Spatial Density Of Particles Research Articles

Experimental development of packing structures in a gas-particle trickle flow heat exchanger for application in concentrating solar tower systems

Ceramic particles represent a viable alternative as heat transfer and storage medium in concentrating solar tower systems. The particles are heated in solar-receivers close to 1000 °C. To utilize the stored energy in the particles, an air-particle direct-contact trickle-flow heat exchanger has been identified as suitable for this task. To date, no design recommendations exist that identify an optimized packing structure capable of providing a high particle volume fraction and a uniform spatial particle density distribution for a given grain type. Consequently, an experimental selection process is presented in this work to assess various packing structures for a given grain type in a trickle-flow reactor. The experiments were conducted with countercurrent flowing air at ambient conditions and 1 mm bauxite particles. A variety of packing structures were investigated at varying media flow rates. For each flow condition, the particle volume fraction was determined, as well as the particle distribution in a separate analysis. The cold experiments yielded a clear image of a preferred packing geometry, which will be discussed in detail. The results will serve as the basis for further hot experiments and thermal performance analysis in future work, where the packing geometry can be refined iteratively if necessary.

Polarized microwave emission from space particles in the upper atmosphere of the Earth

ABSTRACT Tons of space particles enter the Earth atmosphere every year, being detected when they produce fireballs, meteor showers, or when they impact the Earth surface. Particle detection in the showers could also be attempted from space using satellites in low Earth orbit. Measuring the polarization would provide extra crucial information on the dominant alignment mechanisms and the properties of the meteor families. In this article, we evaluate the expected signal to aid in the design of space probes for this purpose. We have used the radmc-3d code to simulate the polarized microwave emission of aligned dust particles with different compositions: silicates, carbonates, and irons. We have assumed a constant spatial particle density distribution of 0.22 cm−3, based on particle density measurements carried during meteor showers. Four different grain size distributions with power indices ranging from −3.5 to −2.0 and dust particles with radius ranging from 0.01 $\mathrm{\mu }$m to 1 cm have been considered for the simulations. Silicates and carbonates align their minor axis with the direction of the solar radiation field; during the flight time into the Earth atmosphere, iron grains get oriented with the Earth’s magnetic field depending on their size. Alignment direction is reflected in the Q-Stokes parameter and in the polarization variation along the orbit. Polarization depends on the composition and on the size distribution of the particles. The simulations show that some specific particle populations might be detectable even with a small probe equipped with high-sensitivity, photon-counting microwave detectors operating in low Earth orbit.

Hydrodynamics for One-Dimensional ASEP in Contact with a Class of Reservoirs

We study the hydrodynamic behaviour of the asymmetric simple exclusion process on the lattice of size n. In the bulk, the exclusion dynamics performs rightward flux. At the boundaries, the dynamics is attached to reservoirs. We investigate two types of reservoirs: (1) the reservoirs that are weakened by $$n^\theta $$ for some $$\theta <0$$ and (2) the reservoirs that create particles only at the right boundary and annihilate particles only at the left boundary. We prove that the spatial density of particles, under the hyperbolic time scale, evolves with the entropy solution to a scalar conservation law on [0, 1] with boundary conditions. The boundary conditions are characterised by the boundary traces [3, 17, 20] at $$x=0$$ and $$x=1$$ which take values from $$\{0,1\}$$ .

The effect of spacetime curvature on statistical distributions

The Boltzmann distribution of an ideal gas is determined by the Hamiltonian function generating single particle dynamics. Systems with higher complexity often exhibit topological constraints, which are independent of the Hamiltonian and may affect the shape of the distribution function as well. Here, we study a further source of heterogeneity, the curvature of spacetime arising from the general theory of relativity. The present construction relies on three assumptions: first, the statistical ensemble is made of particles obeying geodesic equations, which define the phase space of the system. Next, the metric coefficients are time-symmetric, implying that, if thermodynamic equilibrium is achieved, all physical observables are independent of coordinate time. Finally, ergodicity is enforced with respect to proper time, so that ambiguity in the choice of a time variable for the statistical ensemble is removed. Under these hypothesis, we derive the distribution function of thermodynamic equilibrium, and verify that it reduces to the Boltzmann distribution in the non-relativistic limit. We further show that spacetime curvature affects physical observables, even far from the source of the metric. Two examples are analyzed: an ideal gas in Schwarzschild spacetime and a charged gas in Kerr–Newman spacetime. In the Schwarzschild case, conservation of macroscopic constraints, such as angular momentum, combined with relativistic distortion of the distribution function can produce configurations with decreasing density and growing azimuthal rotation velocity far from the event horizon of the central mass. In the Kerr–Newman case, it is found that kinetic energy associated with azimuthal rotations is an increasing function of the radial coordinate, and it eventually approaches a constant value corresponding to non-relativistic equipartition, even though spatial particle density decreases.

