing on the evolution of the force network during sticking periods. Because the available experimental data do not include precise information about individual contact forces, we use an approach developed in our previous work [Basak et al., J. Eng. Mech. 147, 04021100 (2021)0733-939910.1061/(ASCE)EM.1943-7889.0002003] based on networks constructed from measurements of the integrated strain magnitude on each particle. These networks are analyzed using topological measures based on persistence diagrams, revealing that force networks evolve smoothly but in a nontrivial manner throughout each sticking period, even though the intruder and granular particles are stationary. Characteristic features of persistence diagrams show identifiable slip precursors. In particular, the number of generators describing the structure and complexity of force networks increases consistently before slips. Key features of the dynamics are similar for granular materials composed of disks or pentagons, but some details are consistently different. In particular, we find significantly larger fluctuations of the measures computed based on persistence diagrams and, therefore, of the underlying networks, for systems of pentagonal particles.

Solving time-independent Schrödinger equation variationally using random numbers

Finding wavefunctions for even the simplest of interacting particle systems consisting of two particles is extremely difficult. It is therefore highly desirable that an accurate and easily implementable method be available to instructors and students of quantum-mechanics for obtaining wavefunctions for these particles. The usual approach taken to do this is to use parametrized functional form for the wavefunction in conjunction with the variational method to find approximate wavefunction and energy for the ground-state of such systems. In this paper, we employ random numbers to obtain ground-state wavefunctions and energies of two interacting particles in different one-dimensional potentials. The idea behind using random numbers is to search freely for functions that lead to lower and lower energy, converging eventually to its lowest value. The method presented is easily applicable numerically using a simple algorithm, and the wavefunctions obtained are highly accurate. Thus, the method presented makes study of two interacting particles accessible to instructors and students alike in a transparent manner.

Dynamics of Finite Inhomogeneous Particle Systems with Exclusion Interaction

We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. We show that the particle jump rates determine explicitly a unique partition of the system into maximal stable sub-systems, and that this partition can be obtained by a linear-time algorithm using only elementary arithmetic. The internal configuration of each stable sub-system possesses an explicit product-geometric limiting distribution, and the location of each stable sub-system obeys a strong law of large numbers with an explicit speed; the characteristic parameters of each stable sub-system are simple functions of the rate parameters for the corresponding particles. For the case where the entire system is stable, we provide a central limit theorem describing the fluctuations around the law of large numbers. Our approach draws on ramifications, in the exclusion context, of classical work of Goodman and Massey on partially-stable Jackson queueing networks.