Particle Representation Research Articles

Microscopic theory for hyperuniformity in two-dimensional chiral active fluid

Some nonequilibrium systems exhibit anomalous suppression of the large-scale density fluctuations, so-called hyperuniformity. Recently, hyperuniformity was found numerically in a simple model of chiral active fluids (Lei et al 2019 Sci. Adv. 5 eaau7423). We revisit this phenomenon and put forward a microscopic theory to explain it. An effective fluctuating hydrodynamic equation is derived for a simple particle model of chiral active matter. We show that the linear analysis of the obtained hydrodynamic equation captures hyperuniformity. Our theory yields hyperuniformity characterized by the same exponents as the numerical observation, but the agreement with the numerical data is qualitative. We also argue that the hydrodynamic equation for the effective particle representation, in which each rotating trajectory is regarded as an effective particle, has the same form as the macroscopic description of the random organization model with the center of mass conservation.

Simplified description of hard particles in tribological systems using statistical sample particles

AbstractTechnical applications often include tribological systems in which friction and wear occur. Hard particles, such as sand, are often present in the contact between the surfaces of two bodies in contact and affect both the system dynamics and the resulting surface topography of the contacting bodies. Real tribological systems can contain a very high number of particles. Hence, for performance reasons of numerical studies, the explicit representation of each particle in a simulation is often not practical. The approach presented here is based on a model simplification by grouping several particles to form statistical sample particles (SSPs). SSPs can only move as a whole, and thereby simplify the motions of the individual particles, but the contact stiffness and orientation dependence of the force are still determined by the set of individual particles that are part of the statistical sample. Using sample size 1, each individual particle is represented without simplification, while using a sample size larger than one, the total number of particles in the system reduces to a minimum of one SSP representing all particles in the system. This approach provides a very efficient way to specify the model complexity and desired level of detail for the particle representation within a model of a tribological system.

Hubbard Bands and Exotic States in Doped and Undoped Mott Systems: The Kotliar–Ruckenstein Representation

The slave–particle representation is a promising method to treat the properties of exotic strongly correlated systems. We develop a unified approach to describe both the paramagnetic state with possible spin–liquid features and states with strong long-range or short-range magnetic order. Combining the Kotliar–Ruckenstein representation and fractionalized spin–liquid deconfinement picture, the Mott transition and Hubbard subbands are considered. The spectrum in the insulating state is significantly affected by the presence of the spinon spin–liquid spectrum and a hidden Fermi surface. Presenting a modification of the Kotliar–Ruckenstein representation in the spin–wave region, we treat the case of magnetic order, with special attention being paid to the half-metallic ferromagnetic state. The formation of small and large Fermi surfaces for doped current carriers in the antiferromagnetic state is also discussed.

Adaptive Discretization using Voronoi Trees for Continuous POMDPs

Solving continuous Partially Observable Markov Decision Processes (POMDPs) is challenging, particularly for high-dimensional continuous action spaces. To alleviate this difficulty, we propose a new sampling-based online POMDP solver, called A daptive D iscretization using V oronoi T rees (ADVT). It uses Monte Carlo Tree Search in combination with an adaptive discretization of the action space as well as optimistic optimization to efficiently sample high-dimensional continuous action spaces and compute the best action to perform. Specifically, we adaptively discretize the action space for each sampled belief using a hierarchical partition called Voronoi tree, which is a Binary Space Partitioning that implicitly maintains the partition of a cell as the Voronoi diagram of two points sampled from the cell. ADVT uses the estimated diameters of the cells to form an upper-confidence bound on the action value function within the cell, guiding the Monte Carlo Tree Search expansion and further discretization of the action space. This enables ADVT to better exploit local information with respect to the action value function, allowing faster identification of the most promising regions in the action space, compared to existing solvers. Voronoi trees keep the cost of partitioning and estimating the diameter of each cell low, even in high-dimensional spaces where many sampled points are required to cover the space well. ADVT additionally handles continuous observation spaces, by adopting an observation progressive widening strategy, along with a weighted particle representation of beliefs. Experimental results indicate that ADVT scales substantially better to high-dimensional continuous action spaces, compared to state-of-the-art methods.

Positive cross-linguistic influence in the representation and processing of sentence-final particle le by L2 and heritage learners of Chinese.

