System Of Spheres Research Articles

Thermodynamic and structural properties of liquid Al–Au alloys

The mixing properties of liquid Al–Au alloys with respect to the concentration of each constituent is determined using a method based on hard sphere system and pseudo-potential perturbation. These models were used to get relevant information on mixing properties of the Al–Au alloys like the Gibbs energy and the entropy of mixing. The concentration fluctuations, chemical short range order for the hard sphere mixture (quasi-lattice theory) and the activity are calculated to know the extent of order in the liquid alloys. The results revealed that there is a degree of ordering in liquid Al–Au alloy (hetero-coordinated).

Analysis of the 3D microstructure of tape-cast open-porous materials via a combination of experiments and modeling

In the present paper, fabrication, characterization and modeling techniques are combined to analyze the microstructure of tape-cast open-porous materials. This kind of material is highly permeable to gases and at the same time has a high catalytic reactivity which leads to successful applications e.g. in high-temperature fuel cells. However, the microstructure of such material is complex and not fully understood. The main goal of this paper is to provide a realistic model of tape-cast porous microstructures based on the simulation of their fabrication process. In order to accomplish this, four different samples are fabricated by firing the green tapes obtained by the tape casting process. The microstructure of each sample is analyzed by means of micro-tomographic image data. Furthermore, a method for modeling open-porous 3D microstructures is proposed, where the cast slurry is represented by a system of spheres with a given volume fraction and radius distribution. Model-based post-processing of the simulated microstructures is proposed to improve the fit of the surface area. Finally, model validation is performed by means of a detailed statistical analysis of experimentally produced and virtual microstructures.

Quantifying telescope phase discontinuities external to adaptive optics systems by use of phase diversity and focal plane sharpening

We propose and apply two methods to estimate pupil plane phase discontinuities for two realistic scenarios on VLT and Keck. The methods use both Phase Diversity and a form of image sharpening. For the case of VLT, we simulate the `low wind effect' (LWE) which is responsible for focal plane errors in the SPHERE system in low wind and good seeing conditions. We successfully estimate the simulated LWE using both methods, and show that they are complimentary to one another. We also demonstrate that single image Phase Diversity (also known as Phase Retrieval with diversity) is also capable of estimating the simulated LWE when using the natural de-focus on the SPHERE/DTTS imager. We demonstrate that Phase Diversity can estimate the LWE to within 30 nm RMS WFE, which is within the allowable tolerances to achieve a target SPHERE contrast of 10$^{-6}$. Finally, we simulate 153 nm RMS of piston errors on the mirror segments of Keck and produce NIRC2 images subject to these effects. We show that a single, diverse image with 1.5 waves (PV) of focus can be used to estimate this error to within 29 nm RMS WFE, and a perfect correction of our estimation would increase the Strehl ratio of a NIRC2 image by 12\%

Statistical geometry characterization of global structure of TMAO and TBA aqueous solutions

We study the spatial distribution of trimethylamine-N-oxide (TMAO) and tert-butyl alcohol (TBA) molecules in aqueous solutions at low concentrations using molecular dynamics simulation, Voronoi-Delaunay method, and statistical cluster analysis. A comparison of these solutions with the systems of randomly distributed hard spheres is carried out. It is shown that TMAO molecules are generally distributed like random spheres. On the contrary, the distribution of TBA substantially differs from the random one, being the result of the self-association process in TBA solutions. Thus, using the methods of statistical geometry and systems of random spheres as a reference system, one can carry out a quantitative characterization of a global structure of a solution to describe general features of the spatial distribution of the solute molecules.

Method for emissivity measurement of semitransparent coatings at ambient temperature

Coatings deposited on a material surface are effective way of changing its surface properties. For increasing or decreasing radiation heat transfer, coatings with high or low emissivity are used. Measurement of spectral emissivity is a fundamental step to effective use of coatings for this application. Up to now the measurement methods are focused on bulk samples and mainly opaque ones. Here we present a method enabling measurement of emissivity of semitransparent coating itself, although it is deposited on a substrate. The method is based on measurement of transmittance and reflectance using an integration sphere system and Fourier transform infrared (FTIR) spectrometer for samples with two different coating thicknesses deposited on transparent substrates. Measured transmittance of the coating indicates spectral regions of potential emissivity differences using different substrates. From all the measured values, spectral emissivity can be characterized for different coating thicknesses. The spectral range of the method is from 2 μm to 20 μm. The measurement is done at ambient temperature enabling measurement of samples sensitive to heating like biomedical or nanocoatings. The method was validated on known bulk samples and an example of semitransparent coating measurement is shown on high-temperature high-emissivity coating.

