Sufficient Number Of Particles Research Articles

Dynamic phases and combing effects for elongated particles moving over quenched disorder.

We consider a two-dimensional system of elongated particles driven over a landscape containing randomly placed pinning sites. For varied pinning site density, external drive magnitude, and particle elongation, we find a wide variety of dynamic phases, including random structures, stripe or combed phases with nematic order, and clogged states. The different regimes can be identified by examining nematic ordering, cluster size, number of pinned particles, and transverse diffusion. In some regimes we find that the pinning can enhance the particle alignment, producing a nonmonotonic signature in the nematic ordering with a maximum at a particular combination of pinning density and drive. The optimal nematic occurs when a sufficient number of particles can be pinned, generating a local shear and leading to what we call a combing effect. At high drives, the combing effect is reduced when the number of pinned particles decreases. For stronger pinning, the particles form a heterogeneous clustered or clogged state that depins into a fluctuating state with high diffusion.

How the presence of particles at the interface influences the droplet deformation in a simple shear flow?

A lattice Boltzmann method is presented to simulate a particle-laden droplet subject to a simple shear flow, where the effect of particle concentration, viscosity ratio of droplet to ambient fluid and particle inertia on droplet deformation and particle movement is explored. With the increase of particle concentration, droplet deformation increases because of reduced interfacial free energy caused by reduced fluid-fluid interface length. When a sufficient number of particles are added to interface, droplet deformation monotonically decreases with viscosity ratio, but first rises and then declines for clean interface. This difference is attributed to an increased apparent viscosity of the ambient fluid by added particles. The particle inertia enhances droplet deformation remarkably only when the Reynolds number is relatively high. In addition, particles are found to revolve around the deformed droplet along the interface with a period, which is determined solely by deformation parameter at the viscosity ratio of unity. • A LBM is developed to simulate the fluid-fluid-solid three-phase flows. • The particle's revolution period can be determined by the droplet deformation. • The deposition of particles at the interface can enhance the droplet deformation.

Flexible and Efficient Inference with Particles for the Variational Gaussian Approximation.

Variational inference is a powerful framework, used to approximate intractable posteriors through variational distributions. The de facto standard is to rely on Gaussian variational families, which come with numerous advantages: they are easy to sample from, simple to parametrize, and many expectations are known in closed-form or readily computed by quadrature. In this paper, we view the Gaussian variational approximation problem through the lens of gradient flows. We introduce a flexible and efficient algorithm based on a linear flow leading to a particle-based approximation. We prove that, with a sufficient number of particles, our algorithm converges linearly to the exact solution for Gaussian targets, and a low-rank approximation otherwise. In addition to the theoretical analysis, we show, on a set of synthetic and real-world high-dimensional problems, that our algorithm outperforms existing methods with Gaussian targets while performing on a par with non-Gaussian targets.

High-Energy X-ray Tomographic Analysis of Precursor Metal Powders (Ti-6Al-4V) Used for Additive Manufacturing

We used high-energy x-ray tomography to characterize Ti-6Al-4V metal powders (both as-received and recycled) used in powder-bed additive manufacturing process. The image processing workflow was developed to process and analyze large amount of data objectively by computer program. The distribution of size and shape of the metal particles as well as defect (mainly porosity) inside the particles was analyzed with the statistical representation and resolution in micrometer. The result revealed that circular-shaped porosity with various sizes could be embedded in the powder particles. These porosities could potentially be transferred to the 3D printed part and critically affect the mechanical performance of the component. The present study shows the effectiveness of characterizing metal powders using x-ray imaging techniques where sufficient number of particles can be sampled within tens of minutes with a minimum sample preparation and high accuracy. Clear structural differences in the as-received and recycled powders were delineated that helps in determining the feasibility of using the recycled powders.

Selection of an Optimal Abrasion Wheel Type for Nano-Coating Wear Studies under Wet or Dry Abrasion Conditions.

