Particle Representation Research Articles

On Wave Function Representation of Particles as Shock Wave Discontinuities

In quantum theory particles are represented as wave packets. Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contains discontinuities due to a non-zero quantum force. The quantum force causes wave packet dispersion which results in the intersection of characteristic curves developing a shock discontinuity. Since quantum force vanishes for localized quantum density waves [1], it is thus established that localized quantum density waves form the only class of wave function representation of particles in quantum theory without shock wave discontinuities.

As-rigid-as-possible solid simulation with oriented particles

We propose a new as-rigid-as-possible approach to the real-time simulation of physics-based deformable models for interactive applications such as computer games. The key observation is that the efficacy of an embedded oriented particle representation and the stability of a variational implicit formulation of the projective dynamics are complementary to each other. We reformulate the variational implicit formulation to deal with an embedded graph of oriented particles. Our new formulation is extremely stable, and our alternating local/global optimization solver is both easy to implement and computationally efficient. Our method can deal with one-dimensional (cable and rod), two-dimensional (shell), and three-dimensional (solid) models in a uniform manner. Experimental results demonstrate that hundreds of deformable models with an extremely large number of polygons can be simulated robustly in real time using thousands of particles.

Model independent constraints on charges of new particles

Any particle that is charged under $SU(3)_C$ and $U(1)_{EM}$ can mediate the $gg \rightarrow {\gamma}{\gamma}$ process through loops. Near the threshold for the new particle pair production, gauge boson exchanges necessitate the resummation of ladder diagrams. We discuss the leading log order matching of the one-loop result with non-relativistic effective theory resummed result. We show how the diphoton invariant mass spectrum varies depending on decay width, color representation and electric charge of the new particle. The exclusion limits on the product of $SU(3)_C$ and $U(1)_{EM}$ charges of the new scalar or fermion particle are obtained from current LHC data.

Loop effects of heavy new scalars and fermions in b \u2192 s\u03bc+\u03bc\u2212

Recent measurements of b → sμ+μ− processes at LHCb and BELLE have revealed tensions at the 2 − 3σ level between the Standard Model (SM) prediction and the experimental results in the channels B → K*μ+μ− and Bs → ϕμ+μ−, as well as in the lepton-flavor universality violating observable RK = Br(B → Kμ+μ−)/Br(B → Ke+e−). Combined global fits to the available b → sμ+μ− data suggest that these tensions might have their common origin in New Physics (NP) beyond the SM because some NP scenarios turn out to be preferred over the SM by 4 − 5σ. The fact that all these anomalies are related to muons further suggests a connection (and a common NP explanation) with the long-standing anomaly in the anomalous magnetic moment of the muon, aμ. In this article, we study the impact of a generic class of NP models featuring new heavy scalars and fermions that couple to the SM fermions via Yukawa-like interactions. We consider two different scenarios, introducing either one additional fermion and two scalars or two additional fermions and one scalar, and examine all possible representations of the new particles under the SM gauge group with dimension up to the adjoint one. The models induce one-loop contributions to b → sμ+μ− and aμ which are capable of solving the respective anomalies at the 2σ level, albeit a relatively large coupling of the new particles to muons is required. In the case of b → sμ+μ−, stringent constraints from {B}_s-{overline{B}}_s mixing arise which can be relaxed if the new fermion is a Majorana particle.

New mathematical model for the bi-objective inventory routing problem with a step cost function: A multi-objective particle swarm optimization solution approach

• Transportation costs are assumed to behave as a step cost function. • A novel bi-objective mathematical model is proposed to consider this assumption. • Despite this assumption, this type of function is not considered in the IRP. • An efficient multi-objective particle swarm optimization algorithm is presented. • The algorithm's efficiency compared with the augmented ε-constraint method. Inventory management and satisfactory distribution are among the most important issues considered by distribution companies. One of the key objectives is the simultaneous optimization of the inventory costs and distribution expenses, which can be addressed according to the inventory routing problem (IRP). In this study, we present a new transport cost calculation pattern for the IRP based on some real cases. In this pattern, the transportation cost is calculated as a function of the load carried and the distance traveled by the vehicle based on a step cost function. Furthermore, previous methods usually aggregate the inventory and transportation costs to formulate them as a single objective function, but in non-cooperative real-life cases, the inventory-holding costs are paid by retailers whereas the transportation-related costs are paid by the distributor. In this study, we separate these two cost elements and introduce a bi-objective IRP formulation where the first objective is to minimize the inventory-holding cost and the second is minimizing the transportation cost. We also propose an efficient particle representation and employ a multi-objective particle swarm optimization algorithm to generate the non-dominated solutions for the inventory allocation and vehicle routing decisions. Finally, in order to evaluate the performance of the proposed algorithm, the results obtained were compared with those produced using the augmented ε-constraint method, thereby demonstrating the practical utility of the proposed multi-objective model and the proposed solution algorithm.

