Finite Particle Research Articles

An Axiomatic System for a Physical or Digital but Continuous 3-Dimensional Euclidean Geometry, Without Infinite Many Points

This paper is concerned with finding an axiomatic system, so as to define the 3-dimensional Euclidean space, without utilizing the infinite ,that can imply all the known geometry for practical applied sciences and engineering applications through computers , and for more natural and perfect education of young people innbsp the Euclidean geometric thinking. In other words by utilizing only finite many visible and invisible points and only finite sets, and only real numbers with finite many digits, in the decimal representation. The inspiration comes from the physical matter , rigid, liquid and gaseous, which consists of only finite manynbsp particles in the physical reality. Or from the way that continuity is produced in a computer screen from only finite many invisible pixels . We present such a system of axioms and explain why it is chosen in such a way. The result is obviously not equivalent, in all the details, with the classical Euclidean geometry.nbsp Our main concern is consistency and adequacy but not independence of the axioms between them. It is obvious that within the space of a single paper, we do not attempt to produce all the main theorems of the Euclidean geometry, but present only the axioms.

Study on wind-induced response of a large-span roof by using finite particle method

The wind-induced response analysis of large-span roof using finite particle method (FPM) is discussed in this paper. Based on vector mechanics, FPM is an intrinsic method to study responses of structures under dynamic excitation. It adopts separated particles that governed by Newton’s second law to describe structural behaviors, especially geometric nonlinearity. As the previous damping treatments in FPM are inadequate for studying the wind-induced responses of large-san roof, two enhanced treatments based on Rayleigh damping for approximatively estimating damping forces in the FPM are proposed and are verified through numerical pseudo-dynamic example. To study the wind-induced responses of a large-span roof, the wind-tunnel tests of pressure measurement are carried out to obtain time histories of wind loads on the large-span roof. The FPM is further employed to estimate wind-induced responses of the large-span roof. Wind-induced displacement and internal forces responses obtained by FPM are compared with results from finite element method (FEM). The results from FPM meet well with results from the FEM, which presents the capability of FPM to study the wind-induced responses of large-span roof.

Analytical evaluation of the rutting critical response function under the heavy vehicle’s moving in flexible pavement

Accurate and realistic identification of critical response of pavement structure leads to sustainable pavement structure design. This study aimed to obtain and analyse the rutting critical response function under heavy trucks using Abaqus three-dimensional finite element and particle swarm optimization (PSO) methods. For modeling, asphalt viscoelastic properties, data of the Weigh-In-Motion (WIM) device, and the Moving Load method were used to simulate trucks passing over the pavement. The thickness of pavement layers and their elastic and viscoelastic properties were calculated by field study and theoretical relationships, respectively. The truck specifications including loads, axles and wheels configurations, and dimensions were collected by WIM data and field survey. The results showed that the best statistical equation that could be fitted to critical responses was the modified Gaussian function. Also, according to analysis results, the effect of truck speed on the rutting critical responses was greater than its weight.

Physical mechanisms of the dynamical patterns and non-equilibrium processes of self-driven particles in an ASEP network affected by a finite external particle source

When confronting complexity science, complexity systems indicating evolution regularities are addressed due to their nonlinearity, uncertainty, emergence and self-organization. Among them, totally asymmetric simple exclusion process (TASEP) belonging to asymmetric simple exclusion process (ASEP) stands out as a paradigm nonlinear dynamical model depicting microscopic non-equilibrium dynamics of real active particles. Motivated by real multi-physics processes of protein motors, TASEP networks with Langmuir kinetics and finite resources are studied. Partially differential equations for boundary and bulk dynamics in stochastically regular and irregular networks are numerically calculated. Connectivity, effective interactions and concentration coefficient are found to govern system dynamics. Six kinds of density profiles are observed. Fruitful dynamical patterns of global density distributions, weight distributions of each phase, local currents, local densities and related phase diagrams are obtained, which lead to acquisitions of evolvement regularities of physical mechanisms of bulk dynamics and non-equilibrium phase transitions. Three kinds of domination mechanisms including three-phase, two-phase and single-phase dominations of global dynamics are found in irregular networks. Global dynamics gradually become high-density dominated with increasing concentration coefficient or effective attachment rate. While, they gradually become low-density dominated with increasing effective detachment rate or connectivity. However, global dynamics are found to be dominated by low and high coexistence phase in general cases of regular networks. Our work is conducive to modelling nonlinear dynamical behaviors and non-equilibrium phase transition mechanisms in mesoscopic self-driven particle systems.

