Initial Position Of Particle Research Articles

Deposition of particles in the supersonic flow past a wedge

In our previous research, we find three particle motion patterns when submicron particles enter a supersonic laminar boundary layer over a flat plate. In these three patterns the deposition pattern is the most intriguing one because it is the lateral lift force directed to the wall that results in the particle deposition, hence the lateral deposition. In this paper, we investigate the particle motion in the supersonic flow past a wedge instead of a flat plate. The inertial deposition mechanism is introduced when the wedge replaces the flat plate. The inertial deposition is essential for the whole deposition process. Therefore, we build a two dimensional Eulerian Lagrangian numerical model to investigate this process. Several factors including particle initial position, wedge angle, initial Mach number and particle size are studied. It turns out that the higher particle has a more important lateral deposition mechanism, and as the wedge angle, initial Mach number or particle size increase, the importance of inertial deposition increases. Finally, as the three particle motion still exists in the wedge cases, we also propose a non-dimensional number to describe these patterns.

Transport of a partially wetted particle at the liquid/vapor interface under the influence of an externally imposed surfactant generated Marangoni stress

Marangoni flows offer an interesting and useful means to transport particles at fluid interfaces with potential applications such as dry powder pulmonary drug delivery. In this article, we investigate the transport of partially wetted particles at a liquid/vapor interface under the influence of Marangoni flows driven by gradients in the surface excess concentration of surfactants. We deposit a microliter drop of soluble (sodium dodecyl sulfate) aqueous surfactant solution or pure insoluble liquid (oleic acid) surfactant on a water subphase and observe the transport of a pre-deposited particle. Following the previous observation by Wang et al. [1] that a surfactant front rapidly advances ahead of the deposited drop contact line and initiates particle motion but then moves beyond the particle, we now characterize the two dominant, time- and position-dependent forces acting on the moving particle: (1) a surface tension force acting on the three-phase contact line around the particle periphery due to the surface tension gradient at the liquid/vapor interface which always accelerates the particle and (2) a viscous force acting on the immersed surface area of the particle which accelerates or decelerates the particle depending on the difference in the velocities of the liquid and particle. We find that the particle velocity evolves over time in two regimes. In the acceleration regime, the net force on the particle acts in the direction of particle motion, and the particle quickly accelerates and reaches a maximum velocity. In the deceleration regime, the net force on the particle reverses and the particle decelerates gradually and stops. We identify the parameters that affect the two forces acting on the particle, including the initial particle position relative to the surfactant drop, particle diameter, particle wettability, subphase thickness, and surfactant solubility. We systematically vary these parameters and probe the spatial and temporal evolution of the two forces acting on the particle as it moves along its trajectory in both regimes. We find that a larger particle always lags behind the smaller particle when placed at an equal initial distance from the drop. Similarly, particles more deeply engulfed in the subphase lag behind those less deeply engulfed. Further, the extent of particle transport is reduced as the subphase thickness decreases due to the larger velocity gradients in the subphase recirculation flows.

Spatial Variability of Hydrodynamic Timescales in a Broad and Shallow Estuary: Mobile Bay, Alabama

ABSTRACT Webb, B.M. and Marr, C., 2016. Spatial variability of hydrodynamic timescales in a broad and shallow estuary: Mobile Bay, Alabama. Residence, exposure, and flushing times are examples of hydrodynamic timescales that describe the physical mass transport within a water body. The response and spatial variability of these measures to tides and discharge were investigated through hydrodynamic model simulations of Mobile Bay, Alabama using a two-dimensional depth-integrated circulation model coupled with a Lagrangian particle tracking model. Hydrodynamic timescales were estimated and analyzed using the particle tracking results. Flushing of the estuary was found to transition from tidally enhanced to river dominated for Q > 1715 m3 s−1. A simple power law regression was found to accurately represent the spatially averaged timescales (R2 > 0.99) for tidal and river forcing. Spatially averaged timescales generally ranged from 4 to 130 days, with large deviations related to particle initial position, magn...