Nanocoatings have numerous potential applications in the indoor environment, such as flooring finishes with increased scratch- and wear-resistance. However, given concerns about the potential environmental and human health effects of nanomaterials, it is necessary to develop standardized methods to quantify nanomaterial release during use of these products. One key choice for mechanical wear studies is the abrasion wheel. Potential limitations of different wheels include the release of fragments from the wheel during abrasion, wearing of the wheel from the abrasion process, or not releasing a sufficient number of particles for accurate quantitative analysis. In this study, we evaluated five different wheels, including a typically used silicon oxide-based commercial wheel and four wheels fabricated at the National Institute of Standards and Technology (NIST), for their application in nanocoating abrasion studies. A rapid, nondestructive laser scanning confocal microscopy method was developed and used to identify released particles on the abraded surfaces. NIST fabricated a high performing wheel: a noncorrosive, stainless-steel abrasion wheel containing a deep cross-patch. This wheel worked well under both wet and dry conditions, did not corrode in aqueous media, did not release particles from itself, and yielded higher numbers of released particles. These results can be used to help develop a standardized protocol for surface release of particles from nanoenabled products using a commercial rotary Taber abraser.

Errors in particle size and concentration analysis of pharmaceuticals

Good particulate products require that particle segregation has been minimized. Moreover representative sampling is essential for adequate quality control of such products. This requires optimum design of procedures and equipment for both sampling and measurement. Representative test samples primarily require that all constituent particles have had equal chance of being taken from a lot of material, given their proportion. Moreover, a sufficient number of particles is necessary for good precision. This article discusses and exemplifies various potential errors during collection of small amounts from powder lots and during in-situ and on-line measurement, so that optimum consideration can be given to the design of adequate analytical procedures. It should be realized that the errors during sampling of particulate materials are very similar to those during collection of small portions for production of pharmaceutical tablets.

Numerical techniques for fast generation of large discrete-element models

In recent years, civil engineers have started to use discrete-element modelling to simulate large-scale soil volumes thanks to technological improvements in both hardware and software. However, existing procedures to prepare ‘representative elementary volumes’ (REV) are unsatisfactory in terms of computational cost and sample homogeneity. In this work, a simple but efficient procedure to initialise large-scale discrete-element models is presented. Periodic cells are first generated with a sufficient number of particles (enough to consider the cell an REV) matching the desired particle-size distribution and equilibrated at the desired stress state, porosity and coordination number. When the cell is in equilibrium, it is replicated in space to fill the problem domain, and when the model is filled, only a small number of mechanical cycles is needed to equilibrate a large domain. The result is an equilibrated homogeneous sample at the desired initial state in a large volume.

A study of MRI gradient echo signals from discrete magnetic particles with considerations of several parameters in simulations

Modeling MRI signal behaviors in the presence of discrete magnetic particles is important, as magnetic particles appear in nanoparticle labeled cells, contrast agents, and other biological forms of iron. Currently, many models that take into account the discrete particle nature in a system have been used to predict magnitude signal decays in the form of R2* or R2′ from one single voxel. Little work has been done for predicting phase signals. In addition, most calculations of phase signals rely on the assumption that a system containing discrete particles behaves as a continuous medium. In this work, numerical simulations are used to investigate MRI magnitude and phase signals from discrete particles, without diffusion effects. Factors such as particle size, number density, susceptibility, volume fraction, particle arrangements for their randomness, and field of view have been considered in simulations. The results are compared to either a ground truth model, theoretical work based on continuous mediums, or previous literature. Suitable parameters used to model particles in several voxels that lead to acceptable magnetic field distributions around particle surfaces and accurate MR signals are identified. The phase values as a function of echo time from a central voxel filled by particles can be significantly different from those of a continuous cubic medium. However, a completely random distribution of particles can lead to an R2′ value which agrees with the prediction from the static dephasing theory. A sphere with a radius of at least 4 grid points used in simulations is found to be acceptable to generate MR signals equivalent from a larger sphere. Increasing number of particles with a fixed volume fraction in simulations reduces the resulting variance in the phase behavior, and converges to almost the same phase value for different particle numbers at each echo time. The variance of phase values is also reduced when increasing the number of particles in a fixed voxel. These results indicate that MRI signals from voxels containing discrete particles, even with a sufficient number of particles per voxel, cannot be properly modeled by a continuous medium with an equivalent susceptibility value in the voxel.

Efficient Online Learning Algorithms Based on LSTM Neural Networks.

