Particle Simulation Algorithm Research Articles

Machine learning-enhanced predictive modeling for arbitrary deterministic lateral displacement design and test.

The separation of biological particles like cells and macromolecules from liquid samples is vital in clinical medicine, supporting liquid biopsies and diagnostics. Deterministic Lateral Displacement (DLD) is prominent for sorting particles in microfluidics by size. However, the design, fabrication, and testing of DLDs are complex and time-consuming. Researchers typically rely on finite element analysis to predict particle trajectories, which are crucial in evaluating the performance of DLD. Traditional particle trajectory predictions through finite element analysis often inaccurately reflect experimental results due to manufacturing and experimental variabilities. To address this issue, we introduced a machine learning-enhanced approach, combining past experimental data and advanced modeling techniques. Our method, using a dataset of 132 experiments from 40 DLD chips and integrating finite element simulation with a microfluidic-optimized particle simulation algorithm (MOPSA) and a Random Forest model, improves trajectory prediction and critical size determination without physical tests. This enhanced accuracy in simulation across various DLD chips speeds up development. Our model, validated against three DLD chip designs, showed a high correlation between predicted and experimental particle trajectories, streamlining chip development for clinical applications.

GPU-based unresolved LBM-DEM for fast simulation of gas–solid flows

A new discrete particle simulation algorithm, namely unresolved LBM-DEM method, is proposed. In this method, fluid phase and particle phase are calculated by lattice Boltzmann method (LBM) and discrete element method (DEM) respectively, and immersed moving boundary (IMB) is used for treating gas–solid coupling. The additional collision term in IMB is regarded as force source term, and grid equivalent drag force is introduced to modify the weighting function. Due to the intrinsic mesoscopic properties of LBM, unresolved LBM-DEM method is suitable for simulating the hydrodynamics of Geldart A particles. In addition, GPU parallel computation of unresolved LBM-DEM is implemented to improve computational efficiency. To validate GPU-based unresolved LBM-DEM, it is used to simulate three classical gas–solid fluidizations. It was found that the results predicted by GPU-based LBM-DEM are all in good agreement with experimental data. Meanwhile, GPU-based LBM-DEM method brings one to two orders of magnitude speed up ratio compared with CPU or CPU-GPU heterogeneous CFD-DEM algorithm. The proposed unresolved LBM-DEM method has significant advantages over the traditional CFD-DEM in resolution scale and computational efficiency, suggesting it to be a promising computational strategy for fluidization and multiphase flows.

Electromagnetic Particle Algorithm for Beam–Wave Interaction in Traveling Wave Tube of Symmetry

In many fields, such as space astrophysics, plasma and vacuum electronics, there are many nonlinear strong coupling physical problems. In order to solve the problem of electron beam–wave interaction in cylindrical Traveling wave tube (TWT) with symmetrical structure, a multi particle simulation algorithm for beam circuit is designed. The algorithm allows aperiodic time input, nonuniform linearity and large space diagnosis for different particles. In this algorithm, the field of coupled slow-wave transmission line is simulated by finite difference method. Assuming that there is strong coupling between the beam and the circuit, the space center equation of transmission along the line is obtained, and the space charge field is modeled considering the space charge effect, which can easily be ignored. The Particle In Cell (PIC) method of frog leaping step scheme is adopted to evaluate the electric field of each particle center, determine the circuit and space charge field, and design the termination part to compensate for the loss in order to avoid self-excited agitation. Finally, a simple numerical simulation is carried out for the electromagnetic problem and the accuracy of the code is checked against the electromagnetic simulator CHPIC. Therefore, the algorithm can be used to solve the problem of beam–wave interactions in a fixed structure (cylindrical) in multiple fields and can accurately record the data in the process.

Bridge Resistance Updating Based on the General Particle Simulation Algorithms of Complex Bayesian Formulas

The existing bridges are subjected to time-variant loading and resistance degradation processes. How to update resistance probability distribution functions with resistance degradation model and proof load effects has become one of the research hotspots in bridge engineering field. To solve with the above issue, this paper proposed the general particle simulation algorithms of complex Bayesian formulas for bridge resistance updating. Firstly, the complex Bayesian formulas for updating resistance probability model are built. For overcoming the difficulty for the analytic calculation of complex Bayesian formulas, the general particle simulation methods are provided to obtain the particles of complex Bayesian formulas; then, with the improved expectation maximization optimization algorithm obtained with the combination of K-MEANS algorithm and Expectation Maximization (EM) algorithm, the above simulated particles can be used to estimate the posteriori probability density functions of resistance probability model; finally, a numerical example is provided to illustrate the feasibility and application of the proposed algorithms.