This study investigates the representation and processing of written Chinese sentences subject to a semantic condition (i.e., "direction of change") attached to the sentence-final particle (SFP) le in Mandarin Chinese. Three groups of bilingual speakers of Chinese and English who differ in their onset age of bilingualism and proficiency of English were studied. It was anticipated that there would be a positive cross-linguistic influence (CLI) from English due to similarities between the SFP le and the English adverb already in terms of direct semantic transfer. An acceptability judgment (AJ) task and a self-paced reading (SPR) task were conducted to elicit judgment and processing difficulty with and without semantic violations. The participants included English-dominant second language (L2) learners (n = 18) and heritage learners (n = 19) who had advanced proficiency in Chinese, as well as monolingually raised Mandarin speakers from China as a baseline control group (n = 18). The results indicated that sensitivity to violations of the semantic condition varied depending on factors such as the specific structure (noun vs. verb phrase), the task type (offline vs. online), and the type of bilingual speaker (early vs. late). Among the three groups of bilinguals, the heritage learners demonstrated a representation of the semantic condition that resembled the target language across different sentence structures, whereas the L2 learners did not. Furthermore, the heritage learners exhibited earlier sensitivity to violations during online processing compared to the baseline control group. These exceptional results can be attributed to the heritage learners' early exposure to and positive CLI between the SFP le in Mandarin and the English adverb already.

A universal mechanism for the development of self-ordering processes in systems of identical particles

Based on the hypothesis of the existence of wave long-range action and its role in the development of self-ordering processes, expressed by us in previous works, we carried out a methodological analysis of the applicability of wave representations in systems of identical particles. The main attention in the analysis is paid to the practical application of de Broglie waves in systems of interacting particles. For this purpose, Bohr's theory of the hydrogen atom has been revised and inconsistencies that contradict modern ideas have been corrected. Two conclusions are made: wave representations of particles are of a material nature; the de Broglie wavelength should be determined in terms of the relative momentum of the interacting particles . Based on the materiality of wave representations, the features of the long-wave interaction of particles are determined. It is emphasized that in many manifestations this interaction has a resonant character. This interaction is the foundation for the universal mechanism for the development of self-ordering processes in systems of identical particles. The paper presents an algorithm for the emergence and functioning of a universal mechanism. The condition for the emergence is always any withdrawal of the system from the state of isotropic chaos and the formation of an initial subgroup of particles with the same magnitude and direction of momenta. The most common cause leading to the fulfillment of the condition is monoenergization of the spectrum of particles in the system. The causative agent of the mechanism is direct collisions of particles, in which the probability of long-wavelength representations is the highest. The development of the mechanism is limited only by the fulfillment of the percolation condition - overcoming the percolation threshold. The final stage of the mechanism is the formation of a superfluid component - a kind of macroparticle that does not interact with walls and other molecules. A characteristic wave feature of such a macroparticle is its coherence. Several final stages in the development of self-ordering processes for typical special phenomena in systems of identical particles are analyzed.

Model of the Selective Laser Melting Process-Powder Deposition Models in Multistage Multi-Material Simulations

This paper presents one of the final stages in the development of a holistic model of the selective laser melting (SLM) process. The holistic model developed previously allows for modeling of only one stage of SLM, which limits simulations to one cycle with one material. The lattice Boltzmann method is applied for simulation of laser treatment, melting, fluid flow, and solidification. Several models of powder bed generation were developed within the framework of the holistic model and are described in this paper. They were developed on the basis of static and dynamic physical principles with the use of cellular automata, their own code, and the Unity® platform. They employed continuous and discrete particle representation and incorporated a model of powder deposition with particles of atomized or arbitrary shape. The closing of the external simulation circuit, which contains the powder bed generation model, cycle initialization, its realization by the model based on the Lattice Boltzmann Method (LBM), and the powder removal model, allows us to finish one simulation cycle of laser treatment and initialize the next, thereby enabling multistage multi-material simulations. The simulation results of the multistage SLM process with the Ti-6Al-V alloy and bioactive glass are presented in this paper. These simulation results confirm the possibility of modeling several SLM stages with two different materials. The holistic model can be used for simulation, design, and optimization of multistage, multi-material SLM processes.

Holographic fluids: A thermodynamic road to quantum physics

Quantum mechanics, superfluids, and capillary fluids are closely related: It is thermodynamics that links them. In this paper, the Liu procedure is used to analyze the thermodynamic requirements. A comparison with the traditional method of divergence separation highlights the role of spacetime. It is shown that perfect Korteweg fluids are holographic. The conditions under which a complex field can represent the density and velocity fields of the fluid, and where the complex scalar field becomes a wave function of quantum mechanics, are explored. The bridge between the field and particle representations of a physical system is holography, and the key to holography is the Second Law of Thermodynamics.