Compact and Low-Insertion-Loss 1×N Power Splitter in Silicon Photonics

In this paper, a novel design of a 1×N multimode-interference power splitter is proposed and investigated. By using the finite difference time domain method and particle swarm optimization algorithm, our proposed 1×N optical power splitter can be optimized to realize compact size, good uniformity, low insertion loss, and broad bandwidth. To verify the effectiveness of this design, the designed 1×4 and 1×8 multimode-interference power splitters are experimentally demonstrated on an silicon-on-insulator platform. The lengths of the designed 1×4 and 1×8 power splitters are 36 μm and 47.8 μm, respectively. Experimental results show that, for the fabricated 1×4 power splitter, the uniformity ranges from 0.07 to 0.89 dB and the corresponding maximum insertion loss is 0.62 dB within a bandwidth from 1520 to 1624 nm. For the fabricated 1×8 power splitter, within a bandwidth from 1519 to 1623 nm, the uniformity varies from 0.19 to 0.83 dB and a maximum insertion loss of 0.64 dB are obtained.

A finite particle method (FPM) for Lagrangian simulation of conservative solute transport in heterogeneous porous media

When a smoothed particle hydrodynamics (SPH) method, a Lagrangian and meshfree numerical scheme, is used to solve the advection-dispersion equation (ADE), SPH solutions may not be accurate when particles are irregularly distributed, i.e., the distance between two neighbor particles varies irregularly in a simulation domain. Particle irregularity may be caused by nonuniform groundwater flow in a heterogeneous field of hydraulic conductivity. This study explores for the first time whether the Finite Particle Method (FPM) can provide more accurate ADE solutions than SPH does for irregularly distributed particles. FPM is similar to SPH in theory, but uses a modified kernel gradient to construct a SPH approximation of solute concentration gradients. Performance of SPH and FPM with irregularly distributed particles is evaluated by using two numerical cases. The first case considers only diffusive transport, and has an analytical solution for the evaluation. The second case considers both advection and dispersion, and uses a numerical solution as a reference for the evaluation. For each of the two cases, several numerical experiments are conducted using multiple sets of irregularly distributed particles with different levels of particle irregularity due to different levels of heterogeneity of hydraulic conductivity. Numerical results indicate that, for the numerical experiments of this study, FPM outperforms SPH to yield more accurate ADE solutions. However, FPM solutions are still subject to numerical errors, and the errors increase when the level of heterogeneity of hydraulic conductivity increases. Further improvement of FPM is warranted in a future study.

Nonlinear Dynamics Analysis of Flexible Deployable Linkage Mechanisms Using the Finite Particle Method

Deployable mechanisms have notable applications in mechanical engineering, civil engineering, and space technology. Although often ignored, deployable linkage mechanism exhibits additional flexibility beyond rigid folding owing to the deformation of nonrigid components. The actual behavior of flexible deployable linkage usually involves the dynamic effect and geometric nonlinearity. Using the finite particle method (FPM), this study investigated the nonlinear responses of flexible deployable linkage mechanisms. As a particle method, the FPM is displacement based, explicit, and can avoid iterations to solve nonlinear equilibrium equations. It can be used for nonlinear analyses of structures with rigid body motion and infinitesimal mechanisms, and to determine the internal force and structural deformation. To investigate the nonrigid Bennett linkage and Bricard linkage, formulations of a three-dimensional beam element and revolute hinge element were derived for FPM analysis. Agreement between analytical solutions and numerical simulations demonstrated the efficiency of the proposed approach for nonlinear motion analysis of nonrigid mechanisms. The FPM results revealed that mechanism flexibility can cause deviation from rigid compatibility paths, and the internal force and deformation of mechanisms should be considered when designing nonrigid mechanisms.