Confined Assemblies of Colloidal Particles with Soft Repulsive Interactions.

We investigate the microconfinement of charged silica nanoparticles dispersed in refractive index matching monomers in poly(dimethylsiloxane) (PDMS) porous membrane. Here, the silica colloidal particles interact with each other and the pore wall via electrostatic double layer forces. Different from the hard sphere systems where the assembled morphologies are prescribed by the diameter ratio between the cylindrical confinement and the nanoparticles, here we observe a much richer variety of assemblies that are highly sensitive to both bulk and local nanoparticle concentration with fixed particle size and channel size. The experimentally observed assembly morphologies are consistent with theoretical predictions from the literature, based on Yukawa potential in the low packing density regime. Also, most of the configurations found in the experiment are well described by computer simulations using pairwise additive long-range repulsive interactions, demonstrating the ability to control the system to obtain a desired structure.

Quantitative photoacoustic integrating sphere (QPAIS) platform for absorption coefficient and Grüneisen parameter measurements: Demonstration with human blood

Quantitative photoacoustic imaging in biomedicine relies on accurate measurements of relevant material properties of target absorbers. Here, we present a method for simultaneous measurements of the absorption coefficient and Grüneisen parameter of small volume of liquid scattering and absorbing media using a coupled-integrating sphere system which we refer to as quantitative photoacoustic integrating sphere (QPAIS) platform. The derived equations do not require absolute magnitudes of optical energy and pressure values, only calibration of the setup using aqueous ink dilutions is necessary. As a demonstration, measurements with blood samples from various human donors are done at room and body temperatures using an incubator. Measured absorption coefficient values are consistent with known oxygen saturation dependence of blood absorption at 750nm, whereas measured Grüneisen parameter values indicate variability among five different donors. An increasing Grüneisen parameter value with both hematocrit and temperature is observed. These observations are consistent with those reported in literature.

The cage effect in systems of hard spheres.

The cage effect is generally invoked when discussing the delay in the decay of time correlation functions of dense fluids. In an attempt to examine the role of caging more closely, we consider the spread of the displacement distributions of Brownian particles. These distributions are necessarily biased by the presence of neighbouring particles. Accommodation of this bias by those neighbours conserves the displacement distribution locally and presents a collective mechanism for exploring configuration space that is more efficient than the intrinsic Brownian motion. Caging of some particles incurs, through the impost of global conservation of the displacement distribution, a delayed, non-local collective process. This non-locality compromises the efficiency with which configuration space is explored. Both collective mechanisms incur delay or stretching of time correlation functions, in particular the particle number and flux densities. This paper identifies and distinguishes these mechanisms in existing data from experiments and computer simulations on systems of particles with hard sphere interactions.

Density-functional theory for fluid-solid and solid-solid phase transitions.

We develop a theory to describe solid-solid phase transitions. The density functional formalism of classical statistical mechanics is used to find an exact expression for the difference in the grand thermodynamic potentials of the two coexisting phases. The expression involves both the symmetry conserving and the symmetry broken parts of the direct pair correlation function. The theory is used to calculate phase diagram of systems of soft spheres interacting via inverse power potentials u(r)=ε(σ/r)^{n}, where parameter n measures softness of the potential. We find that for 1/n<0.154 systems freeze into the face centered cubic (fcc) structure while for 1/n≥0.154 the body-centred-cubic (bcc) structure is preferred. The bcc structure transforms into the fcc structure upon increasing the density. The calculated phase diagram is in good agreement with the one found from molecular simulations.

Asymptotic orderings and approximations of the Master kinetic equation for large hard spheres systems

In this paper the problem is posed of determining the physically-meaningful asymptotic orderings holding for the statistical description of a large N-body system of hard spheres, i.e., formed by N≡1ε≫1 particles, which are allowed to undergo instantaneous and purely elastic unary, binary or multiple collisions. Starting point is the axiomatic treatment recently developed [Tessarotto et al., 2013–2016] and the related discovery of an exact kinetic equation realized by Master equation which advances in time the 1-body probability density function (PDF) for such a system. As shown in the paper the task involves introducing appropriate asymptotic orderings in terms of ε for all the physically-relevant parameters. The goal is that of identifying the relevant physically-meaningful asymptotic approximations applicable for the Master kinetic equation, together with their possible relationships with the Boltzmann and Enskog kinetic equations, and holding in appropriate asymptotic regimes. These correspond either to dilute or dense systems and are formed either by small-size or finite-size identical hard spheres, the distinction between the various cases depending on suitable asymptotic orderings in terms of ε.

