Description Of Particle Motion Research Articles

Application of high order symplectic integration methods with forward integration steps in beam dynamics

The Hamiltonian describing particle motion in an accelerator belongs to a large class of systems, the members of which can be integrated with a new set of high order symplectic integrators. One benefit of these integrators is their strong numerical stability, which results from the inclusion of only forward integration steps, independent of the order of accuracy. Using these integrators, the transfer map of any multipolar accelerator magnet is derived and presented here. From these maps, the Hamiltonian flow in different lattices is simulated and benchmarked against other well established integration schemes in the accelerator community. By comparing quantities such as the linear phase advance and action invariant, the chromaticity, as well as the working point and the tune spread with amplitude, the superiority of the novel symplectic integrators is demonstrated with respect to accuracy and integration cost.

Exact solutions in radiation reaction and the radiation-free direction

We present new exact solutions of the Landau–Lifshitz (LL) and higher-order LL equations describing particle motion, with radiation reaction, in intense electromagnetic fields. Through these solutions and others we compare the phenomenological predictions of different equations in the context of the conjectured ‘radiation-free direction’ (RFD). We confirm analytically in several cases that particle orbits predicted by the LL equation indeed approach the RFD at extreme intensities, and give time-resolved signals of this behaviour in radiation spectra.

Lower‐Stage Plane Bed Topography Is an Outcome of Rarefied, Intermittent Sediment Transport

AbstractSedimentary bed configurations that are stable under weak fluid‐driven transport conditions can be divided into two groups: (1) mesoscale features that influence flow and sediment transport through roughness and drag partitioning effects (“mesoforms”) and (2) grain‐scale features that can effectively be ignored at the macroscopic scale (“microforms”). In practice, these groups delineate ripples and dunes from quasi‐planar bed configurations. They are thought to be separated by a transition in processes governing the relief of the bed; however, the physical mechanisms responsible for this transition are poorly understood. Previous studies suggest that planar topography is unstable when interactions between moving particles lead to stabilized bed disturbances that initiate morphodynamic pattern coarsening. This study presents a kinetic interpretation of this hypothesis in terms of parameters describing particle motion. We find that the microform/mesoform transition corresponds to a critical transition in particle behavior associated with increasing importance of particle collisions. This transition also corresponds to the point where continuum‐based morphodynamic models are permissible at the most unstable wavelength predicted from linear stability theory, providing a link between descriptive and mathematical theories of bedform initiation.

A Primer on Focused Solar Energetic Particle Transport

The basics of focused transport as applied to solar energetic particles are reviewed, paying special attention to areas of common misconception. The micro-physics of charged particles interacting with slab turbulence are investigated to illustrate the concept of pitch-angle scattering, where after the distribution function and focused transport equation are introduced as theoretical tools to describe the transport processes and it is discussed how observable quantities can be calculated from the distribution function. In particular, two approximations, the diffusion-advection and the telegraph equation, are compared in simplified situations to the full solution of the focused transport equation describing particle motion along a magnetic field line. It is shown that these approximations are insufficient to capture the complexity of the physical processes involved. To overcome such limitations, a finite-difference model, which is open for use by the public, is introduced to solve the focused transport equation. The use of the model is briefly discussed and it is shown how the model can be applied to reproduce an observed solar energetic electron event, providing insights into the acceleration and transport processes involved. Past work and literature on the application of these concepts are also reviewed, starting with the most basic models and building up to more complex models.

Local metric with parameterized evolution

AbstractWe present a canonical Hamiltonian formulation of general relativity in which τ, the parameter of system evolution, is external to spacetime, playing a role similar to what we call time in nonrelativistic mechanics. This approach, known as Stueckelberg–Horwitz–Piron (SHP) theory, inherits the full computational power of classical analytical mechanics while maintaining manifest covariance throughout and eliminating possible conflict with general diffeomorphism invariance. In particular, SHP theory simplifies the initial value problem with potential applications in highly dynamical interactions, such as black hole collisions. By allowing the energy–momentum tensor and metric to depend explicitly on τ, we may describe particle motion in geodesic form with respect to a dynamically evolving background metric. As a toy model, we consider a τ‐dependent mass M(τ), first as a perturbation in the Newtonian approximation and then for a Schwarzschild‐like metric. As expected, the extended Einstein equations imply a nonzero energy–momentum tensor, proportional to dM/dτ, representing a flow of mass and energy into spacetime that corresponds to the changing source mass. In τ‐equilibrium, this system becomes a generalized Schwarzschild solution for which the extended Ricci tensor and energy–momentum tensor vanish.