Efficient Data Dissemination Strategy for UAV in UAV-Assisted VANETs

With development of emerging intelligent transportation systems (ITSs), unmanned aerial vehicles (UVAs) are gaining growing attention to achieve UAV-assisted VANETs for improving performance of data dissemination. However, in UAV-assisted VANETs, the performance of data dissemination can be significantly compromised by the limited bandwidth resource of UAVs. In this paper, we propose a scheduling strategy to provide efficient data dissemination. In particular, first, we take into account a scenario with either unavailable or overloaded infrastructure, where a UAV is employed to provide data dissemination. Furthermore, considering the limited bandwidth resource of the UAV, we formulate a coding-based cooperative caching data dissemination (C3D2) problem which makes use of the synergy between network coding and vehicular caching with the objective of maximizing the bandwidth efficiency of UAVs. Meanwhile, the NP-hardness of the C3D2 problem is proved by constructing a polynomial time reduction from the simultaneous matrix completion problem. Based on the effectiveness of the binary particle swarm optimization (BPSO) framework in solving the complex problems, we propose a BPSO-based cooperative caching scheduling (BPSO_C2S) algorithm consisting of a series of strategies, such as particle representation, particle evaluation, particle update and infeasible solution amendment. In addition, we analyze the computational complexity of the BPSO_C2S. Finally, we build the simulation model and give a comprehensive performance evaluation through the real-world map and taxi trajectories. Simulation results demonstrate the effectiveness and superiority of the proposed solution.

Efficient Adaptive Monte Carlo Uncertainty Forecasting for High Dimensional Nonlinear Dynamic Systems

The problem of uncertainty forecasting for complex dynamical systems in the framework of particle methods can be effectively addressed through the solution methodology known as adaptive Monte Carlo (AMC). Monte Carlo (MC) methods involve discretizing the initial probability density function (pdf) followed by forward propagation of particles through system dynamics to obtain an approximate particle representation of the evolved state uncertainty. While simple to implement, MC faces questions surrounding transient statistical consistency and rate of convergence. AMC (adopted here) addresses these issues on-the-fly using defined bounds on estimation accuracy alongside ensemble enrichment routines. This paper presents several improvements in the ensemble enrichment module of AMC. The AMC platform is re-engineered to include the novel implementation of a parallel global stochastic optimization routine in conjunction with additional module enhancements that work together towards the goal of efficient forecasting. Moreover, the efficacy of algorithms utilized within every submodule of AMC are detailed and improved upon under the framework of arithmetic minimization and parallelization. Each submodule is profiled to determine computational bottlenecks, optimized or replaced with more efficient methods such as simulated annealing (SA), and parallelized ultimately leading to a clock time reduction of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$200 - 400\%$ </tex-math></inline-formula> for benchmark entry descent and landing, Lorenz-96, and Lotka-Volterra models.

Mesh-Based Consensus Distributed Particle Filtering for Sensor Networks

Following the Bayesian inference framework, this paper investigates the problem of distributed particle filtering over a sensor network to achieve consensus. The objective of the posterior-consensus strategy is to fuse the posterior probability distribution functions (PDFs) at different sensor nodes, so that an agreement of belief can be established in terms of the Kullback-Leibler average (KLA). To facilitate the consensus process and reduce the communication load, the local PDFs are approximated with weighted meshes and transmitted between neighboring nodes. The mesh representations are constructed by resorting to a grid partition of the state space, such that the PDF can be approximated by a linear combination of indicator functions. To derive a particle representation of the fused PDFs, a novel importance density function is designed to draw particles with respect to the information from all neighboring nodes. The weights of the particles are calculated via the recursive solution of the KLA. The effectiveness of the proposed filtering approach is demonstrated through two target tracking examples.

Instantaneous support propagation for [formula omitted]-Fleming–Viot processes

For a probability-measure-valued neutral Fleming–Viot process (Zt:t≥0) with Lévy mutation and resampling mechanism associated to a general Λ-coalescent with multiple collisions, we prove the instantaneous propagation of supports. That is, at any fixed time t>0, with probability one the closed support S(Zt) of the Fleming–Viot process satisfies S(ν∗Zt)⊆S(Zt), where ν is the Lévy measure of the mutation process. To show this result, we apply Donnelly–Kurtz’s lookdown particle representation for Fleming–Viot processes.