Mean-field avalanches in jammed spheres.

Disordered systems are characterized by the existence of many sample-dependent local-energy minima that cause a step-wise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three-dimensional systems of soft spheres, either at jamming or at slightly higher densities.

Tracking Control of Ball on Sphere System Using Tuned Fuzzy Sliding Mode Controller Based on Artificial Bee Colony Algorithm

This research is conducted to study the trajectory tracking of a ball on a sphere. Regulating a ball on the upper equilibrium point of a sphere has been studied in previous researches; however, tracking the trajectory of a ball on a sphere is investigated for the first time in this research. To achieve this, an accurate model of the ball on sphere system has been extracted so that firstly, there is a valid dynamical model at the far-reaching points from the upper equilibrium point; and secondly, the designed controller (based on the accurate model) has a good performance, as well. In this research, the proposed controller is a fuzzy sliding mode controller (FSMC) which is robust to the parametric uncertainties. Also, because of the substitution of the fuzzy term instead of the sign function, the chattering about the sliding surface is reduced or eliminated. In addition, to tune the parameters of the fuzzy system, an appropriate objective function has been proposed such that its minimization would cause the decrease in both sliding time and chattering around the sliding surface. Tuning of the fuzzy membership parameters is done using artificial bee colony algorithm, with the aim of minimization of the mentioned objective function. In simulations, ball tracking on three predetermined trajectories on sphere shows superiority of FSMC when compared with sliding mode controller (SMC); in a way that the chattering and RMS of its tracking error in the system output are far less than those of SMC.

Kinetic Theory of a Confined Quasi-Two-Dimensional Gas of Hard Spheres

The dynamics of a system of hard spheres enclosed between two parallel plates separated a distance smaller than two particle diameters is described at the level of kinetic theory. The interest focuses on the behavior of the quasi-two-dimensional fluid seen when looking at the system from above or below. In the first part, a collisional model for the effective two-dimensional dynamics is analyzed. Although it is able to describe quite well the homogeneous evolution observed in the experiments, it is shown that it fails to predict the existence of non-equilibrium phase transitions, and in particular, the bimodal regime exhibited by the real system. A critical revision analysis of the model is presented , and as a starting point to get a more accurate description, the Boltzmann equation for the quasi-two-dimensional gas has been derived. In the elastic case, the solutions of the equation verify an H-theorem implying a monotonic tendency to a non-uniform steady state. As an example of application of the kinetic equation, here the evolution equations for the vertical and horizontal temperatures of the system are derived in the homogeneous approximation, and the results compared with molecular dynamics simulation results.

Locally favoured structures and dynamic length scales in a simple glass-former

We investigate the static and dynamic properties of a weakly polydisperse hard sphere system in the deeply supercooled state, i.e. at densities higher than that corresponding to the mode-coupling transition. The structural analysis reveals the emergence of icosahedral locally favoured structures, previously only found in trace quantities. We present a new approach to probe the shape of dynamically heterogeneous regions, which is insensitive to particle packing effects that can hamper such analysis. Our results indicate that the shape of the dynamically heterogeneous regions changes only weakly and moreover hint that the often-used four-point correlation length may exhibit a growth in excess of that which our method identifies. The growth of the size of the dynamically heterogeneous regions appears instead to be in line with the one of structural and dynamic propensity correlations.

Theoretical algorithm and application of a double-integrating sphere system for measuring leaf transmittance and reflectance spectra.

We present the theoretical background and analytical equations for calculating spectral reflectance and transmittance factors for plant leaves from data collected by a field spectroradiometer attached to a double-integrating sphere. The sphere constants required for the calculations are derived from measurements of an empty sample port and a diffuse reflectance panel. The new method is applied in measuring the spectra of leaves belonging to 13 tree species. The greatest advantages of a double-sphere system compared with the conventional single-sphere substitution method is the speed of measurements, ease of operation, and increased portability and field-ruggedness.