Higher-order moment models for laminar multiphase flows with accurate particle-stream crossing

Modelling of laminar multiphase flow is extremely important in a wide range of engineering and scientific applications. The particle phases are often difficult to model, especially when particles display a range of velocities at each location in space. Lagrangian method can be too costly and many Eulerian methods, though often computationally less taxing, suffer from model deficiencies and mathematical artifacts that lead to non-physical results. In particular, efficient Eulerian models that can accurately predict the crossing of multiple streams of non-interacting particles in laminar flow have traditionally been lacking.The goal of this work is to investigate the predictive capabilities of modern techniques from the kinetic theory of gases to a treatment of disperse multiphase flow. In particular, several moment-methods, including a recently proposed fourteen-moment approximation to the underlying kinetic equation describing particle motion, are applied and their abilities to predict particle-stream crossing are assessed. The derivation, mathematical structure, and physical behaviour of the resulting model are explained. A numerical implementation is presented and results for a flow problem that is designed to demonstrate the fundamental behaviour of each model with respect to particle stream crossing is presented.

Modelling trajectories of solid particle motion in the cyclone

PurposeThis purpose of the paper is to examine the multi-channel cyclone created at the Vilnius Gediminas Technical University (VGTU) Research Institute of Environmental Protection. The paper aims to predict the possible trajectories of solid particle motion in the cyclone with reference to the mechanical forces only.Design/methodology/approachThe numerical calculations were performed on the basis of experimental results. The system of differential equations describing particle motion in the cyclone is analysed and numerically solved using Runge–Kutta–Fehlberg method. Research consists of three examples that illustrate the impact of particle density and velocity on collection and analyses the particle motion trajectories in the first and second channels of the cyclone.FindingsNumerical calculations were performed according to the data from Vilnius Gediminas Technical University Research Institute of Environmental Protection. The particulate matter of wood ash and granite were used. The collection of solid particles of different size was examined when the air inflow velocity varies from 10 to 20 m/s. The possible motion trajectories of the solid particles are defined and the parameters of collected particles have been discussed.Research limitations/implicationsThe obtained results can be used for the analysis of air cleaning efficiency and particulate matter removal from air in a multi-channel cyclone.Practical implicationsThe results lead us to improve the structure of the cyclone so as to effectively collect the solid particles of different size.Originality/valueThis paper presents the results obtained for the multi-channel cyclone created at the Vilnius Gediminas Technical University Research Institute of Environmental Protection.

Numerical Study on the Influence of Operational Settings on Refuse Derived Fuel Co-firing in Cement Rotary Kilns

Cement production in rotary kilns requires large amounts of thermal energy, which is provided by combustion of different fuels. Substitution of fossil fuels by refuse derived fuels (RDF) can minimize production costs and reduce CO2 emissions, but often causes displacement of the sintering zone, impacts flame stability and cement quality. The current paper briefly introduces our numerical approach which describes particle motion and combustion characteristics of typical non-spherical RDF particles. By using these models in CFD simulations, a case study is presented. Fuel properties, primary- and secondary air settings and fuel feed location for a generic rotary kiln of industrial scale are varied to show the effects of operational settings on co-firing of RDF. Shift of flame shape and location as well as particle burnout are analyzed. Based on the information generated, optimized operational settings are identified and discussed.

Magnetomechanics of superparamagnetic beads on a magnetic merry-go-round: from micromagnetics to radial looping

The motion of functionalized superparamagnetic beads provides the foundation for the manipulation of labelled chemical and biological species in microfluidic environments, where patterned ferromagnetic thin films serve as a versatile and reconfigurable platform for biomedical applications. A recurring release and capture of superparamagnetic microbeads is achieved by moving stray magnetic field gradients generated by a circulating micromagnetic state of a soft magnetic disc. The full micromagnetic analysis of the transport dynamics fully describes the fundamental alternating behaviour of microsphere motion. An excellent level of agreement is obtained between experiment and modelling for all stages of motion, confirming the validity of describing particle motion dynamics in the applied quasi ab initio modelling approach. The demonstrated comprehension of the non-linear microbead displacement opens the way towards the modelling of various alternative dynamic excitation schemes, even for complicated integrated micromagnetic platforms, for controlled biological analyte–superparamagnetic bead manipulation.