Computational analysis of the selective capture of binary mixtures of particles by a bubble in quiescent and fluid flow

This paper presents a computer simulation analysis of the selective capture of binary particle mixtures by a central bubble, as influenced by the relative strength of the hydrophobic interaction assigned to each type of particle. The analysis was carried out for a quiescent fluid using two different configurations of initial particle positions, namely: spherical (particles released from within a spherical shell surrounding the bubble) and top (particles released from a horizontal plane located above the bubble) distributions. The top distribution was also used to study the effect of fluid velocity (<0.05m/s). The results show that in the case of a quiescent fluid the collection efficiency was greater for the top distribution than for the spherical one. In addition, when the strength of the hydrophobic force was less than the net particle weight, particles easily detached from the bubble surface. In the presence of fluid flow the collection efficiency followed an exponential decay with the fluid velocity and a quadratic relationship with an effective cross-section for the particle-bubble collision. The latter closely follows the collision models in the literature. Importantly, we have shown that selective capture only occurs when one type of particle possesses a hydrophobic force magnitude close to or less than the net particle weight, while the hydrophobic force for the second type needs to be much larger than the net weight of the particle. Therefore, we have concluded that selectivity does not depend solely on the hydrophobicity differences, but also requires that one type of particle has to be weakly interacting with the bubble.

Transport by breaking internal gravity waves on slopes

We use the results of a direct numerical simulation (DNS) with a particle-tracking model to investigate three-dimensional transport by breaking internal gravity waves on slopes. Onshore transport occurs within an upslope surge of dense fluid after breaking. Offshore transport occurs due to an intrusion of mixed fluid that propagates offshore and resembles an intermediate nepheloid layer (INL). Entrainment of particles into the INL is related to irreversible mixing of the density field during wave breaking. Maximum onshore and offshore transport are calculated as a function of initial particle position, and can be of the order of the initial wave length scale for particles initialized within the breaking region. An effective cross-shore dispersion coefficient is also calculated, and is roughly three orders of magnitude larger than the molecular diffusivity within the breaking region. Particles are transported laterally due to turbulence that develops during wave breaking, and this lateral spreading is quantified with a lateral turbulent diffusivity. Lateral turbulent diffusivity values calculated using particles are elevated by more than one order of magnitude above the molecular diffusivity, and are shown to agree well with turbulent diffusivities estimated using a generic length scale turbulence closure model. Based on a favourable comparison of DNS results with those of a similar two-dimensional case, we use two-dimensional simulations to extend our cross-shore transport results to additional wave amplitude and bathymetric slope conditions.

Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system

The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ?pitchfork? type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, are known. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are created based on the general theorems of dynamics of a variable mass mechanical system [5]. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal control by applying Pontryagin?s maximum principle [1]. A corresponding two-point boundary value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained, which, in a general case, has to be numerically solved [2]. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are determined. The analysis of the brachistochronic motion for different values of the initial position of a variable mass particle B is presented. Also, the interval of values of the initial position of a variable mass particle B, for which there are the TPBVP solutions, is determined.

C/O AND SNOWLINE LOCATIONS IN PROTOPLANETARY DISKS: THE EFFECT OF RADIAL DRIFT AND VISCOUS GAS ACCRETION

The C/O ratio is a defining feature of both gas giant atmospheric and protoplanetary disk chemistry. In disks, the C/O ratio is regulated by the presence of snowlines of major volatiles at different distances from the central star. We explore the effect of radial drift of solids and viscous gas accretion onto the central star on the snowline locations of the main C and O carriers in a protoplanetary disk, H2O, CO2 and CO, and their consequences for the C/O ratio in gas and dust throughout the disk. We determine the snowline locations for a range of fixed initial particle sizes and disk types. For our fiducial disk model, we find that grains with sizes ~0.5 cm < s < 7 m for an irradiated disk, and ~0.001 cm < s < 7 m for an evolving and viscous disk, desorb at a size-dependent location in the disk, which is independent of the particle's initial position. The snowline radius decreases for larger particles, up to sizes of ~7 m. Compared to a static disk, we find that radial drift and gas accretion in a viscous disk move the H2O snowline inwards by up to 40%, the CO2 snowline by up to 60%, and the CO snowline by up to 50%. We thus determine an inner limit on the snowline locations when radial drift and gas accretion are accounted for.

