Pairwise Particle Interactions Research Articles

Quark/gluon discrimination and top tagging with dual attention transformer

Jet tagging is a crucial classification task in high energy physics. Recently the performance of jet tagging has been significantly improved by the application of deep learning techniques. In this study, we introduce a new architecture for jet tagging: the particle dual attention transformer (P-DAT). This novel transformer architecture stands out by concurrently capturing both global and local information, while maintaining computational efficiency. Regarding the self attention mechanism, we have extended the established attention mechanism between particles to encompass the attention mechanism between particle features. The particle attention module computes particle level interactions across all the particles, while the channel attention module computes attention scores between particle features, which naturally captures jet level interactions by taking all particles into account. These two kinds of attention mechanisms can complement each other. Further, we incorporate both the pairwise particle interactions and the pairwise jet feature interactions in the attention mechanism. We demonstrate the effectiveness of the P-DAT architecture in classic top tagging and quark–gluon discrimination tasks, achieving competitive performance compared to other benchmark strategies.

Solvents govern rheology and jamming of polymeric bead suspensions

Despite their apparent simplicity, suspensions of hard spheres in a Newtonian fluid show complex non-Newtonian behaviors and remain poorly understood. Recent works have pointed out the crucial role of interparticle contact forces in these behaviors. Here, we show that the same (polystyrene) particles, when immersed in different Newtonian solvents, show different behaviors at both the microscopic and macroscopic scales. Thanks to interparticle force measurements in each solvent together with rheological measurements, we show how the fine details of the pairwise particle interactions impact the macroscopic behavior. The rheological properties (shear thinning, shear thickening, jamming solid fraction value) of the suspensions, made up of same particles, are shown to depend on the nature of the solvent. Here, we highlight several mechanisms at the particle scale: the swelling of polymeric particles in an organic solvent, the role of colloidal repulsive forces and inertia for particles in a water solution, and the variation of the friction coefficient as a function of the load for particles immersed in silicone oils. Our study provides new quantitative data to test micromechanical models and simulations. It questions the interpretation of previous experimental works. Finally, it shows the need to systematically characterize the interparticle normal and tangential forces when studying a given suspension of hard spheres in a Newtonian fluid

High frequency viscoelasticity of soft particle glasses

The storage and loss moduli for jammed soft particles are studied computationally for a variety of interparticle potentials and volume fractions. The qualitative behavior of the storage modulus is independent of the nature of the interparticle potential. The frequency dependence of the storage modulus computed in the simulations is described by a universal logistic formula exhibiting two plateaus at low and high frequencies. While the high-frequency modulus G∞ follows the prediction of the Zwanzig–Mountain expression, which depends on the pair distribution function and pairwise interparticle potential, no such formula exists for the low-frequency modulus G0. Here, we show that for jammed soft particles at a given volume fraction G0∼G∞/gmax, where gmax is the maximum in the pair distribution function. The qualitative nature of the loss modulus depends on the form of the near-field drag forces between the soft particles. At moderate to high frequency, the loss modulus increases with the frequency according to a power law whose exponent is related to the drag force expression between two sliding particles. Computational predictions of the storage and loss moduli match most experimental observations but some discrepancies are observed indicating behavior beyond pairwise particle interactions at high frequencies.

Continuum and Molecular Dynamics Studies of the Hydrodynamics of Colloids Straddling a Fluid Interface

Colloid-sized particles (10 nm–10 μm in characteristic size) adsorb onto fluid interfaces, where they minimize their interfacial energy by straddling the surface, immersing themselves partly in each phase bounding the interface. The energy minimum achieved by relocation to the surface can be orders of magnitude greater than the thermal energy, effectively trapping the particles into monolayers, allowing them freedom only to translate and rotate along the surface. Particles adsorbed at interfaces are models for the understanding of the dynamics and assembly of particles in two dimensions and have broad technological applications, importantly in foam and emulsion science and in the bottom-up fabrication of new materials based on their monolayer assemblies. In this review, the hydrodynamics of the colloid motion along the surface is examined from both continuum and molecular dynamics frameworks. The interfacial energies of adsorbed particles is discussed first, followed by the hydrodynamics, starting with isolated particles followed by pairwise and multiple particle interactions. The effect of particle shape is emphasized, and the role played by the immersion depth and the surface rheology is discussed; experiments illustrating the applicability of the hydrodynamic studies are also examined.

Dynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons

We consider a many-body Bosonic system with pairwise particle interaction given by $$N^{3\beta -1}v(N^\beta x)$$ where $$0<\beta <1$$ and v a non-negative spherically symmetric function. Our main result is the extension of the local-in-time Fock space approximation of the exact dynamics of squeezed states proved in Grillakis and Machedon (Commun Partial Differ Equ 42(1):24–67, 2017) for $$0<\beta <\frac{2}{3}$$ to a global-in-time approximation for $$0<\beta <1$$ . Our work can also be viewed as a generalization of the results in Boccato et al. (Ann Henri Poincaré 18(1):113–191, 2017) to a more general set of initial data that includes coherent states along with an improved error estimate. The key ingredients in establishing the Fock space approximation are the work of Grillakis and Machedon on the the local well-posedness theory (Grillakis and Machedon in Commun Partial Differ Equ 44(12):1431–1465, 2019), some recent established global estimate in Chong et al. (Commun Partial Differ Equ 56:1–41, 2021), and our quantitative results on the uniform in N global well-posedness of the time-dependent Hartree–Fock–Bogoliubov system.

Micromechanical modeling and experimental characterization for the elastoplastic behavior of a functionally graded material

Functionally Graded Materials (FGMs) are characterized by the distribution in composition and structure gradually over volume, which were recently designed and developed as a key component of a multifunctional building envelope for the high performance of energy efficiency. It was realized by mixing aluminum particles and fine High-Density Polyethylene (HDPE) powders through a vibration-sedimentation process. To investigate the elastoplastic behavior of FGMs, an elastoplastic model based on micromechanics with pairwise particle interactions is developed in this study. The particle phase is assumed to remain in its linearly elastic state while the matrix phase undergoes elastoplastic deformation. The corresponding yield function for the FGMs is investigated, where the pairwise interaction and probabilistic spatial distribution of particles are utilized to accommodate the gradation of particle volume fraction. Accordingly, the overall elastoplastic behavior of FGMs is established through the microscopic homogenization. The proposed algorithm is validated with uniaxial compression test of FGM samples, where the authentic particle distribution is captured statistically through image processing method. Finally, the effect of volume fraction distributions on the overall effective elastoplastic behavior of FMGs is investigated.

Analysis of the Viscosity of Dilute Suspensions Beyond Einstein’s Formula

We provide a mathematical analysis of the effective viscosity of suspensions of spherical particles in a Stokes flow, at low solid volume fraction $\phi$. Our objective is to go beyond the Einstein's approximation $\mu_{eff}=(1+\frac{5}{2}\phi)\mu$. Assuming a lower bound on the minimal distance between the $N$ particles, we are able to identify the $O(\phi^2)$ correction to the effective viscosity, which involves pairwise particle interactions. Applying the methodology developped over the last years on Coulomb gases, we are able to tackle the limit $N \rightarrow +\infty$ of the $O(\phi^2)$-correction, and provide explicit formula for this limit when the particles centers can be described by either periodic or stationary ergodic point processes.

High-energy radiation and pair production by Coulomb processes in particle-in-cell simulations

We present a Monte Carlo implementation of Bremsstrahlung, Bethe-Heitler, and Coulomb Trident processes into the particle-in-cell (PIC) simulation framework. In order to address photon emission and electron-positron pair productions in a wide range of physical conditions, we derive the Bremsstrahlung and Bethe-Heitler cross sections taking account of screening effects in arbitrary ionized plasmas. Our calculations are based on a simple model for the atomic Coulomb potential that describes shielding due to both bound electrons, free electrons, and ions. We then detail a pairwise particle interaction algorithm suited to weighted PIC plasma simulations, for which we perform several validation tests. Finally, we carry out a parametric study of photon and pair production during high-energy electron transport through micrometric solid foils. Compared to the zero-dimensional model of Myatt et al. [Phys. Rev. E 76, 066409 (2009)], our integrated one-dimensional simulations pinpoint the importance of the electron energy losses resulting from the plasma expansion.

Micromechanics-Based Elastoplastic Modeling of Functionally Graded Materials with Pairwise Particle Interactions

AbstractTo understand the inelastic behavior of functionally graded materials (FGMs) containing aluminum particles in high-density polyethylene (HDPE), a micromechanics-based elastoplastic model wa...

Asymptotic Analysis of Boundary Layers in a Repulsive Particle System

This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. This setting covers, for instance, pile-ups of dislocations, dislocation dipoles and dislocation walls. The main challenge in characterising the boundary behaviour is to control the nonlocal nature of the pairwise particle interactions. Using matched asymptotic expansions for the particle positions and rigorous development of an appropriate energy via $\Gamma $ -convergence, we obtain the equilibrium equation solved by the boundary layer correction, associate an energy with an appropriate scaling to this correction, and provide decay rates into the bulk.

