Particle-based Simulation Method Research Articles

A generative model to simulate spatiotemporal dynamics of biomolecules in cells.

Generators of space-time dynamics in bioimaging have become essential to build ground truth datasets for image processing algorithm evaluation such as biomolecule detectors and trackers, as well as to generate training datasets for deep learning algorithms. In this contribution, we leverage a stochastic model, called birth-death-move (BDM) point process, in order to generate joint dynamics of biomolecules in cells. This particle-based stochastic simulation method is very flexible and can be seen as a generalization of well-established standard particle-based generators. In comparison, our approach allows us: (1) to model a system of particles in motion, possibly in interaction, that can each possibly switch from a motion regime (e.g., Brownian) to another (e.g., a directed motion); (2) to take into account finely the appearance over time of new trajectories and their disappearance, these events possibly depending on the cell regions but also on the current spatial configuration of all existing particles. This flexibility enables to generate more realistic dynamics than standard particle-based simulation procedures, by for example accounting for the colocalization phenomena often observed between intracellular vesicles. We explain how to specify all characteristics of a BDM model, with many practical examples that are relevant for bioimaging applications. As an illustration, based on real fluorescence microscopy datasets, we finally calibrate our model to mimic the joint dynamics of Langerin and Rab11 proteins near the plasma membrane, including the well-known colocalization occurrence between these two types of vesicles. We show that the resulting synthetic sequences exhibit comparable features as those observed in real microscopy image sequences.

Learning hydrodynamic equations for active matter from particle simulations and experiments

Recent advances in high-resolution imaging techniques and particle-based simulation methods have enabled the precise microscopic characterization of collective dynamics in various biological and engineered active matter systems. In parallel, data-driven algorithms for learning interpretable continuum models have shown promising potential for the recovery of underlying partial differential equations (PDEs) from continuum simulation data. By contrast, learning macroscopic hydrodynamic equations for active matter directly from experiments or particle simulations remains a major challenge, especially when continuum models are not known a priori or analytic coarse graining fails, as often is the case for nondilute and heterogeneous systems. Here, we present a framework that leverages spectral basis representations and sparse regression algorithms to discover PDE models from microscopic simulation and experimental data, while incorporating the relevant physical symmetries. We illustrate the practical potential through a range of applications, from a chiral active particle model mimicking nonidentical swimming cells to recent microroller experiments and schooling fish. In all these cases, our scheme learns hydrodynamic equations that reproduce the self-organized collective dynamics observed in the simulations and experiments. This inference framework makes it possible to measure a large number of hydrodynamic parameters in parallel and directly from video data.

Implementing a non-local lattice particle method in the open-source large-scale atomic/molecular massively parallel simulator

Using conventional continuum-based simulation frameworks to model crack initiation and extension can be computationally challenging. As an alternative to continuum-based approaches, particle-based simulation methods are well-suited to handle the discontinuities present during fracture propagation. A well-known particle-based method is the lattice particle method (LPM), which discretizes the system into a set of interconnected particles ollowing a periodic arrangement. Discontinuities can be handled simply by removing bonds between particles. For this reason, LPM-based simulations have been employed to simulate fracture propagation in heterogeneous media, notably in civil engineering and biomaterials applications. However, a practical limitation of this method is the absence of implementation within a commonly-used software platform. This work describes such an implementation of a non-local LPM within the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Specifically, we implemented a new LAMMPS bond style with a many-body term to tune Poisson’s ratios. In order to validate the nonlocal formalism and our implementation of this method within LAMMPS, simulated elastic properties are compared to analytical solutions reported in the literature. Good agreement between simulated and analytical values is found for systems with positive Poisson’s ratios. The computational and parallel efficiency of the LPM-LAMMPS implementation is also benchmarked. Finally, we compare the elastic response of a 3D porous structure and an aircraft wing as calculated using the LPM and finite-element analysis.