Trajectory-Diffusive Mechanism of Desilt Basin Operation

Within the framework of the generalized theory of turbulent diffusion, we consider the mean velocities, times, length of alternating transverse up-and-down motion of suspended particles in sediment exhibiting different settling velocities and fluid particles in calm uniform wide open flows. Experimental data obtained by various authors are used to find the maximum heights and lengths of particle saltation in the thin near-bottom region, as well as the magnitude of the dynamic flow velocity, which triggers the motion of particles on the bottom. From the combined trajectory description of particle motion in sediments of different settling velocities over the entire depth of an open flow, the trajectory limit settling velocity of suspended sediments deposited in a rectilinear desilt basin may be determined and, within the framework of relaxation models, the length of silting and erosion at the bottom may be found.

Parallel simulation of particle transport in an advection field applied to volcanic explosive eruptions

Volcanic ash transport and dispersal models typically describe particle motion via a turbulent velocity field. Particles are advected inside this field from the moment they leave the vent of the volcano until they deposit on the ground. Several techniques exist to simulate particles in an advection field such as finite difference Eulerian, Lagrangian-puff or pure Lagrangian techniques. In this paper, we present a new flexible simulation tool called TETRAS (TEphra TRAnsport Simulator) based on a hybrid Eulerian–Lagrangian model. This scheme offers the advantages of being numerically stable with no numerical diffusion and easily parallelizable. It also allows us to output particle atmospheric concentration or ground mass load at any given time. The model is validated using the advection–diffusion analytical equation. We also obtained a good agreement with field observations of the tephra deposit associated with the 2450 BP Pululagua (Ecuador) and the 1996 Ruapehu (New Zealand) eruptions. As this kind of model can lead to computationally intensive simulations, a parallelization on a distributed memory architecture was developed. A related performance model, taking into account load imbalance, is proposed and its accuracy tested.

Eulerian Model for Prediction of Particle Transport and Deposition in Turbulent Duct Flows with Thermophoresis

The Reynolds-averaged equations for turbulent particle population/transport in an Eulerian framework must be closed by specifying models for several terms: a turbophoretic force; a turbulent thermophoretic force; and a turbulent particle-diffusion term. In this article, new models are proposed for the turbophoretic term, as a particle-size dependent extrapolation of the corresponding turbulent fluid-velocity correlation, and for the turbulent thermophoretic term as an eddy-viscosity-scaled multiple of the corresponding mean thermophoretic term, appropriate for small low-inertia particles with τ+p < 10. When the turbophoresis model is incorporated in a system of equations that describes particle motion within the surrounding fluid, it predicts particle deposition velocities that are in good agreement with experimental data over a range of particle sizes. When this equation system is included in a computational model to predict particle transport in turbulent pipe flows, the efficiency of particle deposition in pipes with upstream heating and downstream cooling is found to be in fair agreement with experimental measurements at two different Reynolds numbers, and over a range of particle sizes and temperature differences.Copyright 2015 American Association for Aerosol Research

Periprosthetic wear particle migration and distribution modelling and the implication for osteolysis in cementless total hip replacement