We investigate online nonlinear regression and introduce novel regression structures based on the long short term memory (LSTM) networks. For the introduced structures, we also provide highly efficient and effective online training methods. To train these novel LSTM-based structures, we put the underlying architecture in a state space form and introduce highly efficient and effective particle filtering (PF)-based updates. We also provide stochastic gradient descent and extended Kalman filter-based updates. Our PF-based training method guarantees convergence to the optimal parameter estimation in the mean square error sense provided that we have a sufficient number of particles and satisfy certain technical conditions. More importantly, we achieve this performance with a computational complexity in the order of the first-order gradient-based methods by controlling the number of particles. Since our approach is generic, we also introduce a gated recurrent unit (GRU)-based approach by directly replacing the LSTM architecture with the GRU architecture, where we demonstrate the superiority of our LSTM-based approach in the sequential prediction task via different real life data sets. In addition, the experimental results illustrate significant performance improvements achieved by the introduced algorithms with respect to the conventional methods over several different benchmark real life data sets.

A numerical simulation method for transient behavior of damaged ships associated with flooding

In order to secure the survivability of damaged ships in flooding situations, time-domain simulation is necessary for the quantitative safety assessment, which can predict ship's transient behavior associated with flooding. A numerical simulation method for damaged ships, solving equations of motion with hydrodynamic forces estimated by the semi-implicit MPS (Moving Particle Simulation) for damaged parts and by the potential flow theory for intact parts, has been proposed by the authors (Hashimoto et al., 2013). The validity of the proposed method was demonstrated through comparisons with model experiments in 2-D flooding situations. However it is difficult to apply this simulation method directly to realistic flooding situations because number of particles increases tremendously in 3-D MPS simulation. In this research, the semi-implicit MPS is replaced with the explicit MPS to reduce the CPU cost. In addition, GPGPU (General Purpose computing on Graphics Processing Units) technology is introduced to accelerate the MPS simulation, in which parallel computing runs on GPUs instead of CPUs, so that sufficient number of particles can be used to perform complicated 3-D flooding simulations. In order to validate the developed simulation method, dedicated model experiments are newly conducted. One is a forced roll test for a flooded car-deck compartment and the other is a ship flooding test using a PCTC (Pure Car and Truck Carrier) model. Through comparisons between the model experiment and the numerical simulation, it is well demonstrated that the explicit MPS has good ability to simulate complicated floodwater flows in the car-deck compartment and the developed simulation method can well reproduce ship's transient behavior associated with water flooding.

Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

This study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ∼100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.

Periodic cells for large-scale problem initialization

In geotechnical applications the success of the discrete element method (DEM) in simulating fundamental aspects of soil behaviour has increased the interest in applications for direct simulation of engineering scale boundary value problems (BVP’s). The main problem is that the method remains relatively expensive in terms of computational cost. A non-negligible part of that cost is related to specimen creation and initialization. As the response of soil is strongly dependant on its initial state (stress and porosity), attaining a specified initial state is a crucial part of a DEM model. Different procedures for controlled sample generation are available. However, applying the existing REV-oriented initialization procedures to such models is inefficient in terms of computational cost and challenging in terms of sample homogeneity. In this work a simple but efficient procedure to initialize large-scale DEM models is presented. Periodic cells are first generated with a sufficient number of particles matching a desired particle size distribution (PSD). The cells are then equilibrated at low-level isotropic stress at target porosity. Once the cell is in equilibrium, it is replicated in space in order to fill the model domain. After the domain is thus filled a few mechanical cycles are needed to re-equilibrate the large domain. The result is a large, homogeneous sample, equilibrated under prescribed stress at the desired porosity. The method is applicable to both isotropic and anisotropic initial stress states, with stress magnitude varying in space.

Interactions of carbon nanotubes in a nematic liquid crystal. II. Experiment.

Multiwall carbon nanotube (CNT) colloids with different anchoring conditions are dispersed in pentyl-cyanobiphenyl (5CB), a thermotropic liquid crystal (LC) that exhibits a room-temperature nematic phase. The experiments make use of CNTs treated for strong planar, homeotropic, or Janus anchorings. Observations with a polarizing microscope show that the CNTs placed in a uniform nematic field stabilize parallel or perpendicular to n depending on their anchoring conditions. In the presence of a splay-bend disclination line, they are first attracted toward it and ultimately, they get trapped on it. Their orientation relative to the line is then found to be parallel or perpendicular to it, again depending on the anchoring conditions. When a sufficient number of particles are deposited on a disclination line, they form a micro- or nanonecklace in the shape of a thin thread or of a bottle brush, with the CNTs being oriented parallel or perpendicular to the disclination line according to the anchoring treatment. The system exhibits a rich versatility, even if until now the weak anchorings appear to be difficult to control. In a next step, the necklaces may be glued by means of pyrrole electropolymerization. In this manner, we realize a true materialization of the disclination lines, and we obtain nanowires capable of conducting the electricity in the place of the initial disclinations that just worked as templates. The advantage of the method is that it finally provides nanowires that are automatically connected to predesignated three-dimensional (3D) electrodes. Such a 3D nanowiring could have important applications, as it could allow one to develop electronic circuits in the third dimension. They could thus help with increasing the transistor density per surface unit, although downsizing of integrated circuits will soon be limited to atomic sizes or so. In other words, the predicted limitation to Moore's law could be avoided. For the moment, the nanowires that we obtain are not completely satisfactory, particularly because they are thickened by aggregates in some places. However, the method is far from being optimized. A few electric charges deposited on the CNTs could remedy those aggregates.