On asymptotic behavior of work distributions for driven Brownian motion

We propose a simple conjecture for the functional form of the asymptotic behavior of work distributions for driven overdamped Brownian motion of a particle in confining potentials. This conjecture is motivated by the fact that these functional forms are independent of the velocity of the driving for all potentials and protocols, where explicit analytical solutions for the work distributions have been derived in the literature. To test the conjecture, we use Brownian dynamics simulations and a recent theory developed by Engel and Nickelsen (EN theory), which is based on the contraction principle of large deviation theory. Our tests suggest that the conjecture is valid for potentials with a confinement equal to or weaker than the parabolic one, both for equilibrium and for nonequilibrium distributions of the initial particle position. In addition we obtain a new analytical solution for the asymptotic behavior of the work distribution for the V-potential by application of the EN theory, and we extend this theory to nonequilibrated initial particle positions.

Calculations of the integral invariant coordinates &amp;lt;I&amp;gt;I&amp;lt;/I&amp;gt; and &amp;lt;I&amp;gt;L&amp;lt;/I&amp;gt;* in the magnetosphere and mapping of the regions where &amp;lt;I&amp;gt;I&amp;lt;/I&amp;gt; is conserved, using a particle tracer (ptr3D v2.0), LANL*, SPENVIS, and IRBEM

Abstract. The integral invariant coordinate I and Roederer's L or L* are proxies for the second and third adiabatic invariants, respectively, that characterize charged particle motion in a magnetic field. Their usefulness lies in the fact that they are expressed in more instructive ways than their counterparts: I is equivalent to the path length of the particle motion between two mirror points, whereas L*, although dimensionless, is equivalent to the distance from the center of the Earth to the equatorial point of a given field line, in units of Earth radii, in the simplified case of a dipole magnetic field. However, care should be taken when calculating the above invariants, as the assumption of their conservation is not valid everywhere in the Earth's magnetosphere. This is not clearly stated in state-of-the-art models that are widely used for the calculation of these invariants. The purpose of this work is thus to investigate where in the near-Earth magnetosphere we can safely calculate I and L* with tools with widespread use in the field of space physics, for various magnetospheric conditions and particle initial conditions. More particularly, in this paper we compare the values of I and L* as calculated using LANL*, an artificial neural network developed at the Los Alamos National Laboratory, SPENVIS, a space environment online tool, IRBEM, a software library dedicated to radiation belt modeling, and ptr3D, a 3-D particle tracing code that was developed for this study. We then attempt to quantify the variations between the calculations of I and L* of those models. The deviation between the results given by the models depends on particle initial position, pitch angle and magnetospheric conditions. Using the ptr3D v2.0 particle tracer we map the areas in the Earth's magnetosphere where I and L* can be assumed to be conserved by monitoring the constancy of I for energetic protons propagating forwards and backwards in time. These areas are found to be centered on the noon area, and their size also depends on particle initial position, pitch angle and magnetospheric conditions.

A new data classification method based on chaotic particle swarm optimization and least square-support vector machine

In order to improve the classification accuracy in chemometrics data, chaotic optimization algorithm (COA) and particle swarm optimization (PSO) algorithm are introduced into least square-support vector machine (LS-SVM) model in order to propose an optimized LS-SVM model and a novel data classification (CPL-SVM) method in this paper. In the proposed CPL-SVM method, the COA with the randomness and ergodicity is used to chaotically process the initial position and local extreme position of particle in the PSO algorithm in order to obtain a chaotic particle swarm optimization (CPSO) algorithm, and the CPSO is used to select and optimize the important parameters of LS-SVM, then the optimized parameters are used to obtain a better CPL-SVM classification method. The choice randomness of parameters is avoided and the selection workload of parameters is reduced. And this method can not only overcome the time-consuming and blindness of cross validation method, but also reflect small sample learning ability. In order to verify the effectiveness of CPL-SVM method, binary classification data, IRIS flower data and three relevant data sets with pharmacodynamic properties of drug are selected in this paper. The experiment results show that the proposed CPL-SVM method takes on the better learning performance, strong generalization ability, best sensitivity, Matthews correlation coefficient and classification accuracy. And it can effectively avoid the isolated effects of sample in the learning process.