Effect of amplitude and wavelength in the cooperative motion of Taylor lines

In the present study, we have modeled the clustering of binary Taylor line swimmers in a Newtonian fluid. The fluid is modeled using the particle-based simulation method multiparticle collision dynamics, while for the Taylor line, we use a bead spring arrangement with a sine wave passing through it using a bending wave potential. The binary swimmers have the same propulsion speed, but they differ from each other in the shape of the Taylor line ensured by different amplitudes and lengths. We observe that an optimal amplitude exists for the Taylor line swimmer leading to large clusters formation. The size distribution of the clusters was observed to follow a power-law behavior followed by an exponential cutoff. We also calculated the probability of finding a bead of the swimmer as a function of the fractional distance from the center of the bounding circle and observed that when the amplitude is close to the optimal value, the swimmer forms clusters closer to the walls; otherwise, the swimmer stays almost uniformly distributed around the bounding area. When the ratio of the amplitude is high, the clusters formed at the center of the bounding area become stable and have a wedge-shape. By calculating the speed of the swimmer as a function of the fractional distance from the center of the bounding area, we show that the swimmers speed increases with the maximum at the walls. The simulation with a smaller system has revealed that the maximum clustering happens for an amplitude parameter of ∼0.17.

Dynamics of droplet impact on a ring surface

We investigate the dynamics of droplet impacts on a ring-decorated solid surface, which is reported to reduce the integral of contact area over contact time by up to 80%. By using many-body dissipative particle dynamics (MDPD), a particle-based simulation method, we measure the temporal evolution of the shape and the impact force of two specific types of phenomena, overrun and ejection. The numerical model is first validated with experimental data on a plain surface from literature. Then, it is used to extract the impacting force of the ring and substrate separately, showing the ring does not provide the majority of vertical force to redirect the horizontal spreading. The impacting pressure in different concentric rings is also present as a function of time, showing pressure waves traveling from ring to center. The effect of the ring's height and radius on the impacting force is also discussed. To the best of our knowledge, this is the first MDPD study on droplets impacting on a solid surface with a validated force analysis.

Interactive High-Resolution Simulation of Granular Material

We introduce a particle-based simulation method for granular material in interactive frame rates. We divide the simulation into two decoupled steps. In the first step, a relatively small number of particles is accurately simulated with a constraint-based method. Here, all collisions and the resulting friction between the particles are taken into account. In the second step, the small number of particles is significantly increased by an efficient sampling algorithm without creating additional artifacts. The method is particularly robust and allows relatively large time steps, which makes it well suited for real-time applications. With our method, up to 500k particles can be computed in interactive frame rates on consumer CPUs without relying on GPU support for massive parallel computing. This makes it well suited for applications where a lot of GPU power is already needed for render tasks.

Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods.

Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.

Numerical and experimental investigation of the effect of interstitial gases on conductive heat transfer for dense particulate systems

Many industrial processes involve granular heat transfer. Within these processes are a sub-set of applications where the particles are densely packed and the surrounding gas is predominantly stagnant. For materials with low thermal conductivity much of the heat transfer will occur through the interstitial gases so capturing this effect is critical to represent these systems numerically. Resolving the gas phase explicitly using a fluid solver and coupling to a particle method is possible but computationally expensive. Higher fidelity models often make simulation of applications at the industrial scale intractable. With this in mind we seek a numerical method that captures the important heat transfer phenomena in dense granular systems with minimal additional computational effort. In this work we first characterize one common particle based approach proposed by Rong and Horio that calculates the contribution through a stagnant gas film surrounding each particle. We compare this approach to fluid simulations of a particle-wall and a particle-particle collision to evaluate the validity of the underlying assumptions of the Rong and Horio model. We then use a multi-scale approach to examine the relationship between the local packing structure and the contribution of the interstitial gas. From this we propose a new dimensionless parameter that permits the inclusion of the gas effect in a particle based simulation method with minimal additional computational effort and without explicitly having to include the gas phase. The model is then validated against a static experiment and compared with the Rong and Horio model.

Effect of wave versus particle phonon nature in thermal transport through nanostructures

Comprehensive understanding of thermal transport in nanostructured materials needs large scale simulations bridging length scales dictated by different physics related to the wave versus particle nature of phonons. Yet, available computational approaches implicitly treat phonons as either just waves or as particles. In this work, using a full wave-based Non-Equilibrium Green's Function (NEGF) method, and a particle-based ray-tracing Monte Carlo (MC) approach, we investigate the qualitative differences in the wave and particle-based phonon transport at the vicinity of nanoscale features. For the simple example of a nanoporous geometry, we show that phonon transmission agrees very well for both methods with an error margin of ±15%, across phonon wavelengths even for features with sizes down to 3–4 nm. For cases where phonons need to squeeze in smaller regions to propagate, we find that MC underestimates the transmission of long wavelength phonons whereas wave treatment within NEGF indicates that those long wavelength phonons can propagate more easily. We also find that particle-based simulation methods are somewhat more sensitive to structural variations compared to the wave-based NEGF method. The insight extracted from comparing wave and particle methods can be used to provide a better and more complete understanding of phonon transport in nanomaterials.