Spot formation in three-dimensional Yukawa liquid

Dynamics of a three-dimensional (3D) plane Couette flow (PCF), which subjected to a 3D finite amplitude particle velocity perturbation, is addressed using 3D “classical first principles” molecular dynamics simulation with screened Coulomb potential or a Yukawa potential as the inter-particle interaction. Such systems are often realized in complex plasmas and charged colloids. Parameters are chosen such that the system is a Yukawa liquid whose kinematic viscosity is a time-dependent function of the particle correlation strength Γ controlled by shear heating. This feature is found to facilitate a unique quench study of the Reynolds number Re as a function of time for fixed system size and fixed flow speed. For small cross-sectional aspect ratios ∼20, starting from Re ∼ 1211-717, a laminar 3D PCF initial condition is shown to become unstable to localized 3D finite amplitude perturbation for various increasing amplitude strengths, clearly demonstrating the formation of a turbulent spot. This spot is found to spread in time into the otherwise laminar regions, a signature of subcriticality or co-existence of laminar and turbulent regions in PCF in a 3D Yukawa liquid. It is shown unambiguously that the range of interaction of Yukawa potential determines the nature of spot formation and its dynamics. At long range, a qualitative similarity of our results to those found in turbulent spots of PCF in conventional hydrodynamics is discussed. Our findings may have ramifications for a wide range of physical systems that exhibit sub-critical transition to turbulence.

Interaction rates in cosmology: heavy particle production and scattering

We study transition rates and cross sections from first principles in a spatially flat radiation dominated cosmology. We consider a model of scalar particles to study scattering and heavy particle production from pair annihilation, drawing more general conclusions. The S-matrix formulation is ill suited to study these ubiquitous processes in a rapidly expanding cosmology. We introduce a physically motivated adiabatic expansion that relies on wavelengths much smaller than the particle horizon at a given time. The leading order in this expansion dominates the transition rates and cross sections. Several important and general results are direct consequences of the cosmological redshift and a finite particle horizon: (i) a violation of local Lorentz invariance, (ii) freeze-out of the production cross section at a finite time, (iii) sub-threshold production of heavier particles as a consequence of the uncertainty in the local energy from a finite particle horizon, a manifestation of the anti-Zeno effect. If heavy dark matter is produced via annihilation of a lighter species, sub-threshold production yields an enhanced abundance. We discuss several possible cosmological consequences of these effects.

PROGRAMMABLE INSTABILITY OF SPATIAL STRUCTURES BASED ON KRESLING ORIGAMI

A spatial structure based on the Kresling origami has multiple stability states under external compression. To realize an intelligent structure with a programmable failure mode, the finite particle method (FPM) is used to study the instability of spatial structures based on the Kresling origami. We propose a method of controlling the structural stiffness by adjusting the material, prestress, and structure arrangement. The calculation of the cable, rod, and membrane structures using the FPM is introduced. The method is verified by a bi-stability analysis of the Kresling pattern. The instability modes of the cable-rod model, the cable-rod-membrane model and the nested model based on the Kresling origami are analyzed. The influences of the elastic modulus, prestress level and structural arrangement on the structural instability mode and strain energy conversion are investigated. At last, the programmable failure of a double-layer Kresling structure is realized by adjusting the Young’s modulus of the structure, providing a new method for the design of intelligent structures in the future.

Numerical and experimental studies on capturing behaviors of the inflatable manipulator inspired by fluidic origami structures

Flexible robotic manipulators have significant advantages especially when the capturing task involves strong collisions in engineering. This work introduces a new design of the inflatable manipulator inspired by fluidic origami structures to perform capturing process. To analyze the dynamic inflation and exhaustion processes of fluidic origami structures, a universal framework combining the particle-bar-spring model with the finite particle method is proposed. Fluid effects are considered by fluid–solid interaction, and the analysis of the inflation process of the original fluidic origami structure helps to verify the validity of the proposed method. Contact model is built to consider the collision in the capturing process. The newly designed inflatable manipulator can achieve overall bending and capture the target successfully. The motion trajectory and capturing process of the inflatable manipulator are simulated and analyzed. A prototype of the inflatable manipulator is processed to perform experimental investigations. The experimental results obtained by the digital image correlation technique are consistent with the numerical results. This work not only provides a new kind of inflatable manipulators inspired by fluidic origami structures, but also proposes a framework to analyze the fluidic origami structures.

A Plasmoid model for the Sgr A* Flares Observed With Gravity and CHANDRA

Abstract The Galactic Center black hole Sgr A* shows significant variability and flares in the submillimeter, infrared, and X-ray wavelengths. Owing to its exquisite resolution in the IR bands, the GRAVITY experiment for the first time spatially resolved the locations of three flares and showed that a bright region moves in ellipse-like trajectories close to, but offset from, the black hole over the course of each event. We present a model for plasmoids that form during reconnection events and orbit in the coronal region around a black hole to explain these observations. We utilize general-relativistic radiative-transfer calculations that include effects from finite light travel time, plasmoid motion, particle acceleration, and synchrotron cooling, and obtain a rich structure in the flare light curves. This model can naturally account for the observed motion of the bright regions observed by the GRAVITY experiment and the offset between the center of the centroid motion and the position of the black hole. It also explains why some flares may be double peaked while others have only a single peak and uncovers a correlation between the structure in the light curve and the location of the flare. Finally, we make predictions for future observations of flares from the inner accretion flow of Sgr A* that will provide a test of this model.

