Particle Overlap Research Articles

Estimation of coal particle size distribution by image segmentation

Several industrial coal processes are largely determined by the distribution of particle sizes in their feed. Currently these parameters are measured by manual sampling, which is time consuming and cannot provide real time feedback for automatic control purposes. In this paper, an approach using image segmentation on images of overlapped coal particles is described. The estimation of the particle size distribution by number is also described. The particle overlap problem was solved using image enhancement algorithms that converted those image parts representing material in lower layers to black. Exponential high-pass filter (EHPF) algorithms were used to remove the texture from particles on the surface. Finally, the edges of the surface particles were identified by morphological edge detection. These algorithms are described in detail as is the method of extracting the coal particle size. Tests indicate that using more coal images gives a higher accuracy estimate. The positive absolute error of 50 random tests was consistently less than 2.5% and the errors were reduced as the size of the fraction increased.

Analytical approach to the two-site Bose-Hubbard model: From Fock states to Schrödinger cat states and entanglement entropy

We study the interpolation from occupation number Fock states to Schr\"odinger cat states on systems modeled by two-mode Bose-Hubbard Hamiltonian, like, for instance, bosons in a double well or superconducting Cooper pair boxes. In the repulsive interaction regime, by a simplified single particle description, we calculate, analytically, energy, number fluctuations, stability under coupling to a heat bath, entanglement entropy and Fisher information, all in terms of hypergeometric polynomials of the single particle overlap parameter. Our approach allows us to find how those quantities scale with the number of bosons. In the attractive interaction regime we calculate the same physical quantities in terms of the imbalance parameter, and find that the symmetry breaking, occurring at interaction Uc, predicted by a semiclassical approximation, is valid only in the limit of infinite number of bosons. For a large but finite number, we determine a characteristic strength of interaction, Uc*, which can be promoted as the crossover point from coherent to incoherent regimes and can be identified as the collapse threshold. Moreover, we find that the Fisher information is always in direct ratio to the variance of on-site number of bosons, for both positive and negative interactions. We finally show that the entanglement entropy is maximum close to Uc* and exceeds its coherent value within the whole range of interaction between 2Uc and zero.

Geometrization of Radial Particles in Non-Empty Space Complies with Tests of General Relativity

Curved space-time 4-interval of any probe particle does not contradict to flat non-empty 3-space which, in turn, assumes the global material overlap of elementary continuous particles or the nonlocal Universe with universal Euclidean geometry. Relativistic particle’s time is the chain function of particles speed and this time differs from the proper time of a motionless local observer. Equal passive and active relativistic energy-charges are employed to match the universal free fall and the Principle of Equivalence in non-empty (material) space, where continuous radial densities of elementary energy-charges obey local superpositions and mutual penetrations. The known planetary perihelion precession, the radar echo delay, and the gravitational light bending can be explained quantitatively by the singularity-free metric without departure from Euclidean spatial geometry. The flatspace precession of non-point orbiting gyroscopes is non-New- tonian one due to the Einstein dilation of local time within the Earth’s radial energy-charge rather than due to unphysical warping of Euclidean space.

Disordered Spheres with Extensive Overlap in Projection: Image Simulation and Analysis

This article simulates highly overlapped projections of spherical particles that are distributed randomly in space. The size and number of the features in the projections are examined as well as how these features change with particle size and concentration. First, there are discernable features in projection even when particles overlap extensively, and the size of these discernable features is the expected size of an individual particle. Second, the number of features increases with specimen thickness at a rate of t(0.543) when the specimen thickness is below a critical value and becomes independent of specimen thickness at higher thicknesses. A criterion is established for the critical thickness based on particle size and particle volume fraction. When the specimen thickness is known and smaller than the critical thickness, a single representative transmission electron microscopy (TEM) (or scanning TEM) image exhibiting extensive particle overlap can be used to determine the size and number density of the spherical particles.

