Fictitious Particles Research Articles

A semi-analytical transient undisturbed velocity correction scheme for wall-bounded two-way coupled Euler-Lagrange simulations

Force closure models employed in Euler-Lagrange (EL) point-particle simulations rely on the accurate estimation of the undisturbed fluid velocity at the particle center to evaluate the fluid forces on each particle. Due to the self-induced velocity disturbance of the particle in the fluid, two-way coupled EL simulations only have access to the disturbed velocity. The undisturbed velocity can be recovered if the particle-generated disturbance is estimated. In the present paper, we model the velocity disturbance generated by a regularized forcing near a planar wall, which, along with the temporal nature of the forcing, provides an estimate of the unsteady velocity disturbance of the particle near a planar wall. We use the analytical solution for a singular in-time transient Stokeslet near a planar wall (Felderhof [1]) and derive the corresponding time-persistent Stokeslets. The velocity disturbance due to a regularized forcing is then obtained numerically via a discrete convolution with the regularization kernel. The resulting Green's functions for parallel and perpendicular regularized forcing to the wall are stored as pre-computed temporal correction maps. By storing the time-dependent particle force on the fluid as fictitious particles, we estimate the unsteady velocity disturbance generated by the particle as a scalar product between the stored forces and the pre-computed Green's functions. Since the model depends on the analytical Green's function solution of the singular Stokeslet near a planar wall, the obtained velocity disturbance exactly satisfies the no-slip condition and does not require any fitted parameters to account for the rapid decay of the disturbance near the wall. The numerical evaluation of the convolution integral makes the present method suitable for arbitrary regularization kernels. Additionally, the generation of parallel and perpendicular correction maps enables to estimate the velocity disturbance due to particle motion in arbitrary directions relative to the local flow. The convergence of the method is studied on a fixed particle near a planar wall, and verification tests are performed in the Stokes regime on a settling particle parallel to a wall and a free-falling particle perpendicular to the wall.

Revisiting the gravitomagnetic clock effect

To the first post-Newtonian order, if two test particles revolve in opposite directions about a massive, spinning body along two circular and equatorial orbits with the same radius, they take different times to return to the reference direction relative to which their motion is measured: it is the so-called gravitomagnetic clock effect. The satellite moving in the same sense of the rotation of the primary is slower, and experiences a retardation with respect to the case when the latter does not spin, while the one circling in the opposite sense of the rotation of the source is faster, and its orbital period is shorter than it would be in the static case. The resulting time difference due to the stationary gravitomagnetic field of the central spinning body is proportional to the angular momentum per unit mass of the latter through a numerical factor which so far has been found to be 4π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\\pi $$\\end{document}. A numerical integration of the equations of motion of a fictitious test particle moving along a circular path lying in the equatorial plane of a hypothetical rotating object by including the gravitomagnetic acceleration to the first post-Newtonian order shows that, actually, the gravitomagnetic corrections to the orbital periods are larger by a factor of 4 in both the prograde and retrograde cases. Such an outcome, which makes the proportionality coefficient of the gravitomagnetic difference in the orbital periods of the two counter-revolving orbiters equal to 16π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$16\\pi $$\\end{document}, confirms an analytical calculation recently published in the literature by the present author. It is an important result in view of the astrophysical implications of the gravitomagnetic clock effect around Kerr black holes.

Ab Initio Path Integral Monte Carlo Simulations of the Uniform Electron Gas on Large Length Scales.

The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, materials science, and related disciplines. At finite temperatures, the gold standard is given by ab initio path integral Monte Carlo (PIMC) simulations, which do not require any empirical input but exhibit an exponential increase in the required computation time for Fermionic systems with an increase in system size N. Very recently, computing Fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles has been suggested. In our work, we use this technique to perform very large (N ≤ 1000) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of the investigated properties, i.e., the static structure factor, the static density response function, and the local field correction, over the entire range of length scales.

Fermionic physics from abinitio path integral Monte Carlo simulations of fictitious identical particles.

The abinitio path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion signproblem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the signproblem by carrying out simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the signproblem. Here, we show how the inclusion of the artificial parameter ξ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).