Spider monkey optimisation assisted particle filter for robust object tracking

Particle filters (PFs) are sequential Monte Carlo methods that use particle representation of state‐space model to implement the recursive Bayesian filter for non‐linear and non‐Gaussian systems. Owing to this property, PFs have been extensively used for object tracking in recent years. Although PFs provide a robust object tracking framework, they suffer from shortcomings. Particle degeneracy and particle impoverishment brought by the resampling step result in abysmal construction of posterior probability density function (PDF) of the state. To overcome these problems, this work amalgamates two characteristics of population‐based heuristic optimisation algorithms: exploration and exploitation with PF implementing dynamic resampling method. The aim of optimisation is to distribute particles in high‐likelihood area according to the cognitive effect and improve quality of particles, while the objective of dynamic resampling is to maintain diversity in the particle set. This work uses very efficient spider monkey optimisation to achieve this. Furthermore, to test the efficiency of the proposed algorithm, experiments were carried out on one‐dimensional state estimation problem, bearing only tracking problem, standard videos and synthesised videos. Metrics obtained show that the proposed algorithm outplays simple PF, particle swarm optimisation based PF, and cuckoo search based PF, and effectively handles different challenges inherent in object tracking.

Maxwellian quantum mechanics

Expanding the ordinary Dirac's equation in quaternionic form yields Maxwell-like field equations. As in the Maxwell's formulation, the particle fields are represented by a scalar, ψ0 and a vector ψ→. The analogy with Maxwell's equations requires that the inertial fields are E→D=c2α→×ψ→, and B→D=α→ψ0+cβψ→ and that ψ0=−cβα→·ψ→, where β, α→ and c are the Dirac matrices and the speed of light, respectively. An alternative solution suggests that magnetic monopole-like behavior accompanies Dirac's field. In this formulation, a field-like representation of Dirac's particle is derived. It is shown that when the vector field of the particle, ψ→, is normal to the vector α→, Dirac's field represents a medium with maximal conductivity. The energy flux (Poynting vector) of the Dirac's fields is found to flow in opposite direction to the particle's motion. A system of equivalently symmetrized Maxwell's equations is introduced. A longitudinal (scalar) wave traveling at speed of light is found to accompany magnetic charges flow. This wave is not affected by presence of electric charges and currents. The Lorentz boost transformations of the matter fields are equivalent to cψ→′=cψ→±βα→ψ0,ψ0′=ψ0∓cβα→·ψ→.

Outlier analysis for a silicon nanoparticle population balance model

We assess the impact of individual experimental observations on a multivariate population balance model for the formation of silicon nanoparticles from the thermal decomposition of silane by means of basic regression influence diagnostics. The nanoparticle model is closely related to one which has been used to simulate soot formation in flames and includes morphological and compositional details which allow representation of primary particles within aggregates, and of coagulation, surface growth, and sintering processes. Predicted particle size distributions are optimised against 19 experiments across ranges of initial temperature, pressure, residence time, and initial silane mass fraction. The influence of each experimental observation on the model parameter estimates is then quantified using the Cook distance and DFBETA measures. Seven model parameters are included in the analysis, with five Arrhenius pre-exponential factors in the gas-phase kinetic rate expressions, and two kinetic rate constants in the population balance model. The analysis highlights certain experimental conditions and kinetic parameters which warrant closer inspection due to large influence, thus providing clues as to which aspects of the model require improvement. We find the insights provided can be useful for future model development and planning of experiments.

Numerical modelling of granular materials with spherical discrete particles and the bounded rolling friction model. Application to railway ballast

The Discrete Element Method (DEM) was found to be an effective numerical method for the calculation of engineering problems involving granular materials. However, the representation of irregular particles using the DEM is a very challenging issue, leading to different geometrical approaches. This document presents a new insight in the application of one of those simplifications known as rolling friction, which avoids excessive rotation when irregular shaped materials are simulated as spheric particles. This new approach, called the Bounded Rolling Friction model, was applied to reproduce a ballast resistance test.