Lubrication analysis of interacting rigid cylindrical particles in confined shear flow

Lubrication analysis is used to determine analytical expressions for the elements of the resistance matrix describing the interaction of two rigid cylindrical particles in two-dimensional shear flow in a symmetrically confined channel geometry. The developed model is valid for non-Brownian particles in a low-Reynolds-number flow between two sliding plates with thin gaps between the two particles and also between the particles and the walls. Using this analytical model, a comprehensive overview of the dynamics of interacting cylindrical particles in shear flow is presented. With only hydrodynamic interactions, rigid particles undergo a reversible interaction with no cross-streamline migration, irrespective of the confinement value. However, the interaction time of the particle pair substantially increases with confinement, and at the same time, the minimum distance between the particle surfaces during the interaction substantially decreases with confinement. By combining our purely hydrodynamic model with a simple on/off non-hydrodynamic attractive particle interaction force, the effects of confinement on particle aggregation are qualitatively mapped out in an aggregation diagram. The latter shows that the range of initial relative particle positions for which aggregation occurs is increased substantially due to geometrical confinement. The interacting particle pair exhibits tangential and normal lubrication forces on the sliding plates, which will contribute to the rheology of confined suspensions in shear flow. Due to the combined effects of the confining walls and the particle interaction, the particle velocities and resulting forces both tangential and perpendicular to the walls exhibit a non-monotonic evolution as a function of the orientation angle of the particle pair. However, by incorporating appropriate scalings of the forces, velocities, and doublet orientation angle with the minimum free fraction of the gap height and the plate speed, master curves for the forces versus orientation angle can be constructed.

Numerical resolution of Euler equations through semi-discrete optimal transport

Geodesics along the group of volume preserving diffeomorphisms are solutions to Euler equations of inviscid incompressible fluids, as observed by Arnold. On the other hand, the projection onto volume preserving maps amounts to an optimal transport problem, as follows from the generalized polar decomposition of Brenier. We present, in the first section, the framework of semi-discrete optimal transport, initially developed for the study of generalized solutions to optimal transport and now regarded as an efficient approach to computational optimal transport. In a second and largely independent section, we present numerical approaches for Euler equations seen as a boundary value problem: knowing the initial and final positions of some fluid particles, reconstruct intermediate fluid states. Depending on the data, we either recover a classical solution to Euler equations, or a generalized flow for which the fluid particles motion is non-deterministic. See Minimal Geodesics along Volume Preserving Maps, through Semi-Discrete Optimal Transport, Merigot and Mirebeau 2015, for the proofs of the results presented in these proceedings.

EUNHA: A NEW COSMOLOGICAL HYDRODYNAMIC SIMULATION CODE

We develop a parallel cosmological hydrodynamic simulation code designed for the study of formation and evolution of cosmological structures. The gravitational force is calculated using the TreePM method and the hydrodynamics is implemented based on the smoothed particle hydrodynamics. The initial displacement and velocity of simulation particles are calculated according to second-order Lagrangian perturbation theory using the power spectra of dark matter and baryonic matter. The initial background temperature is given by Recfast and the temperature fluctuations at the initial particle position are assigned according to the adiabatic model. We use a time-limiter scheme over the individual time steps to capture shock-fronts and to ease the time-step tension between the shock and preshock particles. We also include the astrophysical gas processes of radiative heating/cooling, star formation, metal enrichment, and supernova feedback. We test the code in several standard cases such as one-dimensional Riemann problems, Kelvin-Helmholtz, and Sedov blast wave instability. Star formation on the galactic disk is investigated to check whether the Schmidt-Kennicutt relation is properly recovered. We also study global star formation history at different simulation resolutions and compare them with observations.

