Gaussian Particles Research Articles

Nonequilibrium relaxation of soft responsive colloids.

Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching between states. Such a multi-stability is useful for the development of soft functional materials. Here, we introduce a mean-field dynamical density functional theory for a model of responsive colloids to study the nonequilibrium dynamics of a colloidal dispersion in time-dependent external fields, with a focus on the coupling of translational and conformational dynamics during their relaxation. Specifically, we consider soft Gaussian particles with a bimodal size distribution between two confining walls with time-dependent (switching-on and off) external gravitational and osmotic fields. We find a rich relaxation behavior of the systems in excellent agreement with particle-based Brownian dynamics computer simulations. In particular, we find time-asymmetric relaxations of integrated observables (wall pressures, mean size, and liquid center-of-mass) for activation/deactivation of external potentials, respectively, which are tunable by the ratio of translational and conformational diffusion time scales. Our work thus paves the way for studying the nonequilibrium relaxation dynamics of complex soft matter with multiple degrees of freedom and hierarchical relaxations.

Pre-perihelion observations of long-period comet C/2013 X1 (PANSTARRS)

ABSTRACT We present and analyse the results of quasi-simultaneous spectroscopic, photometric, and polarimetric observations of hyperbolic comet C/2013 X1 (PANSTARRS) obtained at the 6-m Big Telescope Alt-azimuth (BTA) telescope Special Astrophysical Observatory (SAO) and 2.6-m Shajn telescope Crimean Astrophysical Observatory (CrAO). A wide fan-shaped structure and a weak tail were detected in the comet. The mean V − R colour of the coma was estimated to be neutral compared to the solar value. The Afρ parameter, a proxy to the dust production in the comet, was about 1672 ± 21 cm in the R band. Emissions of the CN, C2, C3, and NH2 molecules were identified in the cometary spectrum, which covers the wavelength range 3800 – 7100 Å. When the comet was at a distance of 2.66 au from the Sun, the minimum degree of polarization of about −1.5 per cent was detected in the near-nucleus region of the coma, in the range up to about 10 000 km from the optocentre. Further, polarization gradually increased (in absolute value) with distance from the nucleus, reaching −6.5 per cent at about 50 000 km. To reproduce the observed values of linear polarization and the phase-angle dependence of polarization for long-period comets, we used the Sh-matrix method with conjugated Gaussian random particles as light scatters, and the chemical composition of dust particles in the coma of 74 per cent amorphous carbon, 25 per cent of Mg-rich silicates, and 1 per cent of water ice.

Computer Simulation of Explosive Emission Processes in Strong Electromagnetic Fields

The paper discusses the problem of computer simulation of explosive emission processes in strong electromagnetic fields. In this work, a numerical method for calculating electron emission from the surface of a metal cathode for the axial symmetric geometry of a technical system is proposed. For modelling, the particle method and grid calculations of electromagnetic fields based on Maxwell’s equations are applied. The approach uses the representation of large smoothed Gaussian particles and implements calculations of the electromagnetic fields on Cartesian spatial grids. The software realization is directed towards on parallel computing. The calculation of the emission process in a coaxial cylindrical diode with magnetic self-insulation with the use of developed technique was carried out. The process is considered for two situations: with and without the longitudinal plasma layer. The calculations show that the presence of plasma leads to an increase in the emission current. This result is consistent with the results of experiments.

Slope Stability Analysis Based on the Explicit Smoothed Particle Finite Element Method