Toward Complementary Characterization of the Chemical Bond.

A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics of the canonical example of the H2 molecule. This is achieved by starting from an analytic form for the two-particle wave function for electrons forming the bond, in which we single out the atomic contribution (atomicity) in an unequivocal manner. The presence of the atomicity and ionicity factors complements the existing attributes of the bond. In this way, a gradual evolution of the molecular state to its two-atom correspondent is traced systematically with increasing interatomic distance. In effect, a direct relation to the onset of incipient Mott-Hubbard atomicity (Mottness) to the intrinsic covalency and ionicity is established. This goal is achieved formally by combining the single-particle wave function readjustment in the entangled state with a simultaneous determination of two-particle states in the particle (second quantization) representation.

Observation of Rayleigh Benard Convection as A Representation of Learning of Natural Phenomenons Through Water Molecular Movement

Research has been carried out with a device to observe the phenomenon of Rayleigh Benard convection, made of a glass box bounded by a lower plate and an upper plate. The bottom plate is hotter than the top plate which functions to heat the horizontal fluid layer from below. This study aims to observe the phenomenon of water molecule movement. The observation medium was water mixed with teak sawdust as a representation of water particles with an average density of mean=0.99 g/cm3. The variation of water thickness (d) used 5 cm and 6 cm with variations in temperature difference (DT) with an average increase of 50°C. Data was collected with a cellphone camera and run with Windows Movie Maker software which has a time accuracy of up to 0.001 seconds. It was observed that an increase in the temperature difference (DT) between the two plates resulted in an increase in the velocity of motion of water particles in convection which is depicted by a v-DT diagram. Due to the difference in temperature (DT) also results in the movement patterns of water molecules, namely laminar and turbulent. The turbulent phase with the Rayleigh number value R~107, indicated that the flow of water particles is getting faster, the direction of the flow of the particles starts to become irregular and sometimes signs of a water vortex appear. At different fluid immersion results in the start of a turbulent phase. The turbulent phase for d=5cm is observed at DT~30°C, and d=6cm at DT~20°C. Furthermore, this RBC phenomenon is used as a representation of learning natural phenomena in air fluids, namely whirlwinds as an event due to differences in temperature and pressure of a fluid

Conservative Projection Between Finite Element and Particle Bases

Particle-in-cell methods employ particle representations of unknown fields but also employ continuum fields for other parts of the problem. Thus projection between particle and continuum bases is required. Moreover, we often need to enforce conservation constraints on this projection. We derive a mechanism for enforcement based on weak equality and implement it in the PETSc libraries. Scalability is demonstrated to more than one billion particles.

Zero-range potentials for Dirac particles: Bound-state problems

A model in which a massive Dirac particle in R3 is bound by N⩾1 spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle’s bispinor wave function to certain limiting conditions at the potential centers. Each of these conditions is parametrized by a 2 × 2 Hermitian matrix (or, equivalently, a real scalar and a real vector) and mixes the upper and the lower components of the wave function. The problem of determining particle’s bound-state eigenenergies is reduced to the problem of finding real zeros of a determinant of a certain 2N×2N matrix. As the lower component of the particle’s wave function is inverse-square singular at each of the potential centers, the wave function itself is not square-integrable. Nevertheless, one can define a scalar pseudo-product with the property that wave functions belonging to different eigenenergies are orthogonal with respect to it. The wave functions may then be normalized so that their self-pseudo-products are plus one, minus one or zero. An auxiliary set of Sturmian functions is constructed and used to derive an explicit representation of particle’s matrix Green’s function. For illustration purposes, two particular systems are studied in detail: (1) a particle bound in a field of a single zero-range potential, (2) a particle bound in a field of two identical zero-range potentials.

Harmony: A Generic Unsupervised Approach for Disentangling Semantic Content from Parameterized Transformations.