A general formulation for the efficient evaluation of n-electron integrals over products of Gaussian charge distributions with Gaussian geminal functions

In this work, we present a general formulation for the evaluation of many-electron integrals which arise when traditional one particle expansions are augmented with explicitly correlated Gaussian geminal functions. The integrand is expressed as a product of charge distributions, one for each electron, multiplied by one or more Gaussian geminal factors. Our formulation begins by focusing on the quadratic form that arises in the general n-electron integral. Using the Rys polynomial method for the evaluation of potential energy integrals, we derive a general formula for the evaluation of any n-electron integral. This general expression contains four parameters ω, θ, v, and h, which can be evaluated by an examination of the general quadratic form. Our analysis contains general expressions for any n-electron integral over s-type functions as well as the recursion needed to build up arbitrary angular momentum. The general recursion relation requires at most n + 1 terms for any n-electron integral. To illustrate the general method, we develop explicit expressions for the evaluation of two, three, and four particle electron repulsion integrals as well as two and three particle overlap and nuclear attraction integrals. We conclude our exposition with a discussion of a preliminary computational implementation as well as general computational requirements. Implementation on parallel computers is briefly discussed.

Hot and Relaxed Electron Transfer from the CdSe Core and Core/Shell Nanorods

Transient absorption spectroscopy has been used to study the rates of electron transfer (ET) from CdSe and CdSe/ZnS core/shell nanorods to adsorbed methyl viologen, MV2+. The nanorods are excited with 387 nm light, producing electrons 7700 cm−1 above the conduction band edge. Kinetics are measured in particles without adsorbed MV2+, giving electron cooling and electron−hole recombination times. The kinetics obtained with and without adsorbed MV2+ are compared to infer the ET rates. The results indicate that electron cooling occurs on the 0.7−1.8 ps time scale, with the fastest cooling occurring from the highest energy states. Hot electron transfer from the highest energy levels competes with electron cooling, occurring on the 0.5 ps time scale. Bare particle (relaxed) electron transfer occurs on the time scale of less than or about 4 ps. This is faster than biexciton Auger recombination which occurs on the 50 ps time scale. The energy dependence of the ET times can be semiquantitatively understood in terms of penetration of the conduction band wave function past the particle surface and overlap with the adsorbed MV2+. In CdSe/ZnS particles, ET to adsorbed MV2+ is slower than electron cooling, and hot electron transfer does not occur. For a 1.0 nm thick ZnS shell, the ET from the bottom of the conduction band occurs on a range of time scales, with the fastest component of about 45 ps.

Three-dimensional random network model for thermal conductivity in particulate materials

This paper describes a three-dimensional random network model to evaluate the thermal conductivity of particulate materials. The model is applied to numerical assemblies of poly-dispersed spheres generated using the discrete element method (DEM). The grain size distribution of Ottawa 20–30 sand is modeled using a logistic function in the DEM assemblies to closely reproduce the gradation of physical specimens. The packing density and inter-particle contact areas controlled by confining stress are explored as variables to underscore the effects of micro- and macro-scales on the effective thermal conductivity in particulate materials. It is assumed that skeletal structure of 3D granular system consists of the web of particle bodies interconnected by thermal resistor at contacts. The inter-particle contact condition (e.g., the degree of particle separation or overlap) and the particle radii determine the thermal conductance between adjacent particles. The Gauss–Seidel method allows evaluation of the evolution of temperature variation in the linear system. Laboratory measurements of thermal conductivity of Ottawa 20–30 sand corroborate the calculated results using the proposed network model. The model is extended to explore the evolution of thermal conduction depending on the nucleation habits of secondary solid phase as an anomalous material in the pore space. The proposed network model highlights that the coordination number, packing density and the inter-particle contact condition are integrated together to dominate the heat transfer characteristics in particulate materials, and allows fundamental understanding of particle-scale mechanism in macro-scale manifestation.

Textural and mechanical characteristics of carbon aerogels synthesized by polymerization of resorcinol and formaldehyde using alkali carbonates as basification agents

Five organic aerogels were prepared simultaneously by polycondensation of resorcinol and formaldehyde using different alkali carbonates (M(2)CO(3), M = Li, Na, K, Rb and Cs) as basification agents. The gelation time depended on the carbonate used, increasing from Li(2)CO(3) to Cs(2)CO(3). The porosity of the samples is defined during this process, when the three-dimensional packing of primary particles is formed. The slower the gelation, the greater the overlapping of primary particles and the formation of clusters, leading to a mechanical reinforcement of the samples and the progressive displacement of their pore size distribution (PSD) towards larger pores. Carbonization produces certain shrinkage of the structure and increases the microporosity and the Young modulus of the samples. Carbon aerogels change from mesoporous to macroporous materials as the counter-ion size of the carbonate increases.