Bohmian trajectories of Airy packets

The discovery of Berry and Balazs in 1979 that the free-particle Schrödinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schrödinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the corresponding Bohmian trajectories. It is shown that by using general space–time transformations, these trajectories can display a unique variety of cases depending upon the initial position of the individual particle in the Airy wave packet. Further, we report here a myriad of nontrivial Bohmian trajectories associated to the Airy wave packet. These new features are worth introducing to the subject’s theoretical folklore in light of the fact that the evolution of a quantum mechanical Airy wave packet governed by the Schrödinger equation is analogous to the propagation of a finite energy Airy beam satisfying the paraxial equation. Numerous experimental configurations of optics and atom physics have shown that the dynamics of Airy beams depends significantly on initial parameters and configurations of the experimental set-up.

Analysis of Soot Particle Movement in Diesel Engine under the Influence of Drag Force

The formation of soot is influenced by the composition of air entrainment and structure of hydrocarbon in the fuel. Soot will then form during combustion in a diesel engine. Some of the soot particles will be released from the engine through the exhaust nozzle and some will stick to the cylinder walls. The soot that sticks to the cylinder wall can affect the lifetime of the lubricant oil. Subsequently this will decrease the durability of the diesel engine. By understanding the movement of the soot particles, the effect to the engine can be decreased. Therefore, the initial position and last position of soot particle was recognized through this study. The data for the formation of soot particles in the diesel engine was obtained from previous investigation. The study of soot movement at 8° crankshaft angle under the influence of drag force with different radial, axial and angular settings were carried out using a MATLAB routine. The results showed that the movement of soot particle will change with different parameter settings. Besides that, comparison of the results of soot particle movement influenced by drag force and without drag force has been carried out. It was observed that drag force caused shorter soot particle movement path and moves them away from the cylinder wall.

A possible mechanism for the formation of tilted disks in intermediate polars

Using 3D gas dynamics, we numerically simulate accretion-disk formation in typical cataclysmic variable intermediate polars with dipolar magnetic fields (B a = 105−5 × 105 G) and misaligned white-dwarf magnetic and rotation axes. Our simulations confirm that a significant misalignment of the axes results in a significant misalignment of the disk to the orbital plane. However, over time, this disk tilt disappears: early in the simulation, the initial particle positions in the rarefied tilted disk are governed solely by the magnetic field of the white dwarf. Due to the increasing disk mass and hence increasing disk gas pressure, the tilted disk eventually becomes decoupled from the magnetic field. The tidal action of the donor leads to a retrograde (i.e., nodal) precession of the tilted disk’s streamlines, and the disk becomes twisted. When the disk tilt is greater than 4°, the incoming gas stream no longer strikes the disk rim (i.e., bright shocked region). Matter is now transported over and under the disk rim to the inner regions of the disk. Over time, the increased mass of inner parts of the disk due to the action of the colinear gas stream returns the inner-disk regions to a colinear configuration. Meanwhile, the outer regions of the tilted, twisted disk become warped. Our simulations suggest that the lifetime of an intermediate polar’s tilted disk could be several tens to thousands of orbital periods.

Fully-resolved DNS study of rotation behaviors of one and two particles settling near a vertical wall

Abstract An immersed boundary technique with multi-direct forcing scheme for fully-resolved direct numerical simulations of multiphase flows is applied to investigate the rotation behaviors of one and two particles settling near a vertical wall in a Newtonian fluid. Some micro phenomena, such as ‘anomalous rotation’, ‘rotation shift’ and ‘zig-zag’ migration are observed for one particle sedimentation, depending on the initial particle position and the mean terminal settling Reynolds number. The ‘anomalous rotation’ is related to the wall effect, and the ‘rotation shift’ as well as the ‘zig-zag’ migration is closely associated with the vortex shedding. For the cases of two particles settling near a vertical wall side by side, the outside particle always rotates anomalously except when vortex sheds from the particle and the ‘rotation shift’ occurs. But the inside particle may rotate normally or anomalously at the early stage of the sedimentation, depending on the ratio of the initial distance between the two particles to the initial distance between this particle and the wall. For the heavier particle, alternate vortex shedding eventually happens, leading to the ‘rotation shift’. Even for the lighter particle without vortex shedding, ‘rotation shift’ may also appear to the inside particle, which is related to competition between the wall effect and the effect of the outside particle. In addition, it is found that three-dimensionality imposes additional effect on the rotation behaviors of particles.