In total hip replacement (THR), wear particles play a significant role in osteolysis and have been observed in locations as remote as the tip of femoral stem. However, there is no clear understanding of the factors and mechanisms causing, or contributing to particle migration to the periprosthetic tissue. Interfacial gaps provide a route for particle laden joint fluid to transport wear particles to the periprosthetic tissue and cause osteolysis. It is likely that capsular pressure, gap dimensions and micromotion of the gap during cyclic loading of an implant, play defining roles to facilitate particle migration. In order to obtain a better understanding of the above mechanisms and factors, transient two-dimensional computational fluid dynamic simulations have been performed for the flow in the lateral side of a cementless stem-femur system including the joint capsule, a gap in communication with the capsule and the surrounding bone. A discrete phase model to describe particle motion has been employed. Key findings from these simulations include: (1) Particles were shown to enter the periprosthetic tissue along the entire length of the gap but with higher concentrations at both proximal and distal ends of the gap and a maximum rate of particle accumulation in the distal regions. (2) High capsular pressure, rather than gap micromotion, has been shown to be the main driving force for particle migration to periprosthetic tissue. (3) Implant micromotion was shown to pump out rather than draw in particles to the interfacial gaps. (4) Particle concentrations are consistent with known distributions of (i) focal osteolysis at the distal end of the gap and (ii) linear osteolysis along the entire gap length.

Deposition and fine particle production during dynamic flow in a dry powder inhaler: A CFD approach

In this work the dynamic flow as well as the particle motion and deposition in a commercial dry powder inhaler, DPI (i.e., Turbuhaler) is described using computational fluid dynamics, CFD. The dynamic flow model presented here is an extension of a steady flow model previously described in Milenkovic et al. (2013). The model integrates CFD simulations for dynamic flow, an Eulerian-fluid/Lagrangian-particle description of particle motion as well as a particle/wall interaction model providing the sticking efficiency of particles colliding with the DPI walls. The dynamic flow is imposed by a time varying outlet pressure and the particle injections into the DPI are assumed to occur instantaneously and follow a prescribed particle size distribution, PSD. The total particle deposition and the production of fine particles in the DPI are determined for different peak inspiratory flow rates, PIFR, flow increase rates, FIR, and particle injection times. The simulation results for particle deposition are found to agree well with available experimental data for different values of PIFR and FIR. The predicted values of fine particle fraction are in agreement with available experimental results when the mean size of the injected PSD is taken to depend on the PIFR.

Max–min-plus expressions for one-dimensional particle cellular automata obtained from a fundamental diagram

We study one-dimensional neighborhood-five conservative cellular automata (CA), referred to as particle cellular automata five (particle CA5). We show that evolution equations for particle CA5s that belong to certain types can be obtained in the form of max–min-plus expressions from a fundamental diagram. The obtained equations are transformed into other max–min-plus expressions by ultradiscrete Cole–Hopf transformations, which enable us to analyze the asymptotic behaviors of general solutions. The equations in the Lagrange representation, which describe particle motion, are also presented, which can also be obtained from a fundamental diagram. Finally, we discuss the generalization to a one-dimensional conservative neighborhood-n CA, i.e., particle CAn.

Explicit Approximation Solutions and Proof of Convergence of the Space-Time Fractional Advection Dispersion Equations

The space-time fractional advection dispersion equations are linear partial pseudo-differential equations with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. The time fractional order is denoted by β∈ and is devoted to the space fractional order. The time fractional advection dispersion equations describe particle motion with memory in time. Space-fractional advection dispersion equations arise when velocity variations are heavy-tailed and describe particle motion that accounts for variation in the flow field over entire system. In this paper, I focus on finding the precise explicit discrete approximate solutions to these models for some values of with , while the Cauchy case as and the classical case as with are studied separately. I compare the numerical results of these models for different values of and and for some other related changes. The approximate solutions of these models are also discussed as a random walk with or without a memory depending on the value of . Then I prove that the discrete solution in the Fourierlaplace space of theses models converges in distribution to the Fourier-Laplace transform of the corresponding fractional differential equations for all the fractional values of and .

Virtual potentials for feedback traps

The recently developed feedback trap can be used to create arbitrary virtual potentials, to explore the dynamics of small particles or large molecules in complex situations. Experimentally, feedback traps introduce several finite time scales: There is a delay between the measurement of a particle's position and the feedback response, the feedback response is applied for a finite update time, and a finite camera exposure integrates motion. We show how to incorporate such timing effects into the description of particle motion. For the test case of a virtual quadratic potential, we give the first accurate description of particle dynamics, calculating the power spectrum and variance of fluctuations as a function of feedback gain, testing against simulations. We show that for small feedback gains, the motion approximates that of a particle in an ordinary harmonic potential. Moreover, if the potential is varied in time, for example by varying its stiffness, the work that is calculated approximates that done in an ordinary changing potential. The quality of the approximation is set by the ratio of the update time of the feedback loop to the relaxation time of motion in the virtual potential.