Understanding droplet collisions through a model flow: Insights from a Burgers vortex.

We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significantly enhances sharp inhomogeneities in spatial particle densities, related to the rapid ejection of particles from intense vortices. Furthermore our work shows how such spatial clustering leads to an enhancement of collision rates and extreme statistics of collisional velocities. We also study the role of polydisperse suspensions in this enhancement. Our work uncovers an important principle, which, if valid for realistic turbulent flows, may be a factor in how small nuclei water droplets in warm clouds can aggregate to sizes large enough to trigger rain.

Feedback control for shaping density distributions of colloidal particles in microfluidic devices.

Directed self-assembly has great potential for the precise manufacture of structured materials at the micro/nano-scale. A local particle density often has to be controlled to make the assembly of complicated structures with no defects attainable. However, the control of spatial particle density distributions is challenged by the need for multiple actuators, kinetic trapping and the stochastic nature of self-assembly systems. In this paper, a novel feedback control approach for shaping spatial density distributions of colloidal particles is presented. The control objective is to maintain the ratio of the particle densities of two adjacent regions close to a desired value. A microfluidic device with a triple-parallel microelectrode is fabricated to provide multiple actuators for particle manipulation. The multiple-electrode actuators can be operated flexibly to either direct particles between two adjacent regions or to maintain particles within regions by preventing undesired particle movements. A feedback control scheme is implemented to control the density ratio over a broad range of tested set points. The method is generic and can be extended to include additional parallel electrodes for the control of density distributions at higher resolutions due to a modular design.

Exclusion Process with Slow Boundary

We study the hydrodynamic and the hydrostatic behavior of the Simple Symmetric Exclusion Process with \emph{slow boundary}. The term \emph{slow boundary} means that particles can be born or die at the boundary sites, at a rate proportional to $N^{-\theta}$, where $\theta > 0$ and $N$ is the scaling parameter. In the bulk, the particles exchange rate is equal to $1$. In the hydrostatic scenario, we obtain three different linear profiles, depending on the value of the parameter $\theta$; in the hydrodynamic scenario, we obtain that the time evolution of the spatial density of particles, in the diffusive scaling, is given by the weak solution of the heat equation, with boundary conditions that depend on $ \theta $. If $\theta \in(0,1)$, we get Dirichlet boundary conditions, (which is the same behavior if $\theta=0$, see \cite{f}); if $\theta=1$, we get Robin boundary conditions; and, if $\theta\in(1,\infty)$, we get Neumann boundary conditions.

A Quasispecies Continuous Contact Model in a Critical Regime

We study a new non-equilibrium dynamical model: a marked continuous contact model in $d$-dimensional space ($d \ge 3$). We prove that for certain values of rates (the critical regime) this system has the one-parameter family of invariant measures labelled by the spatial density of particles. Then we prove that the process starting from the marked Poisson measure converges to one of these invariant measures. In contrast with the continuous contact model studied earlier in \cite{KKP}, now the spatial particle density is not a conserved quantity.

Pressure-field extraction on unstructured flow data using a Voronoi tessellation-based networking algorithm: a proof-of-principle study

A novel technique is described for pressure extraction from Lagrangian particle-tracking data. The technique uses a Poisson solver to extract the pressure field on a network of data nodes, which is constructed using the Voronoi tessellation and the Delaunay triangulation. The technique is demonstrated on two cases: synthetic Lagrangian data generated for the analytical case of Hill’s spherical vortex, and the flow in the wake behind a NACA 0012 which was impulsively accelerated to \(Re = 7{,}500\). The experimental data were collected using four-camera, three-dimensional particle-tracking velocimetry. For both the analytical case and the experimental case, the dependence of pressure-field error or sensitivity on the normalized spatial particle density was found to follow similar power-law relationships. It was shown that in order to resolve the salient flow structures from experimental data, the required particle density was an order of magnitude greater than for the analytical case. Furthermore, additional sub-structures continued to be identified in the experimental data as the particle density was increased. The increased density requirements of the experimental data were assumed to be due to a combination of phase-averaging error and the presence of turbulent coherent structures in the flow. Additionally, the computational requirements of the technique were assessed. It was found that in the current implementation, the computational requirements are slightly nonlinear with respect to the number of particles. However, the technique will remain feasible even as advancements in particle-tracking techniques in the future increase the density of Lagrangian data.