Statistical distributions of the elastic moduli of particle aggregates at the mesoscale

This study introduces an important development in the modeling of granular media. A recently-developed real-time interface tracking algorithm for particle-based simulation methods can be used to study the bounds of discrete particle aggregates such as sand. The interface tracking algorithm uses an advanced surface extraction technique based on the alpha shape paradigm of computational geometry. When used concurrently with particle-based methods, this algorithm is capable of tracking the evolution of the simulation boundaries and applying accurate micro-boundary conditions on them. The micro-boundary conditions may be of Dirichlet type, Neumann type, or mixed-orthogonal type and may be tensorial.This development makes possible use of particle-based simulations in the homogenization and uncertainty quantification (UQ) of granular media. This is a significant development in the modeling of granular media, as it expands the role of particle-based methods for mesoscale simulations within a multiscale framework. The ultimate goal of this framework is to provide an additional path for constitutive characterization of particle aggregates, particularly in hydrocode modeling of high confinement, finite deformation phenomena.The power and versatility of the micro-mechanical boundary tracking algorithm is demonstrated through a series of numerical simulations of Eglin sand. The mesoscale models are used to compute the probability distribution functions of the moduli of Eglin sand at scales below the scale of the Representative Volume Element (RVE).

Optimal Transmitted Molecules and Decision Threshold for Drift-Induced Diffusive Molecular Channel With Mobile Nanomachines.

We study a drift-induced diffusive mobile molecular communication system where source, destination and cooperative nanomachines follow the one-dimensional Brownian motion. For information exchange from source nanomachine to receiver nanomachine, both direct and decode-forward (DF) relay-assisted cooperative paths are considered. The closed-form expressions for the probabilities of detection and false alarm are derived at the cooperative and destination nanomachines considering the multiple-source interference (MSI) and the inter-symbol-interference (ISI). The closed-form expressions for end-to-end average probability of error, and maximum achievable rate are also obtained. Moreover, to achieve minimum expected probability of error the optimum number of molecules to be transmitted from transmitter and optimal detection threshold in receiver nanomachine are found. The analytical expressions are validated through particle-based and Monte-Carlo simulation methods.

Dissipative particle dynamics simulation of critical pore size in a lipid bilayer membrane.

We investigate with computer simulations the critical radius of pores in a lipid bilayer membrane. Ilton et al. (Ilton et al. 2016 Phys. Rev. Lett. 117, 257801 (doi:10.1103/PhysRevLett.117.257801)) recently showed that nucleated pores in a homopolymer film can increase or decrease in size, depending on whether they are larger or smaller than a critical size which scales linearly with film thickness. Using dissipative particle dynamics, a particle-based simulation method, we investigate the same scenario for a lipid bilayer membrane whose structure is determined by lipid–water interactions. We simulate a perforated membrane in which holes larger than a critical radius grow, while holes smaller than the critical radius close, as in the experiment of Ilton et al. (Ilton et al. 2016 Phys. Rev. Lett. 117, 257801 (doi:10.1103/PhysRevLett.117.257801)). By altering key system parameters such as the number of particles per lipid and the periodicity, we also describe scenarios in which pores of any initial size can seal or even remain stable, showing a fundamental difference in the behaviour of lipid membranes from polymer films.

New dissipative particle dynamics boundary condition for complex geometry

Dissipative particle dynamics (DPD) is a thriving particle-based simulation method of modeling mesoscale fluids. After two decades of evolution, DPD has shown unique advantages in researches about polymer, red blood cell, droplets wetting, etc. However, DPD is limited to relatively simple geometries due to the lack of a satisfactory boundary method. In this paper, we propose an adaptive boundary method for complex geometry, which fulfills the three basic requirements of boundary method: no penetration into the solid, no-slip near boundary, negligible fluctuation of density or temperature near boundary. Specifically, first, a new vector attribution is added to each solid particle, the attribution is named local wall normal (LWN) attribution and it is a function of its neighbor solid particle’s position, the LWN attribution is used to correct the penetrating fluid particles’ velocity and position and is computed only once if the wall is stationary. Second the surface wall particles are identified by neighbor solid fraction (<i>φ</i>), which indicates the percentage of surrounding space occupied by solid particles, then the wall is reconstructed by only the surface particles instead of all solid particles. By doing so, the redundant bulk particles are removed from the simulation. Third, it is detected on-the-fly whether the moving fluid particle penetrates the wall by computing its <i>φ</i>, the fluid particles with <i>φ</i> greater than 0.5 are considered to enter into the solid wall, their position and velocity will be corrected based on the local wall normal attribution. We verify that the method causes negligible density and temperature fluctuation in Poiseuille flow. Then, we illustrate the implementation of LWNM in the cases of complex blood vessel network and micro-structured surface. With this method, the obstacles in flow are no longer restricted to shapes described by functions but can be generated by CAD software, and blood vessels can also be generated by CT scan images or other experimental data. Moreover, we show a case with a bent tube and droplets inside, demonstrating the practicability of constructing complex geometry and the effectiveness of LWNM. This new boundary approach empowered DPD to simulate more realistic problems.