Dust particles in mean motion resonances influenced by an interstellar gas flow

The orbital evolution of a dust particle captured in a mean motion resonance with a planet in circular orbit under the action of the Poynting-Robertson effect, radial stellar wind and an interstellar gas flow of is investigated. The secular time derivative of Tisserand parameter is analytically derived for arbitrary orbit orientation. From the secular time derivative of Tisserand parameter a general relation between the secular time derivatives of eccentricity and inclination is obtained. In the planar case (the case when the initial dust particle position vector, initial dust particle velocity vector and interstellar gas velocity vector lie in the planet orbital plane) is possible to calculate directly the secular time derivative of eccentricity. Using numerical integration of equation of motion we confirmed our analytical results in the three-dimensional case and also in the planar case. Evolutions of eccentricity of the dust particle captured in an exterior mean motion resonance under the action of the Poynting-Robertson effect, radial stellar wind for the cases with and without the interstellar gas flow are compared. Qualitative properties of the orbital evolution in the planar case are determined. Two main groups of the secular orbital evolutions exist. In the first group the eccentricity and argument of perihelion approach to some values. In the second group the eccentricity oscillates and argument of perihelion rapidly shifts.

Particle lifetime in cylindrical cavity with absorbing spot on the wall: Going beyond the narrow escape problem

The mean lifetime of a particle diffusing in a cylindrical cavity with a circular absorbing spot on the cavity wall is studied analytically as a function of the spot radius, its location on the wall, the particle initial position, and the cavity shape determined by its length and radius. When the spot radius tends to zero our formulas for the mean lifetime reduce to the result given by the solution of the narrow escape problem, according to which the mean lifetime is proportional to the ratio of the cavity volume to the spot radius and is independent of the cavity shape, the spot location on the cavity wall, and the particle starting point, assuming that this point is not too close to the spot. When the spot radius is not small enough, the asymptotic narrow escape formula for the mean lifetime fails, and one should use more general formulas derived in the present study. To check the accuracy and to establish the range of applicability of the formulas, we compare our theoretical predictions with the results of Brownian dynamics simulations.

Noncolliding Brownian motion with drift and time-dependent Stieltjes-Wigert determinantal point process

Using the determinantal formula of Biane, Bougerol, and O’Connell, we give multitime joint probability densities to the noncolliding Brownian motion with drift, where the number of particles is finite. We study a special case such that the initial positions of particles are equidistant with a period a and the values of drift coefficients are well-ordered with a scale σ. We show that, at each time t &amp;gt; 0, the single-time probability density of particle system is exactly transformed to the biorthogonal Stieltjes-Wigert matrix model in the Chern-Simons theory introduced by Dolivet and Tierz. Here, one-parameter extensions (θ-extensions) of the Stieltjes-Wigert polynomials, which are themselves q-extensions of the Hermite polynomials, play an essential role. The two parameters a and σ of the process combined with time t are mapped to the parameters q and θ of the biorthogonal polynomials. By the transformation of normalization factor of our probability density, the partition function of the Chern-Simons matrix model is readily obtained. We study the determinantal structure of the matrix model and prove that, at each time t &amp;gt; 0, the present noncolliding Brownian motion with drift is a determinantal point process, in the sense that any correlation function is given by a determinant governed by a single integral kernel called the correlation kernel. Using the obtained correlation kernel, we study time evolution of the noncolliding Brownian motion with drift.