Collinear scattering and long-lived excitations in two-dimensional electron fluids

For a long time, it has been thought that 2D Fermi gases could support long-lived excitations, thanks to the collinear quasiparticle scattering controlled by phase space constraints at a 2D Fermi surface. We present a direct calculation that reveals such excitations. The excitation lifetimes are found to exceed the fundamental bound set by Landau Fermi-liquid theory by a factor as large as $(T_F/T)^\alpha$ with $\alpha \approx 2$. These excitations represent Fermi-surface modulations of an odd parity, one per each odd angular momentum. To explain this surprising behavior, we employ a connection between the linearized quantum kinetic equation and the dynamics of a fictitious quantum particle moving in a 1D reflectionless ${\rm sech^2}$ potential. In this framework, we identify the long-lived excitations in Fermi gases as zero modes that arise from supersymmetry.

Fictitious neutron sinks to trace radiative s-process nucleosynthesis

Context. Asymptotic giant branch (AGB) stars are strong producers of s-process elements, which are synthesized by successive slow neutron captures on elements heavier than iron. The nucleosynthesis calculation involves solving large nuclear networks with hundreds of nuclei, which in a stellar evolution code can greatly extend the computational time. However, the s-process is often measured using a handful of elements located on the neutron magic shells and grouped into tracers called ls, hs, and vhs. Aims. We propose a fictitious network that approximates the production of ls, hs, and vhs species at a minimal computational expense. The network is specifically designed for the radiative s-process in AGB stars. It is an alternative to methods using large networks that can be used as a fast exploratory tool to trace the production of s-elements. Methods. The fictitious network was constructed by assembling species with Z ≥ 18 into seven fictitious particles whose abundances and reaction rates model the effective properties of the corresponding groups. The effective reaction rates were tabulated as a function of neutron density and number of neutrons captured per initial heavy seed (Ncapt) using single-zone nucleosynthesis calculations. The accuracy of our network was tested by comparing the abundances obtained with the fictitious and large networks during the radiative burning of 13C during the interpulse period of a 2 M⊙, [Fe/H] = −2 star. Results. The fictitious network reliably reproduces the abundances of ls, hs, and vhs species during the radiative s-process. The accuracy of the method increases with the strength of the nucleosynthesis as measured by Ncapt, but diminishes when the nuclear distribution is different from the initial distribution. This network is well suited to follow the s-process nucleosynthesis in low-mass AGB stars where neutrons are mainly produced below the envelope by the 13C(α, n) reaction.

FPM-SE: A numerical model for dense gas–solid flows with large non-spherical object

In dense gas–solid flows such as that in fluidized bed gasifier, large non-spherical solid objects co-exist with small bed particles. During the fluidization, the large non-spherical objects experience complex forces depending on their shape, size, and orientation and a diverse and complex dynamics emerges. Here, we present a numerical model for dense gas–solid flows with large non-spherical objects. The proposed model named FPM-SE is based on the combination of Fictitious Particle Method (FPM) for large size differences and Super-Ellipsoid (SE) model for various shapes. We also perform experiments using a Lagrangian sensor system to investigate the influence of object shape on its sinking/floating motions in a gas-fluidized bed. We observe that non-sphericity facilitates the floating of large objects. Not only FPM-SE reasonably captures the experimental observations but it also demonstrates a typical sinking–staying in the bottom–floating behavior with an orientational change of large non-spherical objects.

On the thermodynamic properties of fictitious identical particles and the application to fermion signproblem.

By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature thermodynamic properties of fictitious identical particles with a real parameter ξ interpolating continuously between bosons (ξ = 1) and fermions (ξ = -1). Through general analysis and numerical experiments, we find that the average energy may have good analytical properties as a function of this real parameter ξ, which provides the chance to calculate the thermodynamical properties of identical fermions by extrapolation with a simple polynomial function after accurately calculating the thermodynamic properties of the fictitious particles for ξ ≥ 0. Using several examples, it is shown that our method can efficiently give accurate energy values for finite-temperature fermionic systems. Our work provides a chance to circumvent the fermion signproblem for some quantum systems.

Basis for time crystal phenomena in ultra-cold atoms bouncing on an oscillating mirror

We consider classical dynamics of a one-dimensional system of N particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the manifolds the particles move on and derive the effective secular Hamiltonian for resonant motion of the particles. Proper choice of time periodic oscillations of the mirror allows for engineering of the effective behaviour of the particles. In particular, the system can behave like an N-dimensional fictitious particle moving in an N-dimensional crystalline structure. Our classical analysis constitutes a basis for quantum research of novel time crystal phenomena in ultra-cold atoms bouncing on an oscillating atom mirror.