Axisymmetric charge-conservative electromagnetic particle simulation algorithm on unstructured grids: Application to microwave vacuum electronic devices

We present a charge-conservative electromagnetic particle-in-cell (EM-PIC) algorithm optimized for the analysis of vacuum electronic devices (VEDs) with cylindrical symmetry (axisymmetry). We exploit the axisymmetry present in the device geometry, fields, and sources to reduce the dimensionality of the problem from 3D to 2D. Further, we employ ‘transformation optics’ principles to map the original problem in polar coordinates with metric tensor diag(1,ρ2,1) to an equivalent problem on a Cartesian metric tensor diag(1,1,1) with an effective (artificial) inhomogeneous medium introduced. The resulting problem in the meridian (ρz) plane is discretized using an unstructured 2D mesh considering TEϕ-polarized fields. Electromagnetic field and source (node-based charges and edge-based currents) variables are expressed as differential forms of various degrees, and discretized using Whitney forms. Using leapfrog time integration, we obtain a mixed E−B finite-element time-domain scheme for the full-discrete Maxwell's equations. We achieve a local and explicit time update for the field equations by employing the sparse approximate inverse (SPAI) algorithm. Interpolating field values to particles' positions for solving Newton–Lorentz equations of motion is also done via Whitney forms. Particles are advanced using the Boris algorithm with relativistic correction. A recently introduced charge-conserving scatter scheme tailored for 2D unstructured grids is used in the scatter step. The algorithm is validated considering cylindrical cavity and space-charge-limited cylindrical diode problems. We use the algorithm to investigate the physical performance of VEDs designed to harness particle bunching effects arising from the coherent (resonance) Cerenkov electron beam interactions within micro-machined slow wave structures.

MOPSA: A microfluidics-optimized particle simulation algorithm.

Computer simulation plays a growing role in the design of microfluidic chips. However, the particle tracers in some existing commercial computational fluid dynamics software are not well suited for accurately simulating the trajectories of particles such as cells, microbeads, and droplets in microfluidic systems. To address this issue, we present a microfluidics-optimized particle simulation algorithm (MOPSA) that simulates the trajectories of cells, droplets, and other particles in microfluidic chips with more lifelike results than particle tracers in existing commercial software. When calculating the velocity of a particle, MOPSA treats the particle as a two-dimensional rigid circular object instead of a single point. MOPSA also checks for unrealistic interactions between particles and channel walls and applies an empirical correcting function to eliminate these errors. To validate the performance of MOPSA, we used it to simulate a variety of important features of microfluidic devices like channel intersections and deterministic lateral displacement (DLD) particle sorter chips. MOPSA successfully predicted that different particle sizes will have different trajectories in six published DLD experiments from three research groups; these DLD chips were used to sort a variety of different cells, particles, and droplets. While some of these particles are not actually rigid or spherical, MOPSA's approximation of these particles as rigid spheres nonetheless resulted in lifelike simulations of the behaviors of these particles (at least for the particle sizes and types shown here). In contrast, existing commercial software failed to replicate these experiments. Finally, to demonstrate that MOPSA can be extended to simulate other properties of particles, we added support for simulating particle density to MOPSA and then used MOPSA to simulate the operation of a microfluidic chip capable of sorting cells by their density. By enabling researchers to accurately simulate the behavior of some types of particles in microfluidic chips before fabricating the chips, MOPSA should accelerate the development of new microfluidic devices for important applications.

An optimization method of relativistic backward wave oscillator using particle simulation and genetic algorithms

Optimal design method of high-power microwave source using particle simulation and parallel genetic algorithms is presented in this paper. The output power, simulated by the fully electromagnetic particle simulation code UNIPIC, of the high-power microwave device is given as the fitness function, and the float-encoding genetic algorithms are used to optimize the high-power microwave devices. Using this method, we encode the heights of non-uniform slow wave structure in the relativistic backward wave oscillators (RBWO), and optimize the parameters on massively parallel processors. Simulation results demonstrate that we can obtain the optimal parameters of non-uniform slow wave structure in the RBWO, and the output microwave power enhances 52.6% after the device is optimized.

Experimental simulation of quantum tunneling in small systems.