In many real-life image analysis applications, particularly in biomedical research domains, the objects of interest undergo multiple transformations that alters their visual properties while keeping the semantic content unchanged. Disentangling images into semantic content factors and transformations can provide significant benefits into many domain-specific image analysis tasks. To this end, we propose a generic unsupervised framework, Harmony, that simultaneously and explicitly disentangles semantic content from multiple parameterized transformations. Harmony leverages a simple cross-contrastive learning framework with multiple explicitly parameterized latent representations to disentangle content from transformations. To demonstrate the efficacy of Harmony, we apply it to disentangle image semantic content from several parameterized transformations (rotation, translation, scaling, and contrast). Harmony achieves significantly improved disentanglement over the baseline models on several image datasets of diverse domains. With such disentanglement, Harmony is demonstrated to incentivize bioimage analysis research by modeling structural heterogeneity of macromolecules from cryo-ET images and learning transformation-invariant representations of protein particles from single-particle cryo-EM images. Harmony also performs very well in disentangling content from 3D transformations and can perform coarse and fast alignment of 3D cryo-ET subtomograms. Therefore, Harmony is generalizable to many other imaging domains and can potentially be extended to domains beyond imaging as well.

Compressed-Encoding Particle Swarm Optimization with Fuzzy Learning for Large-Scale Feature Selection

Particle swarm optimization (PSO) is a promising method for feature selection. When using PSO to solve the feature selection problem, the probability of each feature being selected and not being selected is the same in the beginning and is optimized during the evolutionary process. That is, the feature selection probability is optimized from symmetry (i.e., 50% vs. 50%) to asymmetry (i.e., some are selected with a higher probability, and some with a lower probability) to help particles obtain the optimal feature subset. However, when dealing with large-scale features, PSO still faces the challenges of a poor search performance and a long running time. In addition, a suitable representation for particles to deal with the discrete binary optimization problem of feature selection is still in great need. This paper proposes a compressed-encoding PSO with fuzzy learning (CEPSO-FL) for the large-scale feature selection problem. It uses the N-base encoding method for the representation of particles and designs a particle update mechanism based on the Hamming distance and a fuzzy learning strategy, which can be performed in the discrete space. It also proposes a local search strategy to dynamically skip some dimensions when updating particles, thus reducing the search space and reducing the running time. The experimental results show that CEPSO-FL performs well for large-scale feature selection problems. The solutions obtained by CEPSO-FL contain small feature subsets and have an excellent performance in classification problems.

Flowability of Crumbler Rotary Shear Size-Reduced Granular Biomass: An Experiment-Informed Modeling Study on the Angle of Repose

Biomass has potential as a carbon-neutral alternative to petroleum for chemical and energy products. However, complete replacement of fossil fuel is contingent upon efficient processes to eliminate undesirable characteristics of biomass, e.g., low bulk density, variability, and storage-induced quality problems. Mechanical size reduction via comminution is a processing operation to engineer favorable biomass flowability in handling. Crumbler rotary shear mill has been empirically demonstrated to produce more uniformly shaped particles with higher flowability than hammermilled biomass. This study combines modeling and experimentation to unveil fundamental understandings of the relation between granular particle characteristics and biomass flow behavior, which elucidate underlying mechanisms and guide selection of critical processing parameters. For this purpose, the impact of critical material attributes, including particle size (2–6 mm), particle shape (briquette, chip, clumped-sphere, cube, etc.), and surface roughness, on the angle of repose (AOR) of milled pine chips were investigated using discrete element method (DEM) simulations. Forest Concepts Crumbler rotary shear system is used to produce milled pine particles within the same size range considered in DEM simulations. AOR of different sets of these particles were measured experimentally to benchmark DEM results against experimental data. Specific energy consumption for the comminution of biomass with different particle size and moisture content are measured for technoeconomic analysis. Our results show that the smaller size (2 mm) of pine particle achieves better followability (i.e., smaller AOR) while the energy cost of comminution is significantly higher and bulk density is almost the same as the 6-mm pine particles. For the 2-mm particle size, Crumbles from veneer have better flow properties than Crumbles from chips. Contrarily, no significant difference was observed between the AOR of the two materials for the 6-mm particle size. Furthermore, from DEM simulations, mechanical interlocking between particles was found as a dominant factor in determining AOR of complex-shaped particles such as milled pine, which cannot be accurately captured by using simple particle shapes (e.g., mono-sphere) with a rolling resistance model. Conversely, clumped-sphere model alleviates this limitation without increasing computational cost significantly and can be used for accurate representation of biomass granular particles when simulating free-flow behavior.

POSSIBILITIES OF GENERALIZING FIELD THEORY PARADIGM WITHIN THE SCOPE OF THE SKYRME - FADDEEV CHIRAL MODEL

Main points of the Einstein program for creating the consistent field formulation of particle physics are discussed. The basis of this program includes the representation of particles as clots of some material field satisfying nonlinear equations. It is shown how the stability criterion implies the characteristic features of the corresponding field model.