Density based visualization for molecular simulation

Molecular visualization of structural information obtained from computer simulations is an important part of research work flow. A good visualization technique should be capable of eliminating redundant information and highlight important effects clarifying the key phenomena in the system. Current methods of presenting structural data are mostly limited to variants of the traditional ball-and-stick representation. This approach becomes less attractive when very large biological systems are simulated at microsecond timescales, and is less effective when coarse-grained models are used. Real time rendering of such large systems becomes a difficult task; the amount of information in one single frame of a simulation trajectory is enormous given the large number of particles; at the same time, each structure contains information about one configurational point of the system and no information about statistical weight of this specific configuration. In this paper we report a novel visualization technique based on spatial particle densities. The atomic densities are sampled on a high resolution 3-dimensional grid along a relatively short molecular dynamics trajectory using hundreds of configurations. The density information is then analyzed and visualized using the open-source ParaView software. The performance and capability of the method are demonstrated on two large systems simulated with the MARTINI coarse-grained force field: a lipid nanoparticle for delivering siRNA molecules and monolayers with a complex composition under conditions that induce monolayer collapse.

Collective Dynamics of Interacting Particles in Unsteady Flows

We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive potential field known as Morse potential. We assume Stokesian drag force between particles and their carrier fluid, and find analytic single-peaked traveling solutions for the spatial density of particles in the catastrophic phase. In steady flow conditions the streaming velocity of particles is identical to their carrier fluid, but we show that particle streaming is asynchronous with an unsteady carrier fluid. Using linear perturbation analysis, the stability of traveling solutions is investigated in unsteady conditions. It is shown that the resulting dispersion relation is an integral equation of the Fredholm type, and yields two general families of stable modes: singular modes whose eigenvalues form a continuous spectrum, and a finite number of discrete global modes. Depending on the value of drag coefficient, stable modes can be over-damped, critically damped, or decaying oscillatory waves. The results of linear perturbation analysis are confirmed through the numerical solution of the fully nonlinear Fokker-Planck equation.

Overdamped dynamics of long-range systems on a one-dimensional lattice: Dominance of the mean-field mode and phase transition

We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice and in the presence of thermal noise. The internal degree of freedom of each particle is a periodic variable that is coupled to those of other particles with an attractive XY-like interaction. The coupling strength decays with the interparticle separation r in space as 1/r^{α}; 0<α<1. We study the dynamics of the model in the continuum limit by considering the Fokker-Planck equation for the evolution of the spatial density of particles. We show that the equation allows a linearly stable stationary state, which is always uniform in space, being nonuniform in the internal degrees below a critical temperature T=1/2 and uniform above, with a phase transition between the two at T=1/2. The state is the same as the equilibrium state of the mean-field version of the model, obtained by considering α=0. Our analysis also allows us to compute the growth and decay rates of spatial Fourier modes of density fluctuations. The growth rates compare very well with numerical simulations.

Optimal Gradient Estimates and Asymptotic Behaviour for the Vlasov–Poisson System with Small Initial Data

The Vlasov–Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays as t −3 at late times. In this paper this statement is refined to show that each derivative of the density which is taken leads to an extra power of decay, so that in N dimensions for $${N \geqq 3}$$ the derivative of the density of order k decays as t −N-k . An asymptotic formula for the solution at late times is also obtained.

Distribution- Versus Correlation-Induced Anomalous Transport in Quenched Random Velocity Fields

We study mechanisms of anomalous transport in quenched random media. Broad disorder point distributions and strong disorder correlations cause anomalous transport and can lead to the same anomalous scaling laws for the mean and variance of the particle displacements. The respective mechanisms, however, are fundamentally different. This difference is reflected in the spatial particle densities and first passage time distributions, which provide an indicator to identify the origins of anomalous transport.

A physical model of particulate wash-off from rough impervious surfaces

Summary Current urban water quality models rely on empirical, catchment-scale functions of particulate wash-off that do not clearly represent the governing physical erosion and transport processes. We proposed a saltation-type wash-off model in which particles are repeatedly ejected from an impervious surface by raindrop impacts and are transported laterally by overland flow while settling back to the surface. The rate that particles are ejected is proportional to rain intensity and the spatial density of particles on the surface. We found that for low particle spatial densities, ejection is proportional to spatial density, but for high spatial densities, the ejection rate is independent of spatial density. We tested our model against data from small (10.5 × 80 cm) flume experiments in which rain intensity and upslope overland flow could be independently controlled. We used a rough flume surface (∼1 mm roughness element height) and sand particles (diameter = 500–590 μm). Rainfall rates, upslope overland flow rates, and initial particle amounts were varied among experiments with ranges of, 4.2–7.8 cm h −1 , 300–565 mL min −1 , and 0.01–0.07 g cm −2 , respectively. The model predictions agreed well with the experiments ( R 2 > 0.85). This work provides a basis for developing new, uniquely mechanistic models for predicting “wash-off” from urban surfaces.