It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon of a unique quantum nature, via NMR techniques. Our experiment is based on a digital particle simulation algorithm and requires very few spin-1/2 nuclei without the need of ancillary qubits. The occurrence of quantum tunneling through a barrier, together with the oscillation of the state in potential wells, are clearly observed through the experimental results. This experiment has clearly demonstrated the possibility to observe and study profound physical phenomena within even the reach of small quantum computers.

Optimal design of high-power microwave source based on particle simulation and genetic algorithms

Optimal design method of high-power microwave source based on particle simulation and parallel genetic algorithm is presented in this paper. The output power of the high-power microwave device, simulated by the fully electromagnetic particle simulation code UNIPIC, is given as a fitness function, and the float-encoding genetic algorithm is used to optimize the high-power microwave device. Using this method, we encode the position and height of the Bragg reflector of the relativistic backward wave oscillator (RBWO), and optimize the parameters for a massively parallel processor. Simulation results demonstrate that we can obtain the global optimal parameters of the Bragg reflector of the RBWO.

Corrections to “Time-Step Considerations in Particle Simulation Algorithms for Coulomb Collisions in Plasmas” [Sep 10 2394-2406

An error in (17) of B. I. Cohen, A. M. Dimits, A. Friedman, and R. E. Caflisch, IEEE Trans. Plasma Sci. 38, 2394 (2010), is corrected. The consequences of this error, which are minor, are discussed.

Time-Step Considerations in Particle Simulation Algorithms for Coulomb Collisions in Plasmas

The accuracy of first-order Euler and higher-order time-integration algorithms for grid-based Langevin equations collision models in a specific relaxation test problem is assessed. We show that statistical noise errors can overshadow time-step errors and argue that statistical noise errors can be conflated with time-step effects. Using a higher-order integration scheme may not achieve any benefit in accuracy for examples of practical interest. We also investigate the collisional relaxation of an initial electron-ion relative drift and the collisional relaxation to a resistive steady-state in which a quasi-steady current is driven by a constant applied electric field, as functions of the time step used to resolve the collision processes using binary and grid-based, test-particle Langevin equations models. We compare results from two grid-based Langevin equations collision algorithms to results from a binary collision algorithm for modeling electron-ion collisions. Some guidance is provided on how large a time step can be used compared to the inverse of the characteristic collision frequency for specific relaxation processes.

Nonlinearδfparticle simulations of collective excitations and energy-anisotropy instabilities in high-intensity bunched beams

Collective effects with strong coupling between the longitudinal and transverse dynamics are of fundamental importance for applications of high-intensity bunched beams. The self-consistent Vlasov-Maxwell equations are applied to high-intensity finite-length charge bunches, and a generalized particle simulation algorithm is developed for bunched beams with or without energy anisotropy. The nonlinear method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. Systematic studies are carried out under conditions corresponding to strong 3D nonlinear space-charge forces in the beam frame. For charge bunches with isotropic energy, finite bunch-length effects are clearly evident by the fact that the spectra for an infinitely long coasting beam and a nearly spherical charge bunch have strong similarities, whereas the spectra have distinctly different features when the bunch length is varied between these two limiting cases. For bunched beams with anisotropic energy, there exists no exact kinetic equilibrium because the particle dynamics do not conserve transverse energy and longitudinal energy separately. A reference state in approximate dynamic equilibrium has been constructed theoretically, and a quasi-steady state has been established in the simulations for the anisotropic case. Collective excitations relative to the reference state have been simulated using the generalized algorithm. In particular, the electrostatic Harris instability driven by strong energy anisotropy is investigated for a finite-length charge bunch. The observed growth rates are larger than those obtained for infinitely long coasting beams. However, the growth rate decreases for increasing bunch length to a value similar to the case of a long coasting beam. For long bunches, the instability is axially localized symmetrically relative to the beam center, and the characteristic wavelength in the longitudinal direction is comparable to the transverse dimension of the beam.

Nonlinear [formula omitted] particle simulations of collective effects in high-intensity bunched beams

Collective effects with strong coupling between the longitudinal and transverse dynamics are of fundamental importance for applications of high-intensity bunched beams. The self-consistent Vlasov–Maxwell equations are applied to high-intensity bunched beams, and a generalized δ f particle simulation algorithm is developed for bunched beams with or without energy anisotropy. Numerically, the distribution function is spit into a reference distribution and a perturbed part. The perturbed distribution function is represented as a weighted summation over discrete particles, where the particle orbits are advanced by the equations of motion in the focusing field and self-generated fields, and the particle weights are advanced by an equation equivalent to the nonlinear Vlasov equation. The nonlinear δ f method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. Systematic studies are carried out for the particle dynamics under conditions corresponding to strong 3D nonlinear space-charge force. The simulations showed that finite bunch-length effects on the collective excitations become insignificant when the aspect ratio ( z b / r b ) is larger than 10 for a moderately intense beam with normalized intensity s b = ω p b 2 / 2 ω β 2 = 0.27 . For bunched beams with energy anisotropy ( T ∥ / T ⊥ < 1 ) , a reference state has been constructed and a dynamic equilibrium is established in the simulations. Collective excitations relative to the dynamic equilibrium have also been successfully simulated by the generalized δ f algorithm.