Brownian systems perturbed by mild shear: comparing response relations

We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear flow. We collect six different routes for computing the response, two of which are based on the symmetry of the considered system and observable with respect to the shear axes. We include the extension of the Green–Kubo relation to underdamped cases, which shows two unexpected additional terms. These six computational methods are applied to investigate the relaxation of the response towards the steady state for different observables, where interesting effects due to interactions and a finite particle mass are observed. Moreover, we compare the different response relations in terms of their statistical efficiency, identifying their relative demand on experimental measurement time or computational resources in computer simulations. Finally, several measures of breakdown of linear response theory for larger shear rates are discussed.

In-silico analysis of airflow dynamics and particle transport within a human nasal cavity

We present a numerical investigation of the airflow dynamics and particle transport through an averaged human nasal cavity. The effect of particle size and breathing rate on the deposition patterns are explored. The simulations reveal that smaller particles penetrate deeper into the airway, whereas larger particles agglomerate near the anterior portion of the nasal cavity. Increasing the flow rate augmented the penetration of the particles. The complex interplay of the finite particle size and the flow inertia decided the spatial deposition of the particles. The findings from this study demonstrate the efficacy of state-of-art simulation frameworks for targeting respiratory disorders.

High-order consistent SPH with the pressure projection method in 2-D and 3-D

Mesh-free methods such a smoothed particle hydrodynamics (SPH) have advantages over mesh-based methods for flow in complex domains but attaining consistent high-order accurate solutions with the conventional form of SPH has yet to be resolved. The high-order smoothing error dominates the SPH error until increasingly fine resolutions cause the low-order discretisation error to dominate; this is related to discretising a volume integral into a summation. In this paper, a high-order consistency correction based on modified SPH (MSPH) and the modified finite particle method (FPM) is proposed for improving the order of the limiting discretisation error. The new technique is an arbitrarily high-order extension of these schemes where the complexity of the consistency correction and the required computations are reduced by using simplified versions of the smoothing kernel derivatives. Tested in Eulerian form, the proposed high-order consistent SPH technique (HOCSPH) is combined with new high-order SPH kernel functions, designed to improve the order of the SPH smoothing error, and the resulting hybrid technique is shown to converge according to the smoothing error initially before converging according to the HOCPSH error once the latter becomes dominant. The initial high-order convergence lowers the computational effort required to achieve higher accuracy with hybrid HOCSPH in comparison to HOCSPH with second-order smoothing accuracy kernel functions. However, for highly irregular distributions it is found that the use of kernels with second-order smoothing accuracy provides more consistent convergence properties. A number of flows are simulated in 2-D and 3-D using the new HOCSPH technique in combination with the pressure projection method, and the results show that the method is accurate and able to model highly complex flow patterns. Some issues with stability of the projection method related to pressure–velocity collocation are identified, and several remedies are proposed. While effective for the test cases herein, these remedies are new in this context and require further attention for generalisation in future studies.

Modelling of nucleation – Isotropic surface growth for finite platelet-like particles

This article concerns the realistic modelling of gas–solid reactions ubiquitous in industrial reactors. A simplistic deterministic model describing the stochastic isotropic nucleation-growth process in a powder of platelets has been strongly improved. Comparisons with a rigorous Monte-Carlo (MC) method that was used as a benchmark show that for realistic platelets, the current deterministic approach can strongly overestimate the reaction rate and underestimate the reaction duration because it considers the platelet surface to be infinite. A new deterministic model considering the finite dimensions of the platelets was developed and leads to the same results as MC simulations. Virtual experimental data were generated with this new model. Kinetic parameters were then optimised using the old and new deterministic method. The optimal curves obtained under the infinite platelet hypothesis are far from the measurements. This paper underscores that chemical kinetic parameters are only reliable if the underlying theoretical model is sound.