Prospective chemistry teachers’ perceptions of their profession: The state of the art in Slovenia and Finland

The main purpose of this paper is to present Slovenian and Finnish prospective chemistry teachers? perceptions of their future profession, especially with regard to their understanding of the role of the triple nature of chemical concepts (macro, submicro and symbolic) and their representations in chemistry learning. A total of 19 prospective teachers (10 Slovenian, 9 Finnish) at master?s level in chemical education participated in the research. The prospective teachers? opinions were gathered using an electronic questionnaire comprising six open-ended questions. The study revealed many parallels between Slovenian and Finnish prospective chemistry teachers? perceptions of their future profession and their understanding of the role of the triple nature of chemical concepts, especially particle representations, in chemistry learning. The majority of the prospective teachers from both countries believe that personal characteristics are the most important attribute of a successful chemistry teacher. Thus, they highly value teachers? enthusiasm for teaching and the use of contemporary teaching approaches in chemistry. The prospective teachers displayed an adequate understanding of the role of the triple nature of chemical concepts (i.e., particle representations) in the planning and implementation of a specific chemistry lesson.

Matter as a Flow of Random Elementary Events in the Context of Discrete Time

The paper concerns certain consequences of discrete time hypothesis including physical regularities of a particle representation in the form of a flow of elementary events. In the context of the proposed formal description, particle observability has been determined; dependence of observability on a particle energy value has been shown. In terms of the proposed approach, a statistical rationale was given to the relative amount of dark (unobservable) matter.

Form factors and related quantities in clothed-particle representation

We show new applications of the notion of clothed particles in quantum field theory. Its realization by means of the clothing procedure put forward by Greenberg and Schweber allows one to express the total Hamiltonian H and other generators of the Poincare group for a given system of interacting fields through the creation (annihilation) operators for the so-called clothed particles with physical (observed) properties. Here such a clothed particle representation is used to calculate the matrix elements (shortly, form factors) of the corresponding Nother current operators sandwiched between the H eigenstates. Our calculations are performed with help of an iterative technique suggested by us earlier when constructing the NN → πNN transition operators. As an illustration, we outline some application of our approach in the spinor quantum electrodynamics.

Comparison of multi-sphere and superquadric particle representation for modelling shearing and flow characteristics of granular assemblies

In the current study, complex-shaped particles are simulated with the Discrete Element Method (DEM) using two different approaches, namely Multi-spheres (MS) and Superquadrics (SQ). Both methods have been used by researchers to represent the shape of real particles. However, despite the growing popularity of utilizing MS and SQ particles in DEM simulations, few insights have been given on the comparison of the macro scale characteristics arising from the two methods. In this respect, initially the characteristics of the two shape representation methods are evaluated in a direct shear test simulation. The results suggest that controlling the sharpness of the edges for SQ particles can lead to a good agreement with the results of MS particles. This way, a set of SQ and MS particles, which are numerically calibrated in the shear tester, are obtained. Furthermore, the macro-scale responses of the numerically calibrated particles are assessed during a slow shearing scenario, which is achieved through simulating quasi-static flow of the particles from a flat-bottom silo. The results for mass discharge, flow profile and wall pressure show a good quantitative agreement. These findings suggest that the numerically calibrated MS and SQ particles in the shear tester can provide similar bulk-scale flow properties. Moreover, the results highlight that surface bumpiness for MS particles and corner sharpness for SQ particles change the characteristics of particles and play a significant role in the shear strength of the material composed of these particles.

A structure-based model for transport in stably stratified homogeneous turbulent flows

We present an extension that allows a recently proposed structure-based model for turbulent scalar transport to account for buoyancy effects. The proposed model is based on a generalization of the Interactive Particle Representation Model (IPRM) and is accompanied by a four-equation transport model that provides the turbulence scales needed for the closure of the complete structure-based model (SBM). The structure tensors and their invariants are used to model the additional buoyancy terms that emerge in the four-equation transport equations. Model parameters are set by matching the asymptotic decay exponents in decaying turbulence. The validity of the model is considered for a large number of different types of stably stratified flows at different Richardson numbers (Ri), showing encouraging results. The complete structure-based model achieves fair agreement with LES and DNS predictions for vertical shear in the presence of vertical mean stratification, while the structure tensors are shown to be suitable for use as diagnostic tools for the morphology of highly anisotropic turbulent structures. Additionally, the proposed model is shown to be sensitive to the variation of the inclination angle θ between the direction of the mean velocity gradient and the orientation of the mean scalar gradient. Furthermore, the model correctly predicts that the evolution of the inverse shear parameter is insensitive to the choice of inclination angle, yielding a turbulent Prandtl number close to unity, in accordance with DNS results.