The meteoroid environment of comet 9P/Tempel 1 and the Deep Impact spacecraft

On the 4th of July 2005 the Deep Impact probe reached comet 9P/Tempel 1. The flyby spacecraft observed the collision from a distance of several hundred kilometres. Here we examine the meteoroid environment of the nucleus and present a method for computing the spatial density of particles, as well as the number of collisions any probe is supposed to endure. The model is calibrated from observations of the comet taken at the Pic-du-Midi observatory. In particular we measured [Afρ]=272 ± 25 cm, at Rh=1.579 au and φ=29.4°. The data acquired by the Stardust spacecraft were also used. Several thousands of 100 μm-size meteoroids are expected to have collided with Deep Impact. Centimeter-size particles were a threat to the probe and the upper limit of the number of collision computed here was higher than unity. However the results depend on the differential size population index s, which is taken to be constant. Preliminary results show that a few collisions were recorded but no cm-size meteoroids were encountered. Interpreting this result as a change of s with the meteoroid size, we derive s>3.5 for cm-size and larger particles ejected by comet 9P/Tempel 1. This can be caused by a fragmentation process and shows the relevance of any observation of large meteoroids ejected by cometary nuclei, as it provides constraints on s. This method can be used in preparation of any space mission to a comet.

EPMA mapping of small particles of α-AlFeSi and β-AlFeSi in AA6063 alloy billets

It is well known that the spatial distribution and the spatial density of the particles oα-AlFeSi and β-AlFeSi in the billets of Al-Mg-Si alloys, such as AA6063 alloys affect the quality of anodizing performance of their extrusions. For this reason it is very important to control the spatial distribution and the spatial density of both AlFeSi particles at extrusion plants. The X-ray diffraction method (XRD) has been used for discrimination between α-AlFeSi and β-ALFeSi particles. However it is not an appropriate method for determining the spatial distributions of particles in the alloys. As an alternative method an electron probe microanalyzer (EPMA) has been used for determining the spatial distributions of each element in the microstructures. However, unfortunately it is difficult to discriminate between the particles composed of the same elements like α-AlFeSi and β-AlFeSi particles. Thus, we tried to develop a convenient method to discriminate between α-AlFeSi and β-AlFeSi particles in the microstructure of AA6063 alloys and developed the EPMA mapping of α-AlFeSi and β-AlFeSi particles. First, in order to discriminate between the two particles, we tried to use the relative X-ray intensity ratio, the I Fe/I Si ratio instead of the Fe/Si mass ratio. Then, we calculated the value of the I Fe/I Si ratio from α-AlFeSi and β-AlFeSi by using Monte Carlo calculations and obtained the critical value of the I Fe/I Si ratio, to distinguish between α-AlFeSi and β-AlFeSi. After that, using the discrimination value, we developed the EPMA mapping program (EPMA method) to observe the distributions of α-AlFeSi and β-AlFeSi, and to calculate the areas (%) of α-AlFeSi and β-AlFeSi. Finally, we checked the correlation between the EPMA and the XRD methods. Consequently, the two methods were in good agreement. Today, this EPMA method instead of the XRD method is successfully used in the quality control of 6063 aluminum alloy billets after heat treatment at our aluminum extrusion works.

Evaluation of Free-Fall Particle CT Images Using State Transition Matrix

Spatial particle density distribution images in a pipe cross section have been evaluated by means of state transition matrix, which is a parameter indicating the dominant particle density transition patterns among time series images consisting of CT 2-D space and 1-D time. State transition characterizes the transition patterns for positions in a cross section as monotonous transitions, sudden transitions, and extreme value transitions. In a simulation, the real part of the state transition matrix is negative and the imaginary part is zero in the case of monotonous transition. The real part is positive and the imaginary part is zero in the case of extreme value transition. The imaginary part is nonzero in the case of sudden transition. In free-fall particles in a vertical pipe, high, sudden, and extreme value transitions do not occur because the particle flow rate at this position is low, and therefore the probability of collision among particles is also low. High, sudden, and extreme value transitions occur near the pipe center when the particle flow rate is high, because the probability of collision among particles is high.

粒子追跡法の再帰的相関法を用いた改良

An improved Particle Tacking velocimetry (PTV) algorithm was proposed in the present paper. The path tracking of the traced particle was achieved through a recursive cross-correlation operation of small interrogation window around the studied particles at two time steps. The particles are tracked by using grid points velocities calculated by the recursive cross-correlation method. To reduce the tracking error, a variable interrogation window size setting which changed with the interrogation window size according with spatial density of particles was introduced to the recursive cross-correlation method. The performance of the improved algorithm is evaluated by the synthetic particle images.

Trapping reactions for mobile particles and a trap in the laboratory frame.

We have used a stochastic model to obtain the exact spatial particle density profile for the trapping process A+B-->B in a one-dimensional lattice with a single trap, as seen from the laboratory frame. We obtain the profile for either perfect or imperfect reactions when A particles are immobile, but only for perfect absorption in the general case where both particles are mobile with different diffusivities. This profile is found to be similar to that seen from the reference system attached to the trap, the most noticeable difference being near the origin.