Role of the potential landscape on the single-file diffusion through channels.

Transport of colloid particles through narrow channels is ubiquitous in cell biology as well as becoming increasingly important for microfluidic applications or targeted drug delivery. Membrane channels in cells are useful models for artificial designs because of their high efficiency, selectivity, and robustness to external fluctuations. Here, we model the passive channels that let cargo simply diffuse through them, affected by a potential profile along the way. Passive transporters achieve high levels of efficiency and specificity from binding interactions with the cargo inside the channel. This however leads to a paradox: why should channels which are so narrow that they are blocked by their cargo evolve to have binding regions for their cargo if that will effectively block them? Using Brownian dynamics simulations, we show that different potentials, notably symmetric, increase the flux through narrow passive channels - and investigate how shape and depth of potentials influence the flux. We find that there exist optimal depths for certain potential shapes and that it is most efficient to apply a small force over an extended region of the channel. On the other hand, having several spatially discrete binding pockets will not alter the flux significantly. We also explore the role of many-particle effects arising from pairwise particle interactions with their neighbours and demonstrate that the relative changes in flux can be accounted for by the kinetics of the absorption reaction at the end of the channel.

Finite element implementation of a non-local particle method for elasticity and fracture analysis

A finite element formulation for a non-local particle method is proposed in this paper for elasticity and fracture analysis of 2D solids. The model is based on a new particle method which incorporates a non-local multi-body particle interaction into the conventional pair-wise particle interactions. The non-local particle method is capable of modeling solids with arbitrary Poisson׳s ratio. Finite element formulation is proposed for the implicit solution of elasticity and fracture problems under static/quasi-static conditions, which is very efficient compared to the direct explicit solution in particle dynamics. Energy minimization principle is used to develop a new finite element with both local pair-wise and non-local multi-body particle interactions. The developed finite element formulation is verified with classical finite element simulation of some benchmark problems. Fracture simulation using the proposed particle-based finite element formulation is demonstrated. Some conclusions and future work is drawn based on the current investigation.

Stability of ring patterns arising from two-dimensional particle interactions

Pairwise particle interactions arise in diverse physical systems ranging from insect swarms to self-assembly of nanoparticles. In the presence of long-range attraction and short-range repulsion, such systems can exhibit bound states. We use linear stability analysis of a ring equilibrium to classify the morphology of patterns in two dimensions. Conditions are identified that assure the well-posedness of the ring. In addition, weakly nonlinear theory and numerical simulations demonstrate how a ring can bifurcate to more complex equilibria including triangular shapes, annuli, and spot patterns with N-fold symmetry. Many of these patterns have been observed in nature, although a general theory has been lacking, in particular how small changes to the interaction potential can lead to large changes in the self-organized state.

A Fourier-series-based kernel-independent fast multipole method

We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides also economic operators for the multipole-to-multipole, multipole-to-local, and local-to-local translations that are typical and essential in the FMM algorithms. The multipole-to-local translation operator, in particular, is readily diagonal and does not dominate in arithmetic operations. FKI-FMM provides an alternative and competitive option, among other kernel-independent FMM algorithms, for an efficient application of the FMM, especially for applications where the kernel function consists of multi-physics and multi-scale components as those arising in recent studies of biological systems. We present the complexity analysis and demonstrate with experimental results the FKI-FMM performance in accuracy and efficiency.

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

A micromechanical framework is proposed to predict effective elastic moduli of particle-reinforced composites. First, the interacting eigenstrain is derived by making use of the exterior-point Eshelby tensor and the equivalence principle associated with the pairwise particle interactions. Then, the near-field particle interactions are accounted for in the effective elastic moduli of spherical-particle-reinforced composites. On the foundation of the proposed interacting solution, the consistent versus simplified micromechanical field equations are systematically presented and discussed. Specifically, the focus is upon the effective elastic moduli of two-phase composites containing randomly distributed isotropic spherical particles. To demonstrate the predictive capability of the proposed micromechanical framework, comparisons between the theoretical predictions and the available experimental data on effective elastic moduli are rendered. In contrast to higher-order formulations in the literature, the proposed micromechanical formulation can accommodate the anisotropy of reinforcing particles and can be readily extended to multi-phase composites.