A landslide is a common natural disaster that causes environmental damage, casualties and economic losses, which seriously affects the sustainable development of society. In geomechanics, it is one of the largest deformation problems. Herein, the GPU-accelerated explicit smoothed particle finite element method (eSPFEM) for large deformation analysis in geomechanics was developed on the CUDA platform based on high-performance computing using a self-designed eSPFEM program code. The eSPFEM combines the strain smoothing nodal integration techniques found in the particle finite element method (PFEM) framework, which allows for the use of low-order triangular elements without volume locking and avoids frequent information transfer and mapping errors between Gaussian points and particles in PFEM. A numerical simulation of slope instability using the eSPFEM and based on a strength reduction technique was conducted using various examples, including a cohesive homogeneous slope, a non-cohesive homogeneous slope, a non-homogeneous slope and a slope with a thin soft band. The calculation results show that the eSPFEM can be applied to slope stability analysis under different working conditions, simulating the entire process of slope instability initiation, sliding and reaccumulation, and obtaining reliable FOS values. A numerical simulation was conducted to analyse a landslide that occurred in the Zhangjiazhuang tunnel on the Lanzhou–Xinjiang high-speed railway line on 18 January 2016. A natural unsaturated soil slope, a soil slope with a high moisture content and a soil slope with a high moisture content subjected to an earthquake were analysed. The findings of this study are in good agreement with the actual slope failure conditions. The primary triggers identified for the landslide were heavy rainfall and earthquakes. The verification results indicate that the eSPFEM can effectively simulate an actual landslide case, showcasing high accuracy and applicability in simulating the large deformation behaviour of landslides.

Characterization of the radiation beam of a tomotherapy equipment with MCNP

This work aims to model and characterize the radiation beam of one Accuray tomotherapy equipment using the Monte Carlo Code MCNP5 (Monte Carlo N-Particle). This tomotherapy equipment is used for delivering high doses of radiation in tumor regions to kill cancer cells and shrink the tumor during radiation therapy of cancer patients, however, the radiation can damage surrounding areas and nearby organs at risk (OAR) if the radiation field is not well delimited. In particular, intensity-modulated radiotherapy treatments (IMRT) with tomotherapy equipment offer great benefits to patients allowing treatment of tumor regions without affecting surrounding areas and OAR. Nowadays, it is well known that a correct simulation of transport of radiation in tomotherapy equipment facilitates considerably the estimation of ideal doses in the tumor, surrounding regions, and OAR. For that reason, in this work, we simulated the geometry of the 6 MV ACCURAY Tomotherapy equipment of the CECAN using the MCNP5. The model includes a TomoLINAC consisting of an electron source that emits Gaussian distribution particles with an average energy of 5.7 MeV and width of 0.3 MeV. The emitted particles impact the tungsten target and pass through primary collimators and jaws that define the irradiation field in the isocenter. To validate the geometry and radiation transport in the TomoLINAC the curves of depth dose percentage (PDD) estimated by simulation and the curves measured experimentally were tuned. In the same way, the simulated transverse and longitudinal profiles were compared with the experimental results. In addition, a comparison between the qualities of the radiation beam characterized with MCNP and measured experimentally in CECAN showed a deviation of 1%. For the simulations, cylindrical detectors located inside a water phantom were considered and it was employed the tally *F8. A good agreement was observed between the PDD's curves obtained from the simulation and those measured experimentally for a field of 5 × 10 cm2 in the isocenter and SSD (distance from the source to the surface) of 85 cm. Also, the comparison between the simulated and experimental transverse profiles obtained at 1.5 cm, 10 cm and 15 cm depth with a radiation field of 5 × 40 cm2 showed very good agreement. The longitudinal profiles were estimated with the same depths as the transverse ones, but for each of them, the openings of the jaws were 5.0 cm, 2.5 cm and 1.0 cm in the longitudinal direction, which corresponds to the direction in which the patient's table moves. The comparison between the simulated and experimental longitudinal profiles showed good concordance too. Once the radiation beam of the ACCURAY tomotherapy equipment had been characterized, experimental dose measurements were made using a Cheese phantom and two A1SL ionization chambers. These results obtained experimentally were compared with those estimated with MCNP for a field of 5 × 40 cm2 at the isocenter and SAD of 85 cm and, it was concluded that both results were similar considering the regions of uncertainty. Finally, we must highlight that the modeling and characterization of the radiation beam of CECAN's ACCURAY tomotherapy equipment can be a key tool for dose estimations in different cancer treatment plans and future research.