An efficient parallel implementation of the Monte Carlo particle simulation algorithm on a network of personal computers

MC-PVM, an efficient parallel implementation of the Monte Carlo device simulation on a network of personal computers, is presented. A more efficient leap-frog derivative of the MC-PVM algorithm is also discussed. The network of personal computers has been employed into a parallel virtual machine (PVM). To demonstrate the viability of employing a network of personal computers for the parallel implementation of the MC simulation, 60 MHz Pentium computers were utilized. The accuracy and efficiency of the proposed parallel algorithms have been investigated by applying it to a simulation of a millimeter-wave Gunn-effect relaxation oscillator. Finally, a few conclusions will be drawn about the work presented here. Copyright © 2000 John Wiley & Sons, Ltd.

Execution behavior analysis and performance prediction for a shared-memory implementation of an irregular particle simulation method

Many computational-intensive problems from science and engineering are irregular in nature. This makes it difficult to develop an efficient parallel implementation, even for shared-memory machines. As a typical example, we investigate a parallel implementation of an irregular particle simulation algorithm. We concentrate on the issue which programming and system support is needed to yield an efficient implementation for a large number of processors. As an execution platform we use the SB-PRAM, a shared memory machine with up to 2048 processors. The processors of the SB-PRAM can access the global memory in unit time which is the basis for an exact performance prediction. Common approaches for parallel implementations like lock protection for concurrent accesses and sequential or distributed task queues are replaced by more efficient access mechanisms and data structures which can be realized by the powerful multiprefix operations of the SB-PRAM. Their use simplifies the implementation and yields large speedup values.

Particle simulations of ion cloud in a magnetic field

This work describes a 3D time-dependent particle simulation algorithm used to model the electrodynamics of ion clouds in magnetic fields. The algorithm includes step-wise sequential stages of field evaluation, particle push, and boundary detection. Composite fields due to the ion cloud are computed by superimposing solutions for discrete point sources, together with the use of ground plane and image plane symmetries. A second-order modified Euler predictor-corrector method is used for integration of the equations of motion. Results are presented for an ion cloud under the influence of a bias E-field and the B-field from a magnetized spherical carrier bead used in laser printing applications. We consider cases with the dipole axis oriented parallel and perpendicular to the direction of cloud motion.

Partially Linearized Algorithms in Gyrokinetic Particle Simulation

In this paper, particle simulation algorithms with time-varying weights for the gyrokinetic Vlasov-Poisson system have been developed. The primary purpose is to use them for the removal of the selected nonlinearities in the simulation of gradient-driven microturbulence so that the relative importance of the various nonlinear effects can be assessed. It is hoped that the use of these procedures will result in a better understanding of the transport mechanisms and scaling in tokamaks. Another application of these algorithms is for the improvement of the numerical properties of the simulation plasma. For instance, implementations of such algorithms (1) enable us to suppress the intrinsic numerical noise in the simulation, and also (2) make it possible to regulate the weights of the fast-moving particles and, in turn, to eliminate the associated high frequency oscillations. Examples of their application to drift-type instabilities in slab geometry are given. We note that the work reported here represents the first successful use of the weighted algorithms in particle codes for the nonlinear simulation of plasmas.

Transport model of optical beams in a plasma

Abstract A new kind of a particle simulation algorithm suitable for following long time scale evolution of electromagnetic beams in plasma is presented. The algorithm is based on particle and field equations averaged over the rapid laser oscillations and the model constitutes the electromagnetic counterpart for the Zakharov's model for electrostatics. This code can be reduced to a fully fluid code, if so desired, by replacing the electron dynamics. Computational remarks upon implementation of the algorithm are given. Test results of the code applied to the Rayleigh spread and self-focusing of an intense laser beam in a plasma are discussed.

Approximate Integration of Stochastic Differential Equations

Approximate Integration of Stochastic Differential Equations