A FIBER BEAM ELEMENT FOR THE FINITE PARTICLE METHOD CONSIDERING SHEAR AND TORSION DEFORMATON

To improve the accuracy of the finite particle method (FPM) for solving structural elastoplastic problems, the fiber beam model is combined with the solution framework of FPM. The formulas for solving the particle internal forces of the FPM fiber beam element considering shear and torsion deformation are deduced. The element uses the Timoshenko beam theory to describe the deformation state of the beam section. The displacements of an arbitrary point on the section are determined by the element pure deformation components in the element. The three-dimensional constitutive relationships of fiber materials are used in the element to consider the coupling effects between bending, shear and torsion deformation. Several numerical tests are conducted. The results show that the proposed fiber beam element can effectively simulate the elastoplastic behavior of the structure and shows higher accuracy than the plastic hinge method.

The nascent coffee ring: how solute diffusion counters advection

We study the initial evolution of the coffee ring that is formed by the evaporation of a thin, axisymmetric, surface-tension-dominated droplet containing a dilute solute. When the solutal Péclet number is large, we show that diffusion close to the droplet contact line controls the coffee-ring structure in the initial stages of evaporation. We perform a systematic matched asymptotic analysis for two evaporation models – a simple, non-equilibrium, one-sided model (in which the evaporative flux is taken to be constant across the droplet surface) and a vapour-diffusion limited model (in which the evaporative flux is singular at the contact line) – valid during the early stages in which the solute remains dilute. We call this the ‘nascent coffee ring’ and describe the evolution of its features, including the size and location of the peak concentration and a measure of the width of the ring. Moreover, we use the asymptotic results to investigate when the assumption of a dilute solute breaks down and the effects of finite particle size and jamming are expected to become important. In particular, we illustrate the limited validity of this model in the diffusive evaporative flux regime.

Full-Scale Simulation and Validation of Wear for a Mining Rope Shovel Bucket

Failure in industrial processes is often related to wear and can cause significant problems. It is estimated that approximately 1–4% of the gross national product for an industrialized nation is related to abrasive wear. This work aims to numerically predict development of wear for full-scale mining applications in harsh sub-arctic conditions. The purpose is to increase the understanding of wear development in industrial processes and optimize service life and minimize costs related to wear. In the present paper, a granular material model consisting of the discrete element method (DEM) and rigid finite element particles is utilized to study wear in full-scale mining applications where granular materials and steel structures are present. A wear model with the basis in Finnie’s wear model is developed to calculate wear from combined abrasive sliding and impact wear. Novel in situ full-scale experiments are presented for calibration of the wear model. A simulation model of the rope shovel loading process is set up where the bucket filling process is simulated several times, and the wear is calculated with the calibrated wear model. From the full-scale validation, it is shown that the simulated wear is in excellent agreement when compared to the experiments, both regarding wear locations and magnitudes. After validation, the model is utilized to study if wear can be minimized by making small changes to the bucket. One major conclusion from the work is that the presented wear simulator is a suitable tool that can be used for product development and optimization of the loading process.

Phase Stability and Raman/IR Signatures of Ni-Doped MoS2 from Density Functional Theory Studies

Ni-doped MoS$_2$ is a layered material with useful tribological, optoelectronic, and catalytic properties. Experiment and theory on doped MoS$_2$ has focused mostly on monolayers or finite particles: theoretical studies of bulk Ni-doped MoS$_2$ are lacking and the mechanisms by which Ni alters bulk properties are largely unsettled. We use density functional theory calculations to determine the structure, mechanical properties, electronic properties, and formation energies of bulk Ni-doped 2H-MoS$_2$ as a function of doping concentration. We find four meta-stable structures: Mo or S substitution, and tetrahedral (t-) or octahedral (o-) intercalation. We compute phase diagrams as a function of chemical potential to guide experimental synthesis. A convex hull analysis shows that t-intercalation (favored over o-intercalation) is quite stable against phase segregation and in comparison with other compounds containing Ni, Mo, and S; the doping formation energy is around 0.1 meV/atom. Intercalation forms strong interlayer covalent bonds and does not increase the $c$-parameter. Ni-doping creates new states in the electronic density of states in MoS$_2$ and shifts the Fermi level, which are of interest for tuning the electronic and optical properties. We calculate the infrared and Raman spectra and find new peaks and shifts in existing peaks that are unique to each dopant site, and therefore may be used to identify the site experimentally, which has been a challenge to do conclusively.