Modified cell-linked list method using dynamic mesh for discrete element method

Discrete element method (DEM) is one of the most important particle-based simulation methods widely applied in various fields. However, further large-scale engineering applications by DEM are still limited due to the deficiency of computing capability of computers. In the simulations of engineering problems, uneven distribution of particles is a common phenomenon with high-concentration and empty particulate domains, which will occupy extra memory for mesh in no-particle domain by using the conventional cell-linked list method for contact detection. For better utilization of memory, the conventional method is modified to perform large-scale simulations with uneven distribution of particles by using dynamic mesh in this study, and the modified method is called the dynamic mesh cell-linked list (DMCL) method. To verify the applicability of the DMCL method, the simulations of particles transported by a screw conveyor and a belt conveyor are done. The simulation results indicate that using the DMCL method can extraordinarily reduce the memory usage and is comparably efficient compared with the conventional method. The DMCL method can be used in both spherical and non-spherical particulate systems, and is also applicable to other particle-based simulations

Multi-architecture Monte-Carlo (MC) simulation of soft coarse-grained polymeric materials: SOft coarse grained Monte-Carlo Acceleration (SOMA)

Multi-component polymer systems are important for the development of new materials because of their ability to phase-separate or self-assemble into nano-structures. The Single-Chain-in-Mean-Field (SCMF) algorithm in conjunction with a soft, coarse-grained polymer model is an established technique to investigate these soft-matter systems. Here we present an implementation of this method: SOft coarse grained Monte-Carlo Acceleration (SOMA). It is suitable to simulate large system sizes with up to billions of particles, yet versatile enough to study properties of different kinds of molecular architectures and interactions.We achieve efficiency of the simulations commissioning accelerators like GPUs on both workstations as well as supercomputers. The implementation remains flexible and maintainable because of the implementation in the scientific programming language C enhanced by OpenACC pragmas for the accelerators.We present implementation details and features of the program package, investigate the scalability of our implementation SOMA, and discuss two applications, which cover system sizes that are difficult to reach with other, common particle-based simulation methods. Program summaryProgram Title: SOMAProgram Files doi:http://dx.doi.org/10.17632/j3thz43k93.1Licensing provisions: GNU Lesser General Public License version 3Programming language: C99, OpenACC, OpenMP, MPI, pythonNature of problem: Efficient simulation of polymer materials, their phase-separation or self-assembly using a highly coarse-grained, soft, particle-based model [1]. The simulations help predicting self-assembled structures that, for example, find application in the fabrication of large-scale, dense arrays of nano-structures by Directed Self-Assembly (DSA).Solution method: Representation of soft, non-bonded interactions by quasi-instantaneous fields on a collocation grid using the Single-Chain-in-Mean-Field (SCMF) [2] algorithm, and sampling of configuration space using local random Monte-Carlo (MC) displacements and Smart Monte-Carlo (SMC). Parallelization using MPI and accelerators such as Graphics Processing Units (GPUs).Restrictions: The program has not been tested for more than 10 billion particles.Unusual Features: Efficient simulation on different hardware architectures and accelerators, including multi-core Central Processing Units (CPUs) and GPUs. Furthermore, it is possible to combine different architectures within a single simulation.[1] M. Müller, J. Stat. Phys. 145 (2011) 967[2] K. C. Daoulas, M. Müller, J. Chem. Phys. 125 (2006) 184904

Studying the field-controlled change of shape and elasticity of magnetic gels using particle-based simulations

Ferrogels are soft elastic materials into which magnetic particles are embedded. The resulting interplay between elastic and magnetic interactions and the materials’ response to external fields makes them promising candidates for applications such as actuation and drug delivery. In this article, after providing a very brief introduction to particle-based simulation methods, we give an overview on how they can be applied to magnetic gels. We focus on the different mechanisms by which ferrogels can deform in an external magnetic field. Based on examples from our previous work, we show how these mechanisms can be captured by particle-based simulations. Lastly, we provide some links to simulation techniques on larger length scales.