Strain-rate dependent shear viscosity of the Gaussian core model fluid

Nonequilibrium molecular dynamics simulations are reported for the shear viscosity of the Gaussian core model (GCM) fluid over a wide range of densities, temperatures and strain rates. A transition from Newtonian and non-Newtonian behavior is observed in all cases for sufficiently high strain rates. On the high-density side of the solid region where re-entrant melting occurs, the shear viscosity decreases significantly when the density is increased at constant temperature and Newtonian behavior persists until very high strain rates. This behavior, which is attributed to particle overlap, is in contrast to the monotonic increase in shear viscosity with density observed for the Lennard-Jones potential. Contrary to the behavior of normal fluids, the viscosity is observed to increase with increasing temperatures at high densities. This reflects a peculiarity of the GCM, namely the approach to the "infinite-density ideal-gas limit." The behavior is also consistent with viscosity measurements of cationic surfactant solutions. In contrast to other potentials, the shear viscosities for the Gaussian core potential at low to moderate strain rates are obtained with modest statistical uncertainties. Zero shear viscosities extrapolated from the nonequilibrium simulations are in good agreement with equilibrium Green-Kubo calculations.

Rheology and Microstructure of Entangled Polymer Nanocomposite Melts

The rheology and microstructure of 44 nm diameter silica particles suspended in entangled poly(ethylene oxide) (PEO) melts are studied through measurement of filled melt viscosity and X-ray scattering measurement of interparticle structure factors, S(q,ϕc), where q is the scattering vector and ϕc is the silica volume fraction. The particles have a similar refractive index to PEO which minimizes van der Waals attractions acting between particles. The introduction of particles causes an elevation in the viscosity of the nanocomposite melt more than would be expected of particles merely interacting with hard core repulsions. Further addition of particles causes a rise in the elastic and viscous moduli. The rheological characterization of these nanocomposite melts is discussed in terms of several critical particle volume fractions that result from confinement of polymer, adsorption of polymer segments to the particle surface, and overlap and entanglement of adsorbed polymer as the particle volume fraction is ...

Fabrication of hierarchical porous carbide-derived carbons by chlorination of mesoporous titanium carbides

Mesoporous titanium carbides were prepared via carbothermal reduction of organic–inorganic gels using titanium n-butoxide as a Ti source and sucrose as a carbon precursor. The as-made titanium carbides were used as starting materials for producing carbide-derived carbons (CDCs) through thermochemical treatment in a chlorine environment. The influence of the ratio of titanium n-butoxide to sucrose ( R) on the porous structure and physical properties of the mesoporous titanium carbide and the resulting CDCs were investigated using X-ray diffraction, Raman spectroscopy, scanning and transmission electron microscopy, and N 2 adsorption. It was found that mesoporosity and macroporosity developed in the course of the formation of the titanium carbides can be preserved and transmitted to the carbon material after chlorine treatment, while microporosity was formed by extraction titanium atoms from the carbide. The obtained CDCs have a hierarchical structure of multiscaled pores, including uniform micropores produced from carbides, mesopores with diameter of 3-4 nm original from the residual free carbon and macropores formed by interconnection and overlapping of the carbon particles. By changing the R, the Brunauer–Emmett–Teller specific surface areas and total pore volumes of the CDCs could be adjusted in the range of 1479-1 640 m 2/g and 1.06-2.03 cm 3/g, respectively. These hierarchical porous carbons would have potential applications for use in catalysis, adsorption, gas separation, and electrochemical energy storage.

Diffusion with Moving Boundary on Spherical Surfaces

In this work, we illustrate two approaches to the simulation of surface diffusion over a sphere coupled with the formation of a cluster by reactive particles as a paradigm of a wide variety of problems occurring in many areas of nanosciences and biology. The problem is treated using a Brownian motion approach and a numerical solution of the corresponding continuous Fick's laws of diffusion. While being computationally more expensive, the Brownian motion approach allows one to consider a wider range of situations, particularly those corresponding to relatively high concentrations of diffusing particles and the ensuing problem of particle overlap when they are ascribed finite sizes.