Mechanism of Particle Collection in a Cylindrical Cyclone Separator (1st Report, Validation of Large Eddy Simulation and Investigation on Detailed Flow Structures)

A cyclone separator separates particles by using centrifugal force that acts on the particles in a swirl flow and the separated particles finally fall to the bottom part of the separator by the gravity force. For a gas cyclone separator, the Reynolds number of the bulk flow is typically in the order of 104 to 105, and complicated vortical structures are generated. The particle behaviors in such vortical flows have not yet been fully understood. The final goal of the present study is to clarify the mechanism of particle separation in a cyclone separator and to improve the separation efficiency. To achieve this goal, the unsteady flow in cyclone separators is firstly computed by large-eddy simulation. The computed flow velocities will then be fed to the subsequent analysis of particle tracking. This first report describes results of validations for the large-eddy simulation, where we compared the computed velocity profiles with the experimental data. We also compared the precession frequency of the vortex rope with that reported in the literature. Regarding the vortical structures in the cyclone separator, we identified longitudinal vortices which are generated in the periphery of the large vortex rope. These vortices have one end attached to the inner wall and their strength is stronger than the longitudinal vortices in the boundary layer on the wall. The identified vortices are most likely to play an important role in the particle separation, which will be proven in the second report that describes particle motion in the cyclone separator.

General description of electromagnetic radiation processes based on instantaneous charge acceleration in “endpoints”

We present a methodology for calculating the electromagnetic radiation from accelerated charged particles. Our formulation-the "endpoint formulation"-combines numerous results developed in the literature in relation to radiation arising from particle acceleration using a complete, and completely general, treatment. We do this by describing particle motion via a series of discrete, instantaneous acceleration events, or "endpoints," with each such event being treated as a source of emission. This method implicitly allows for particle creation and destruction, and is suited to direct numerical implementation in either the time or frequency domains. In this paper we demonstrate the complete generality of our method for calculating the radiated field from charged particle acceleration, and show how it reduces to the classical named radiation processes such as synchrotron, Tamm's description of Vavilov-Cherenkov, and transition radiation under appropriate limits. Using this formulation, we are immediately able to answer outstanding questions regarding the phenomenology of radio emission from ultra-high-energy particle interactions in both the earth's atmosphere and the moon. In particular, our formulation makes it apparent that the dominant emission component of the Askaryan effect (coherent radio-wave radiation from high-energy particle cascades in dense media) comes from coherent "bremsstrahlung" from particle acceleration, rather than coherent Vavilov-Cherenkov radiation.

Development of the quantum theory of T-odd asymmetries for prescission and evaporated third particles in ternary nuclear fission induced by cold polarized neutrons

A comparative analysis of the results obtained by experimentally and theoretically studying T-odd asymmetries for various third particles in the true and delayed ternary nuclear fission induced by cold polarized neutrons was performed. It was confirmed that the appearance of these asymmetries was associated with the effect of rotation of a polarized system undergoing fission on the angular distributions of prescission and evaporated third particles with respect to the direction along which the emerging fission fragments flew apart, this effect being determined by the Coriolis interaction of the rotational and the internalmotion of the fissioning system. A quantum-mechanical description of particle motion in a rotating coordinate system was generalized to the case where gamma-ray emission was present. It was shown that the separation of the motions of an axially symmetric fissile system into a rotational and an internal motion was valid in the external region as well, where ternary-fission products had already been formed, if it was considered that the motion of fission fragments was tightly connected with the system symmetry axis, which rotated in the laboratory frame. It was found that the dependence of the fissile-system moment of inertia appearing in the Coriolis interaction Hamiltonian on the distance between the fission fragments flying apart generated an additional phase in the amplitude of the radial distribution of fission fragments. It was shown that this phase might change sizably the contribution of the interference between fission amplitudes of neutron resonances excited in a fissile compound nucleus to the absolute values of T -odd asymmetries, especially for third particles such as neutrons and photons, which interacted only slightly with fission fragments.