Quantitative simulation of selective laser melting of metals enabled by new high-fidelity multiphase, multiphysics computational tool

Laser powder bed fusion represents the future for metal additive manufacturing. Advance of this emerging technology is bottlenecked by the unavailability of high-fidelity prediction tools for cost-effective optimization on printing design. Simulations of selective laser melting of metals must tackle a complex granular solids and multiphase fluids system that undergoes intra- and inter-phase interactions and thermal-induced phase changes, including melting, vaporization, and solidification, which are challenging to model. We develop a high-fidelity computational tool to provide high-resolution simulations of the multiphase, multiphysics processes of selective laser melting (SLM). Key to this tool is a multi-phase, semi-coupled resolved Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM). It contains innovative features including (1) a fully resolved immersed boundary CFD with fictitious particle domain coupling with DEM for resolving mechanical interactions and heat transfers between solid particles and surrounding fluid; (2) An evaporation model in consideration of the Knudsen layer implemented in the volume of fluid (VOF) method which is enriched by two sharp interface capture schemes, isoAdvector and MULES, for accurate identification of the vaporization process and phase boundaries of fluids with different Courant numbers; and (3) a ray tracing model compatible with the VOF method for high-resolution of absorbed laser energy. We demonstrate the proposed method can quantitatively reproduce key observations from synchrotron experiments and captures critical interdependent physics involving melt pool morphology evolution, vapor-driven keyhole dynamics and powder motions. This new computational tool opens a new avenue for quantitative design and systematic optimization of laser powder bed fusion and may find wider engineering applications where thermal induced phase changes in a multi-phase system are important.

Statistically optimal analysis of the extended-system adaptive biasing force (eABF) method

The extended-system adaptive biasing force (eABF) method and its newer variants offer rapid exploration of the configuration space of chemical systems. Instead of directly applying the ABF bias to collective variables, they are harmonically coupled to fictitious particles, which separates the problem of enhanced sampling from that of free energy estimation. The prevalent analysis method to obtain the potential of mean force (PMF) from eABF is thermodynamic integration. However, besides the PMF, most information is lost as the unbiased probability of visited configurations is never recovered. In this contribution, we show how statistical weights of individual frames can be computed using the Multistate Bennett's Acceptance Ratio (MBAR), putting the post-processing of eABF on one level with other frequently used sampling methods. In addition, we apply this formalism to the prediction of nuclear magnetic resonance shieldings, which are very sensitive to molecular geometries and often require extensive sampling. The results show that the combination of enhanced sampling by means of extended-system dynamics with the MBAR estimator is a highly useful tool for the calculation of ensemble properties. Furthermore, the extension of the presented scheme to the recently published Gaussian-accelerated molecular dynamics eABF hybrid is straightforward and approximation free.

The Kinks, the Solitons and the Shocks in Series‐Connected Discrete Josephson Transmission Lines

The localized running waves in the discrete Josephson transmission lines (JTL), constructed from Josephson junctions (JJ) and capacitors, are analytically studied. The quasicontinuum approximation reduces calculation of the running wave properties to the problem of equilibrium of an elastic rod in the potential field. Making additional approximation, the problem is reduced to the motion of the fictitious Newtonian particle in the potential well. It is shown that there exist running waves in the form of supersonic kinks and solitons and their velocities and profiles are calculated. It is shown that the nonstationary smooth waves which are small perturbations on the homogeneous nonzero background are described by Korteweg–de Vries equation and those on zero background by modified Korteweg–de Vries equation. The effect of dissipation on the running waves in JTL is also studied and it is found that in the presence of the resistors, shunting the JJ and/or in series with the ground capacitors, the only possible stationary running waves are the shock waves, whose profiles are also found. Finally, in the framework of Stocks expansion, the nonlinear dispersion and modulation stability in the discrete JTL are studied.