On the usefulness of discrete element computer modeling of particle packing for material characterization in concrete technology

Discrete element modeling (DEM) in concrete technology is concerned with design and use of models that constitute a schematization of reality with operational potentials. This paper discusses the material science principles governing the design of DEM systems and evaluates the consequences for their operational potentials. It surveys the two families in physical discrete element modeling in concrete technology, only touching upon probabilistic DEM concepts as alternatives. Many common DEM systems are based on random sequential addition (RSA) procedures; their operational potentials are limited to low configuration-sensitivity features of material structure, underlying material performance characteristics of low structure-sensitivity. The second family of DEM systems employs concurrent algorithms, involving particle interaction mechanisms. Static and dynamic solutions are realized to solve particle overlap. This second family offers a far more realistic schematization of reality as to particle configuration. The operational potentials of this family involve valid approaches to structure-sensitive mechanical or durability properties. Illustrative 2D examples of fresh cement particle packing and pore formation during maturation are elaborated to demonstrate this. Mainstream fields of present day and expected application of DEM are sketched. Violation of the scientific knowledge of to day underlying these operational potentials will give rise to unreliable solutions.

Fast off-lattice Monte Carlo simulations with “soft” repulsive potentials

The basic idea of fast off-lattice Monte Carlo (FOMC) simulations is to use "soft" repulsive potentials that allow particle overlapping in continuum Monte Carlo (MC) simulations. For multichain systems, this gives much faster chain relaxation and better sampling of the configurational space than conventional molecular simulations using "hard" excluded-volume interactions that prevent particle overlapping. Such coarse-grained models are particularly suitable for the study of equilibrium properties of soft materials. Since soft potentials are commonly used in polymer field theories, it is another advantage of FOMC simulations that using the same Hamiltonian in both FOMC simulations and the theories enables quantitative comparisons between them without any parameter fitting to unambiguously reveal the consequences of approximations in the theories. Moreover, FOMC simulations can be performed with various chain models and in any statistical ensemble, and all the advanced off-lattice MC techniques proposed to date can be implemented to further improve the sampling efficiency. We have performed canonical-ensemble FOMC simulations with an isotropic soft pair potential for three systems: we first used (small-molecule) soft spheres to demonstrate the improved sampling of FOMC simulations over conventional molecular simulations; we then used single-chain simulations to show that the effects of excluded-volume interactions can be well captured by the soft repulsive potential; finally, for compressible homopolymer melts, we compared FOMC results with those under the random-phase approximation to demonstrate that FOMC simulations can be used to unambiguously and quantitatively reveal the fluctuation/correlation effects in the system. In addition, we examined in detail in our single-chain simulations the spatial discretization scheme used in all previous FOMC simulations.

Assessing the Reliability of Particle Number Density Measurements Obtained by Image Analysis

AbstractParticle number density measurements obtained by image analysis are biased by edge effects and particle overlap. This paper presents an estimator for particle number density that accounts for both edge effects and particle overlap. Using the output of advanced image analysis applied to artificial images, the estimator is shown to enable effective estimation of particle number density for monodisperse particulate systems at high densities. This paper also proposes a single dimensionless number that correlates with the reliability of the inferred PSD based on the likely number of overlaps per particle. As this dimensionless group becomes large, the degree of overlap and occlusion in the images makes image analysis difficult and unreliable. This parameter can aid practitioners in finding the proper sampling conditions to obtain accurate PSD measurements.

Errors in two particle tracking at close distances

Tracking single and multiple particles is of great importance for many physical investigations in a variety of different areas. It is essential to find and eliminate sources of systematic errors in the particle position determination (PPD) and to determine the limits of its applicability to a given problem. Particularly when measuring the interactions between colloids at close distances, artifacts in the image taking process pose a great problem. By means of a simulation technique, we investigated the accuracy of the PPD using two-dimensional Gaussian and Gaussian-like fitting functions. For the distance between the two colloidal particles this revealed a systematic overestimation of the inter-particle distance of up to 1.9% of the particle diameter for the Gaussian fitting function. This deviation can be explained by the differences between the intensity distribution of the overlap of the simulated particles and the linear superposition of the Gaussian functions. Modifications of the fitting functions can reduce the systematic error significantly.