Better Than Counting: Density Profiles from Force Sampling.

Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. Here, we investigate an alternative method based on a histogram of the local force density. Via an exact sum rule, the density profile is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations. We have tested the method in MonteCarlo, Brownian dynamics, and molecular dynamics simulations. The results carry a statistical uncertainty smaller than that of the standard counting method, reducing therefore the computation time.

A fast framework construction and visualization method for particle-based fluid

Fast and vivid fluid simulation and visualization is a challenge topic of study in recent years. Particle-based simulation method has been widely used in the art animation modeling and multimedia field. However, the requirements of huge numerical calculation and high quality of visualization usually result in a poor computing efficiency. In this work, in order to improve those issues, we present a fast framework for 3D fluid fast constructing and visualization which parallelizes the fluid algorithm based on the GPU computing framework and designs a direct surface visualization method for particle-based fluid data such as WCSPH, IISPH, and PCISPH. Considering on conventional polygonization or adaptive mesh methods may incur high computing costs and detail losses, an improved particle-based method is provided for real-time fluid surface rendering with the screen-space technology and the utilities of the modern graphics hardware to achieve the high performance rendering; meanwhile, it effectively protects fluid details. Furthermore, to realize the fast construction of scenes, an optimized design of parallel framework and interface is also discussed in our paper. Our method is convenient to enforce, and the results demonstrate a significant improvement in the performance and efficiency by being compared with several examples.

High intensity impulsive loading by explosively accelerated granular matter

The mechanism by which a spherical shell of granular matter is accelerated by an internal explosion together with its subsequent loading of a high ductility, edge clamped steel plate are investigated by a combination of instrumented experimentation and particle-based simulation. By using a large spherical explosive charge to drive the expansion of a water saturated synthetic sand shell, it has been possible to create sand front impact speeds with a test plate that exceeded 1200m/s. Direct observations of the evolution of the sand front were made using a pair of high speed video cameras, and revealed rapid initial acceleration of the sand accompanied by the formation of locally faster sand spikes, followed by deceleration. The pressure evolution and specific impulse during particle impact were measured using the Kolsky bar. A discrete particle-based numerical simulation method implemented in the IMPETUS Afea code was then used to simulate the pressure and impulse applied to the Kolsky bar and to model dynamic deformation of the plate and its support structure. The simulation analyzed the interactions between the explosively accelerated high explosive, air, and sand particles and the shock fronts that propagated though each interface after detonation. The impulse applied to the test plate and its support structure were well reproduced by the simulation. The simulations also revealed significant dispersion of the sand, with some sand particles attaining radial velocities that were almost 50% higher than that of the main front. They also identified the presence of an experimentally unobservable instability at the energetic material-wet sand interface. The deceleration of the sand with distance of propagation was found to be the result of momentum transferring collisions with the background air, resulting in the formation of a strong air shock ahead of the sand front. This processes resulted in the eventual transfer of all the sand momentum to the air and significantly influenced the dynamically changing topology of the sand-air interface. While the differential acceleration of the sand particles to form a dispersed front, and their deceleration by air drag were well modeled, the topology of the sand instabilities at the sand front-air interface were not resolved by the simulations.

Stochastic Rotation Dynamics simulations of wetting multi-phase flows

Multi-color Stochastic Rotation Dynamics (SRDmc) has been introduced by Inoue et al. as a particle based simulation method to study the flow of emulsion droplets in non-wetting microchannels. In this work, we extend the multi-color method to also account for different wetting conditions. This is achieved by assigning the color information not only to fluid particles but also to virtual wall particles that are required to enforce proper no-slip boundary conditions. To extend the scope of the original SRDmc algorithm to e.g. immiscible two-phase flow with viscosity contrast we implement an angular momentum conserving scheme (SRDmc+). We perform extensive benchmark simulations to show that a mono-phase SRDmc fluid exhibits bulk properties identical to a standard SRD fluid and that SRDmc fluids are applicable to a wide range of immiscible two-phase flows. To quantify the adhesion of a SRDmc+ fluid in contact to the walls we measure the apparent contact angle from sessile droplets in mechanical equilibrium. For a further verification of our wettability implementation we compare the dewetting of a liquid film from a wetting stripe to experimental and numerical studies of interfacial morphologies on chemically structured surfaces.