Eulerian formulation of the interacting particle representation model of homogeneous turbulence

The original interacting particle representation model (IPRM) is a stochastic Lagrangian model that focuses on turbulent structures to improve prediction of Reynolds stresses. A deterministic Eulerian formulation of the IPRM that increases the rate of statistical convergence is introduced.

Implementation of warm-cloud processes in a source-oriented WRF/Chem model to study the effect of aerosol mixing state on fog formation in the Central Valley of California

Abstract. The source-oriented Weather Research and Forecasting chemistry model (SOWC) was modified to include warm cloud processes and was applied to investigate how aerosol mixing states influence fog formation and optical properties in the atmosphere. SOWC tracks a 6-D chemical variable (X, Z, Y, size bins, source types, species) through an explicit simulation of atmospheric chemistry and physics. A source-oriented cloud condensation nuclei module was implemented into the SOWC model to simulate warm clouds using the modified two-moment Purdue Lin microphysics scheme. The Goddard shortwave and long-wave radiation schemes were modified to interact with source-oriented aerosols and cloud droplets so that aerosol direct and indirect effects could be studied. The enhanced SOWC model was applied to study a fog event that occurred on 17 January 2011, in the Central Valley of California. Tule fog occurred because an atmospheric river effectively advected high moisture into the Central Valley and nighttime drainage flow brought cold air from mountains into the valley. The SOWC model produced reasonable liquid water path, spatial distribution and duration of fog events. The inclusion of aerosol–radiation interaction only slightly modified simulation results since cloud optical thickness dominated the radiation budget in fog events. The source-oriented mixture representation of particles reduced cloud droplet number relative to the internal mixture approach that artificially coats hydrophobic particles with hygroscopic components. The fraction of aerosols activating into cloud condensation nuclei (CCN) at a supersaturation of 0.5 % in the Central Valley decreased from 94 % in the internal mixture model to 80 % in the source-oriented model. This increased surface energy flux by 3–5 W m−2 and surface temperature by as much as 0.25 K in the daytime.

Hydrodynamics in adaptive resolution particle simulations: Multiparticle collision dynamics

A new adaptive resolution technique for particle-based multi-level simulations of fluids is presented. In the approach, the representation of fluid and solvent particles is changed on the fly between an atomistic and a coarse-grained description. The present approach is based on a hybrid coupling of the multiparticle collision dynamics (MPC) method and molecular dynamics (MD), thereby coupling stochastic and deterministic particle-based methods. Hydrodynamics is examined by calculating velocity and current correlation functions for various mixed and coupled systems. We demonstrate that hydrodynamic properties of the mixed fluid are conserved by a suitable coupling of the two particle methods, and that the simulation results agree well with theoretical expectations.

Can fractional quantum Hall effect be due to the formation of coherent wave structures in a 2D electron gas?

A microscopic theory of integer and fractional quantum Hall effects is presented here. In quantum density wave representation of charged particles, it is shown that, in a two-dimensional electron gas coherent structures form under the low temperature and high density conditions. With a sufficiently high applied magnetic field, the combined [Formula: see text] particle quantum density wave exhibits collective periodic oscillations. As a result the corresponding quantum Hall voltage function shows a step-wise change in multiples of the ratio [Formula: see text]. At lower temperatures further subdivisions emerge in the Hall resistance, exhibiting the fractional quantum Hall effect.

Derivative interactions and perturbative UV contributions in N Higgs doublet models

We study the Higgs derivative interactions on models including arbitrary number of the Higgs doublets. These interactions are generated by two ways. One is higher order corrections of composite Higgs models, and the other is integrating out heavy scalars and vectors. In the latter case, three point couplings between the Higgs doublets and them are the sources of the derivative interactions. The representations of these heavy particles are constrained to couple with the doublets. We explicitly calculate the all derivative interactions generated by integrating out. Their degrees of freedom and conditions to impose the custodial symmetry are discussed. We also study the vector boson scattering processes with a couple of two Higgs doublet models to see experimental signals of the derivative interactions. They are differently affected by each heavy field.

Ion cell performance using single particle representation of battery electrode

The aim of study is to predict the performance of lithium-ion cells using the single particle representation of battery electrode model. The model is developed starting from the concentration solution theory and porous-electrode formulation, with Fick's law governing the diffusion of ions in the solid electrode. Since the solution of the governing equations is difficult due to their non-linear nature, simplifying assumptions are made that considerably reduce the computational time needed to predict cell performance. The model is then used to determine the concentration of lithium in solid phase and the electrode potential, assuming that the lithium concentration remains fixed in electrolyte. Further this model is compared with the pseudo two-dimensional model to simulate cyclic performance of lithium-ion cells under various operating conditions.