Interactions of carbon nanotubes in a nematic liquid crystal. I. Theory.

Elongated and rodlike objects such as carbon nanotubes (CNTs) are studied when immersed in a nematic liquid crystal. Their interaction energy in a uniform nematic field depends on their orientation relative to the director n, and its minimum determines if they stabilize parallel or perpendicular to n. Using free energy calculations, we deduce the orientation at equilibrium that they choose in a uniform director field n or when they are in contact with a splay-bend disclination line. Naturally, the CNT orientations also depend on the anchoring conditions at their surface. Essentially, three types of anchorings are considered, planar, homeotropic, and Janus anchorings in the cases of weak and strong anchoring strengths. In the presence of a splay-bend disclination line, they are attracted toward it and ultimately, they get out of the colloidal dispersion to stick on it. Their orientation relative to the line is found to be parallel or perpendicular to it, again depending on the anchoring conditions. When a sufficient number of particles are deposited on a disclination line, we finally obtain a micro- or nanonecklace in the shape of a thin thread or of a bottle brush, according to the CNTs being oriented parallel or perpendicular to the disclination line, respectively. The system exhibits a rich versatility even if up to now the weak anchorings appear to be difficult to control. As discussed in the associated experimental paper, these necklaces could be a step toward interesting applications for realizing nanowires self-connected in three dimensions to predesignated electrodes. This method could provide a way to increase the number of transistors that may be connected together on a small volume.

Spatial dimensions of the electron diffusion region in anti-parallel magnetic reconnection

Abstract. Spatial dimensions of the detailed structures of the electron diffusion region in anti-parallel magnetic reconnection were analyzed based on two-dimensional fully kinetic particle-in-cell simulations. The electron diffusion region in this study is defined as the region where the positive reconnection electric field is sustained by the electron inertial and non-gyrotropic pressure components. Past kinetic studies demonstrated that the dimensions of the whole electron diffusion region and the inner non-gyrotropic region are scaled by the electron inertial length de and the width of the electron meandering motion, respectively. In this study, we successfully obtained more precise scalings of the dimensions of these two regions than the previous studies by performing simulations with sufficiently small grid spacing (1∕16–1∕8 de) and a sufficient number of particles (800 particles cell−1 on average) under different conditions changing the ion-to-electron mass ratio, the background density and the electron βe (temperature). The obtained scalings are adequately supported by some theories considering spatial variations of field and plasma parameters within the diffusion region. In the reconnection inflow direction, the dimensions of both regions are proportional to de based on the background density. Both dimensions also depend on βe based on the background values, but the dependence in the inner region ( ∼ 0.375th power) is larger than the whole region (0.125th power) reflecting the orbits of meandering and accelerated electrons within the inner region. In the outflow direction, almost only the non-gyrotropic component sustains the positive reconnection electric field. The dimension of this single-scale diffusion region is proportional to the ion-electron hybrid inertial length (dide)1∕2 based on the background density and weakly depends on the background βe with the 0.25th power. These firm scalings allow us to predict observable dimensions in real space which are indeed in reasonable agreement with past in situ spacecraft observations in the Earth's magnetotail and have important implications for future observations with higher resolutions such as the NASA Magnetospheric Multiscale (MMS) mission.