Smart Polymeric Membranes: Self-Control of Pore Size Induced by Variations in pH

A new kind of synthetic membrane was designed that has the ability to adjust the pore diameter in a wide range of sizes (from 0.8 to 22.3 μm) just by changing the pH of the aqueous media where they are immersed; in this way changing the pH can externally control the pore size of these membranes. A non-linear mathematical model, based on the overlap of charged particles, was developed to explain the behavior of the adjustment of pore size when the pH was varied. This model fits correctly the oscillatory behavior of the pore size as a function of pH. It has been reported by us that a similar behavior was found when the external temperature is changed. It is then possible to design smart membranes which respond to external parameters like temperature or pH.

Critical contact stiffness concept and simulation of crack generation in particle models of large length-scales

When the particle simulation method is used to simulate large length-scale problems, such as crustal length-scale problems in the field of geology, it is necessary to include gravity effect into the particle model. To consider gravity effect appropriately, there is a minimum value requirement for the contact stiffness of a particle so that unexpected particle overlap can be avoided. This minimum value is called the critical contact stiffness of a particle due to gravity effect. Using the vertical force equilibrium condition of a particle at the bottom of a two-dimensional particle model, a theoretical formula has been successfully derived for determining the critical contact stiffness of the particle in this paper. For the two-dimensional particle model consisting of circular particles of unit thickness, there is a relationship between the critical contact stiffness of a particle and the critical elastic modulus of the particle material when a linear-elastic-contact model between any two particles is used. Since the elastic moduli of most crustal rocks are greater than the corresponding critical elastic modulus of the particle material, it has been theoretically demonstrated that the particle simulation method, which is based on the linear-elastic-contact model between any two particles, is suitable for simulating gravity effect within the particle model of a large length-scale. The related simulation results have demonstrated the usefulness of the particle simulation method for simulating spontaneous crack generation patterns within brittle crustal rocks.

Spatial updating grand canonical Monte Carlo algorithms for fluid simulation: Generalization to continuous potentials and parallel implementation

Spatial updating grand canonical Monte Carlo algorithms are generalizations of random and sequential updating algorithms for lattice systems to continuum fluid models. The elementary steps, insertions or removals, are constructed by generating points in space either at random (random updating) or in a prescribed order (sequential updating). These algorithms have previously been developed only for systems of impenetrable spheres for which no particle overlap occurs. In this work, spatial updating grand canonical algorithms are generalized to continuous, soft-core potentials to account for overlapping configurations. Results on two- and three-dimensional Lennard-Jones fluids indicate that spatial updating grand canonical algorithms, both random and sequential, converge faster than standard grand canonical algorithms. Spatial algorithms based on sequential updating not only exhibit the fastest convergence but also are ideal for parallel implementation due to the absence of strict detailed balance and the nature of the updating that minimizes interprocessor communication. Parallel simulation results for three-dimensional Lennard-Jones fluids show a substantial reduction of simulation time for systems of moderate and large size. The efficiency improvement by parallel processing through domain decomposition is always in addition to the efficiency improvement by sequential updating.

Immobilization of olfactory receptors onto gold electrodes for electrical biosensor

We investigate the immobilization of native nanovesicles containing functional olfactory receptors onto gold electrodes by means of atomic force microscopy in liquid. We show that nanovesicles can be adsorbed without disrupting them presenting sizes once immobilized ranging from 50 nm to 200 nm in diameter. The size of the nanovesicles shows no dependence on the electrode hydrophobicity being constant in a height/width ratio close to 1:3. Nevertheless, electrode hydrophobicity does affect the surface coverage, the surface coverage is five times higher in hydrophilic electrodes than on hydrophobic ones. Surface coverage is also affected by nanovesicles dimensions in suspension, the size homogenization to around 50 nm yields a further five fold increment in surface coverage achieving a coverage of about 50% close to the hard spheres jamming limit (54.7%). A single layer of nanovesicles is always formed with no particle overlap. Present results provide insights into the immobilization on electrodes of olfactory receptors for further olfactory electrical biosensor development.