DEM study of granular discharge rate through a vertical pipe with a bend outlet in small absorber sphere system

Absorber sphere pneumatic conveying is a special application of pneumatic conveying technique in the pebble bed High Temperature Gas-Cooled Reactor (HTGR or HTR). Granular discharge through a vertical pipe with a bend outlet is one of the control modes to determine solid mass flowrate which is an important parameter for the design of absorber sphere pneumatic conveying. Granular discharge rate through the vertical pipe with a bend outlet in the small absorber sphere system are investigated by discrete element method simulation. The effect of geometry parameters on discharge rate, the discharge rate fluctuation in the vertical pipe, and the effect of friction on steady discharge rate (Ws) are analyzed and discussed. The phenomena of discharge rate fluctuation in the vertical pipe are observed, which are mainly resulted from the evolution of the average downward granular velocity. The steady discharge rate decreases rapidly with sliding friction coefficient increasing from 0.125 to 0.5, and gradually saturates with the friction coefficient further increasing from 0.5 to 1. It is interesting that the linear relation between Ws2/5 and pipe internal diameter D with zero intercept are found for the vertical pipe discharge with a bend outlet, which is different from the orifice discharge through a hopper or silo with none-zero intercept. A correlation similar to Beverloo’s correlation is developed to predict the steady discharge rate through the vertical pipe with a bend outlet. These results are helpful for the design of sphere discharge rate through the vertical pipe with a bend outlet in the small absorber sphere system of the pebble bed HTGR.

A new method to obtain the Carnahan–Starling equation and its generalization

We obtain the Carnahan–Starling equation for a system of hard spheres using the Euler method of accelerated series convergence. For this purpose, the virial series is transformed into a new series with coefficients that differ slightly from each other, even when considering the eleven currently known virial coefficients. The method of accelerated convergence was applied to this series; it allowed us to obtain the Carnahan–Starling equation. In this work, this equation is derived for the first time using the method of accelerated convergence. It is generalized to accurately reproduce all of the known virial coefficients and the asymptotic behavior of the free energy at high densities. This also makes it possible to describe a metastable region with a high degree of accuracy and to obtain the equation of state for a homogeneous system of hard spheres with the accuracy of a computer experiment.

A Granular System of Ellipses under Linear Shear

Shear of granular systems of disks (in 2D) and spheres (3D) has been studied extensively. However, less is known about systems of non-spherical particles, i.e., ellipses and polygons, etc. Here we studied a quasi 2D granular system composed of ellipses in a novel apparatus, which provided homogeneous simple shear by utilizing the weak friction between ellipses and the deformable base of the apparatus. Shear jamming, which was first reported for a disk system [1], was also observed for our ellipse system. We contrast shear jamming for systems of disks and systems of ellipses. By tracking the positions and orientations of the ellipses, we observed that the ellipses gradually rotated to align along a preferred direction as the shear strain increased. We also applied Voronoi tessellation to the packing of ellipses, showing that the distribution of the local density changed during shear. By contrast, such a change in the distribution was not observed in a disk system [2].

The rheology and microstructure of an aging thermoreversible colloidal gel

Colloidal gels exhibit time-dependent bulk properties. However, the processes and mechanisms by which aging occurs are poorly understood, which complicates the prediction of macroscopic behavior in these systems. Using a model, thermoreversible, adhesive hard sphere system consisting of octadecyl-coated silica nanoparticles dispersed in tetradecane, rheological aging is quantitatively related to structural aging. By simultaneously measuring the bulk properties and gel microstructure using rheometry and small angle neutron scattering, respectively, we show a one-to-one correspondence between the time-dependent storage modulus and the microstructure, and further, that this correspondence is independent of the gel's thermal and shear history. At the working volume fraction, the gel is homogeneous and, unlike phase-separated gels, aging behavior is not due to heterogeneous coarsening. Instead, the results presented here are consistent with homogeneous, local particle rearrangements as the mechanism of rheolog...

How cube-like must magnetic nanoparticles be to modify their self-assembly?

Systems whose magnetic response can be finely tuned using control parameters, such as temperature and external magnetic field strength, are extremely desirable, functional materials. Magnetic nanoparticles, in particular suspensions thereof, offer opportunities for this controllability to be realised. Cube-like particles are particularly mono-disperse examples that, together with their favourable packing behaviour, make them of significant interest for study. Using a combination of analytical calculations and molecular dynamics we have studied the self-assembly of permanently magnetised dipolar superballs. The superball shape parameter was varied in order to interpolate the region between the already well-studied sphere system and that of the recently investigated cube. Our findings show that as a superball particle becomes more cubic the chain to ring transition, observed in the ground state of spherical particles, occurs at an increasingly larger cluster size. This effect is mitigated, however, by the appearance of a competing configuration; asymmetric rings, a conformation that we show superballs can readily adopt.