Micro–Flow Imaging and Resonant Mass Measurement (Archimedes) – Complementary Methods to Quantitatively Differentiate Protein Particles and Silicone Oil Droplets

Our study aimed to comparatively evaluate Micro-Flow Imaging (MFI) and the recently introduced technique of resonant mass measurement (Archimedes, RMM) as orthogonal methods for the quantitative differentiation of silicone oil droplets and protein particles. This distinction in the submicron and micron size range is highly relevant for the development of biopharmaceuticals, in particular for products in prefilled syringes. Samples of artificially generated silicone oil droplets and protein particles were quantified individually and in defined mixtures to assess the performance of the two techniques. The built-in MFI software solution proved to be suitable to discriminate between droplets and particles for sizes above 2 μm at moderate droplet/particle ratios (70:30-30:70). A customized filter developed specifically for this study greatly improved the results and enabled reliable discrimination also for more extreme mixing ratios (95:5-15:85). RMM showed highly accurate discrimination in the size range of about 0.5-2 μm independent of the ratio, provided that a sufficient number of particles (>50 counted particles) were counted. We recommend applying both techniques for a comprehensive analysis of biotherapeutics potentially containing silicone oil droplets and protein particles in the submicron and micron size range.

Investigating the testing procedure limits for measuring particle strength distribution

Abstract A new design of a compression tester and an investigation of the testing procedure are presented. The tester enables us to accurately measure the force versus displacement of single particles down to 0.1 mm. By a numerical evaluation of test accuracy the required number of particles is obtained. For most of the investigated materials only 50–70 tested particles are sufficient to fall below an error of ± 5%. This procedure allows a sufficient number of particles that accurately result in the reliable breakage force, strength and energy distribution and prevent unnecessary tests. Usually, a quasi-static experiment is required leading to small compression force rates. Increasing the compression force rate may significantly reduce the test time. Therefore, the effect of the compression force rate on the breakage force of salt and glass spheres is examined to check the limit of the quasi-static region. It is shown that for glass spheres the limit is about 7 N/s.

Comparison of a new kernel method and a sampling volume method for estimating indoor particulate matter concentration with Lagrangian modeling

This study develops a new concentration estimation method for Lagrangian modeling of airborne particulate matter (PM) in indoor environment. This new method, based on the cubic spline kernel function with the smoothing length and solid building boundary treatment, is considered herein to study the accuracy and efficiency of indoor airborne PM concentration calculation. The commonly used sampling volume method is also adopted for numerical performance test. Reliable measured PM concentration profiles in indoor chambers are used to verify the accuracy and efficiency of the above methods. A comparison of the relative merits and shortcomings of these two methods is emphasized. The results show that the sampling volume method is simple and easy to formulate in indoor environment. However, it produces sensitive and scattered concentration profiles, especially in recirculation zones, if the released particle number is not large enough. This problem can only be solved by using a sufficient number of particles, which should be determined by the sensitivity analysis. The kernel method can provide accurate and smooth profiles even though the released particle number is one order less than the sampling volume method. Under the same PM concentration estimation accuracy, the kernel method is much more efficient compared to the sampling volume method.

Comparison of particle filtering and extended Kalman filtering for acoustic-based tracking of low-flying aircraft

This presentation summarizes a comparative study of particle filtering and extended Kalman filtering applied to acoustic-based tracking of high-speed, low-flying aircraft. A distributed network of small acoustic arrays, each reporting real-time azimuthal bearings and elevation angles to acoustic sources to a central processing unit, are synthesized into real-time three-dimensional tracks. The primary challenge of the problem is the significant propagation delay between the source and the receivers. Both tracking methods are applied to simulated and field test data and reveal nearly equivalent tracking performance in all cases as along as a sufficient number of particles are utilized. Computational requirements of the extended Kalman filter are significantly less than the particle filters.

Group averaging for de Sitter free fields

Perturbative gravity about global de Sitter space is subject to linearization-stability constraints. Such constraints imply that quantum states of matter fields couple consistently to gravity only if the matter state has vanishing de Sitter charges, i.e. only if the state is invariant under the symmetries of de Sitter space. As noted by Higuchi, the usual Fock spaces for matter fields contain no de Sitter-invariant states except the vacuum, though a new Hilbert space of de Sitter-invariant states can be constructed via so-called group-averaging techniques. We study this construction for free scalar fields of arbitrary positive mass in any dimension, and for linear vector and tensor gauge fields in any dimension. Our main result is to show in each case that group averaging converges for states containing a sufficient number of particles. We consider general N-particle states with smooth wavefunctions, though we obtain somewhat stronger results when the wavefunctions are finite linear combinations of de Sitter harmonics. Along the way we obtain explicit expressions for general boost matrix elements in a familiar basis.