Border mapping multi-resolution (BMMR) technique for incompressible projection-based particle methods

A novel multi-resolution technique called border mapping multi-resolution (BMMR) is proposed for projection-based particle methods. The BMMR aims to obtain background equivalent particle distributions in the two sides of a border between sub-domains with a 2:1 resolution ratio so that a single resolution framework is adopted to near-border particles calculations. The novelty of the BMMR is that it obtains the background grid from the mapping of the actual particle distribution in the border and, as a result, the location of the particles in the background grid exactly matches the location of the actual particles. In this way, such technique aims to reduce the error from the interpolation of the physical quantities in the background grid and to avoid sudden changes in the particle distribution that may lead to unstable local pressure calculation. In the coarse side of the border, the refinement is made by a triangulation and by placing fictitious particles in the midpoints of the triangles. In the fine side of the border, the derefinement is made by defining a set of fine particles that result in a particle distribution that best resembles a coarse one. The accuracy and computational performance of the BMMR implemented in a moving particle semi-implicit (MPS) simulation system are verified by using benchmark test cases of 2D free surface flows.

First-encounter time of two diffusing particles in two- and three-dimensional confinement.

The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two- and three-dimensional domains with reflecting boundaries. Based on the outcome of the simulations, we give a comprehensive overview of the behavior of the survival probability S(t) and the associated first-encounter time probability density H(t) over a broad time range spanning several decades. In addition, we provide numerical estimates and empirical formulas for the mean first-encounter time 〈T〉, as well as for the decay time T characterizing the monoexponential long-time decay of the survival probability. Based on the distance between the boundary and the center of mass of two particles, we obtain an empirical lower bound t_{B} for the time at which S(t) starts to significantly deviate from its counterpart for the no boundary case. Surprisingly, for small-sized particles, the dominant contribution to T depends only on the total diffusivity D=D_{1}+D_{2}, in sharp contrast to the one-dimensional case. This contribution can be related to the Wiener sausage generated by a fictitious Brownian particle with diffusivity D. In two dimensions, the first subleading contribution to T is found to depend weakly on the ratio D_{1}/D_{2}. We also investigate the slow-diffusion limit when D_{2}≪D_{1}, and we discuss the transition to the limit when one particle is a fixed target. Finally, we give some indications to anticipate when T can be expected to be a good approximation for 〈T〉.

Optimization with delay-induced bifurcations.

Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none guaranteeing an optimal solution. Here, we conceive a principle behind optimization based on delay-induced bifurcations, which is potentially implementable in non-quantum analog devices. Often, optimization techniques are interpreted via a particle moving in multi-well energy landscape and to prevent confinement to a non-global minima they should incorporate mechanisms to overcome barriers between the minima. Particularly, simulated annealing digitally emulates pushing a fictitious particle over a barrier by random noise, whereas quantum computers utilize tunneling through barriers. In our principle, the barriers are effectively destroyed by delay-induced bifurcations. Although bifurcation scenarios in nonlinear delay-differential equations can be very complex and are notoriously difficult to predict, we hypothesize, verify, and utilize the finding that they become considerably more predictable in dynamical systems, where the right-hand side depends only on the delayed variable and represents a gradient of some potential energy function. By tuning the delay introduced into the gradient descent setting, thanks to global bifurcations destroying local attractors, one could force the system to spontaneously wander around all minima. This would be similar to noise-induced behavior in simulated annealing but achieved deterministically. Ideally, a slow increase and then decrease of the delay should automatically push the system toward the global minimum. We explore the possibility of this scenario and formulate some prerequisites.

Study on flexible deformation of waste plastic film by fictitious particle method

Waste plastic sorting and recycling is an efficient and energy-saving way of domestic waste treatment. The deformation of waste plastic film affects the accuracy of plastic sorting. In this paper, a new method for calculating the deformation of waste plastic film, fictitious particle method, is proposed. The calculation model of film deformation is established and the formula of line element is deduced. The deformation law of plastic film is studied and the calculation results of fictitious particle method are obtained. The experimental platform was set up to obtain the film deformation data. The two-way fluid–solid coupling method was used for simulation experiment. Compared with the experimental results and simulation results, it is verified that the algorithm is in good agreement. The average error rate of the fictitious particle method is 4.26%, and the calculation time is 3.5 s. The algorithm has small amount of calculation and fast calculation speed. It laid the foundation for effectively improving the accuracy of wind separation and the optimization of plastic film wind separation machinery. • A new numerical calculation method called fictitious particle method is proposed. • The deformation law of the film in the separation process of waste plastic film was explored. • The fictitious particle method reduces the calculation amount and the calculation speed is fast. • The superiority of fictitious particle method in studying the deformation of waste plastic film was verified. • Improve the accuracy of wind sorting waste plastic film.