A PRIORI ESTIMATES FOR MANY-BODY HAMILTONIAN EVOLUTION OF INTERACTING BOSON SYSTEM

We study the evolution of a many-particle system whose wave function obeys the N-body Schrödinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the absence of an external potential. We derive a priori dispersive estimates that express the overall repulsive nature of the particle interactions. These estimates hold for a wide class of two-body interaction potentials which are independent of the particle number, N. We discuss applications of these estimates to the BBGKY hierarchy for reduced density matrices analyzed by Elgart, Erdős, Schlein and Yau.

Effective elastic moduli of three-phase composites with randomly located and interacting spherical particles of distinct properties

A micromechanical analytical framework is presented to predict effective elastic moduli of three-phase composites containing many randomly dispersed and pairwisely interacting spherical particles. Specifically, the two inhomogeneity phases feature distinct elastic properties. A higher-order structure is proposed based on the probabilistic spatial distribution of spherical particles, the pairwise particle interactions, and the ensemble-volume homogenization method. Two non-equivalent formulations are considered in detail to derive effective elastic moduli with heterogeneous inclusions. As a special case, the effective shear modulus for an incompressible matrix containing randomly dispersed and identical rigid spheres is derived. It is demonstrated that a significant improvement in the singular problem and accuracy is achieved by employing the proposed methodology. Comparisons among our theoretical predictions, available experimental data, and other analytical predictions are rendered. Moreover, numerical examples are implemented to illustrate the potential of the present method.

A Micromechanics-Based Elastoplastic Model for Amorphous Composites With Nanoparticle Interactions

A constitutive model is proposed to investigate the strengthening mechanism and the relationship between nanostructures and effective mechanical properties of the aluminum-based amorphous nanocomposites. A continuum micromechanics-based, three-phase composite model comprises of Al particles, rare-earth enriched interlayers, and the amorphous aluminum matrix. The local stress field and deformation are formulated based on the concept of eigenstrain and equivalent inclusion method with consideration of both the particle-interlayer-matrix interaction and the particle-particle interaction. An ensemble-volume averaging technique is conducted to obtain the overall elastoplastic constitutive behavior for amorphous nanocomposites with randomly distributed spherical nanoparticles. Explicit expressions of the effective elastic stiffness and yield function in terms of the constituent properties and nanostructures are obtained. The effective elastoplastic stress-strain curves for uniaxial loading and the initial yield surfaces for axisymmetric loading are calculated. Simulations are conducted to investigate the effects of the particle size and pairwise particle interaction on the effective mechanical properties.

Magnetoelastic modelling of composites containing randomly dispersed ferromagnetic particles

Coupled magnetoelastic behaviour is investigated for two-phase composites containing randomly dispersed ferromagnetic particles under both magnetic and mechanical loading. The pair-wise particle interactions for magnetic field and elastic field are first defined by the solution for two particles embedded in the infinite domain, which is explicitly solved by the Green's function technique. By integrating the interactions from all other particles in the representative volume element, the homogenized magnetic and elastic fields are then obtained. Effective magnetostriction due to the magnetic interaction force is further derived. Without consideration of magnetic loading, this micromechanical model provides an effective elasticity with the pair-wise particle interactions. By dropping the interaction term, this model is reduced into Mori–Tanaka's model. Finally, magnetoelasticity is numerically solved by considering the magnetomechanical coupling effect. It is predicted that the effective Young's modulus and shear modulus decrease along with the increase of magnetic loading for random composites.

The role of natural organic matter in suspension stability: 2. Modelling of particle–particle interaction

The role of natural organic matter (NOM) in changing the interaction between particles and subsequently the flow properties of concentrated particulate slurries has been modelled using electrokinetic and shear yield stress measurement data. Natural organic matter from soil, coal and peat sources as well as full and fractionated samples from aquatic sources has been examined. The data shows that the majority of the humic and fulvic rich samples adsorb in a flat configuration on a model alumina surface where the interaction is driven by a combination of electrostatics and chemical contributions to the adsorption free energy. Using a DLVO based model that assumes that the rheology response of a concentrated suspension of particles at low strain is the result of the summation of pair-wise particle interactions, the assumption of either a flat or molecularly dense adsorption configuration for most of the species at high additive addition rates was found to be valid. The model showed a consistent relationship between the measured rheology and electrokinetic data in terms of colloidal stability. The same modelling exercise for selected NOM samples at low dose showed a discrepancy between the electrokinetic and rheology data. This was for the NOM samples dominated by the neutral and hydrophilic fractions. The model indicated that the measured electrokinetics were poorly representative of the colloid stability possibly due to the presence of a poorly contiguous adsorbed layer that affects the hydrodynamic flow during electrokinetic measurements.