Triplon current generation in solids

A triplon refers to a fictitious particle that carries angular momentum S=1 corresponding to the elementary excitation in a broad class of quantum dimerized spin systems. Such systems without magnetic order have long been studied as a testing ground for quantum properties of spins. Although triplons have been found to play a central role in thermal and magnetic properties in dimerized magnets with singlet correlation, a spin angular momentum flow carried by triplons, a triplon current, has not been detected yet. Here we report spin Seebeck effects induced by a triplon current: triplon spin Seebeck effect, using a spin-Peierls system CuGeO3. The result shows that the heating-driven triplon transport induces spin current whose sign is positive, opposite to the spin-wave cases in magnets. The triplon spin Seebeck effect persists far below the spin-Peierls transition temperature, being consistent with a theoretical calculation for triplon spin Seebeck effects.

A Local Semi-Fixed Ghost Particles Boundary Method for WCSPH

Due to the convenience and flexibility in modeling complex geometries and deformable objects, local ghost particles methods are becoming more and more popular. In the present study, a novel local semi-fixed ghost particles method is proposed for weakly compressible smoothed particle hydrodynamics (WCSPH). In comparison with the previous local ghost particles methods, the new boundary method can effectively reduce spurious pressure oscillations and smooth the flow field. Besides, the new generation mechanism of fictitious particles is simple and robust, which is suitable for all kinds of kernel functions with different sizes of the support domain. The numerical accuracy and stability of the new smoothed particle hydrodynamics (SPH) scheme are validated for several typical benchmark cases. A detailed investigation into the pressure on solid walls and the surface elevation in dynamic simulations is also conducted. A comparison of numerical results shows that the new boundary method helps reduce the oscillations in the numerical solutions and improves the numerical accuracy of the pressure field.

Semi-coupled resolved CFD–DEM simulation of powder-based selective laser melting for additive manufacturing

We present a semi-coupled resolved Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) to simulate a class of granular media problems that involve thermal-induced phase changes and particle–fluid interactions. We employ an immersed boundary (IB) method to model the viscous fluids surrounding solid particles in conjunction with a fictious CFD domain occupied by the actual positions of the particle. Heat transfers between the actual fluids and the fictitious particle are treated as a multiphase problem by the CFD to resolve the temperature gradient distribution within each granular particle and its possible phase change (e.g., melting or partial melting). The mechanical interactions between the solid particles and the fluids are modeled by coupled DEM and CFD. The proposed method is validated by simulations of a typical powder-based selective laser melting (PB-SLM) process. Three key SLM input parameters, laser power, laser energy distribution and hatch distance, are examined on the effect of melting. The simulation results capture key features and observations of PB-SLM found in experiments and are quantitatively consistent with available testing data. The study provides a physically based, high-fidelity computational approach for future PB-SLM additive manufacturing.

Macroscopic Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is a highly simplified model for fluid flows using a few limited fictitious particles. It has been developed into a very efficient and flexible alternative numerical method in computational physics, demonstrating its great power and potential for resolving more and more challenging physical problems in science and engineering covering a wide range of disciplines such as physics, chemistry, biology, material science and image analysis. The LBM is implemented through the two routine steps of streaming and collision using the three parameters of the lattice size, particle speed and collision operator. A fundamental question is if the two steps are integral to the method or if the three parameters can be reduced to one for a minimal lattice Boltzmann method. In this paper, it is shown that the collision step can be removed and the standard LBM can be reformulated into a simple macroscopic lattice Boltzmann method (MacLAB). This model relies on macroscopic physical variables only and is completely defined by one basic parameter of the lattice size δx, bringing the LBM into a precise “lattice” Boltzmann method. The viscous effect on flows is naturally embedded through the particle speed, making it an ideal automatic simulator for fluid flows. Three additional advantages compared to the existing LBMs are that: (i) physical variables can directly be retained as the boundary conditions; (ii) much less computational memory is required; and (iii) the model is unconditionally stable. The findings are demonstrated and confirmed with numerical tests including flows that are independent of and dependent on fluid viscosity, 2D and 3D cavity flows and an unsteady Taylor–Green vortex flow. This provides an efficient and powerful model for resolving physical problems in various disciplines of science and engineering.