Simulation of Emission Processes in Strong Electromagnetic Fields

The problem of calculating the processes of electron emission from metal surfaces in strong electromagnetic fields is considered with allowance for relativistic effects. One of the methods of simulation in these processes is the particle method combined with grid calculation of fields on the basis of Maxwell’s equations. Similar techniques have been developed since the 1960s to the present. However, existing approaches have certain limitations. In this work, for an axisymmetric geometry of the generating system, a new numerical technique simulating the processes of electron emission from metal cathode surfaces is presented. The technique uses the representation of large smoothed Gaussian particles and implements the calculation of electromagnetic fields on Cartesian spatial grids. The software implementation is oriented to parallel computing. The aim of numerical experiments was to determine the parameters of electron emission. Diode and triode cylindrical systems were chosen as test problems. In numerical calculations, the spatiotemporal characteristics of relativistic electron beams generated by emission processes are obtained, including the reproduction of the Child–Langmuir current. The numerical technique developed has confirmed its correctness and efficiency.

Компьютерное моделирование процессов электронной эмиссии в сильных электромагнитных полях

The paper discusses the problem of computer simulation of electron emission processes in strong electromagnetic fields. In this work, a numerical method for calculating electron emission from the surface of a metal cathode for the axial symmetric geometry of a technical system is proposed. For modelling, the particle method and grid calculations of electromagnetic fields based on Maxwell's equations are applied. The approach uses the representation of large smoothed Gaussian particles and implements calculations of the electromagnetic fields on Cartesian spatial grids. The software realization is directed towards on parallel computing. The calculation of the emission process in a coaxial cylindrical diode with magnetic self-insulation with the use of developed technique was carried out. The process is considered for two situations: with and without the longitudinal plasma layer. The calculations show that the presence of plasma leads to an increase in the emission current. This result is consistent with the results of experiments.

Packed media radiative-transfer modeling with Gaussian particles: Application to spectra of icy regolith of Saturnian satellites

The radiative transfer theory with packed media correction (RTT-PM) is a balanced, physically rigorous, and practical light scattering model that is suitable for modeling reflectance and similar spectra of densely packed particulate media. The static structure factor correction to the classical radiative transfer solution and actualization of fundamental particles of media with spheres or aggregates are key properties of this model that ensure both physical rigor and practical efficiency. We improved upon the assumptions in the RTT-PM method by incorporating irregularly shaped Gaussian particles into its scheme. This incorporation of Gaussian particles is a notable advancement for applications of the RTT-PM method to planetary surfaces that often are layers of irregularly shaped particles. With the Gaussian particle RTT-PM method, we modeled spectra of Saturnian moons Dione, Rhea, and Tethys observed with the Cassini Visual and Infrared Mapping Spectrometer (VIMS), assuming pure water ice composition. For Rhea and Tethys, the Gaussian particle RTT-PM technique modeled VIMS spectra better than models with spherical or aggregate particles, strengthening prior suggestion that particles on Rhea and Tethys are solid, non-spherical particles. Dione's spectra were best modeled not with Gaussian particles but rather with an aggregate of 128 monomers. This makes Dione's icy regolith different from that on Rhea and Tethys. Prior studies have indicated that the cause for the difference might arise from the presence of surface macrostructures or absorbing materials on Dione, but according to our modeling results, increased multiple scattering from small fluffy aggregate particles is an alternative explanation.

Asteroid (3200) Phaethon: results of polarimetric, photometric, and spectral observations

ABSTRACT We present results of polarimetric, photometric, and spectral observations of the near-Earth asteroid (3200) Phaethon carried out at the 6-m BTA telescope of the Special Astrophysical Observatory and the 2.6-m and 1.25-m telescopes of the Crimean Astrophysical Observatory over a wide range of phase angles during its close approach to the Earth at the end of 2017 (α = 19°–135°) and in 2020 at α = 52.2°. Using our and other available in literature data, we found that the maximum degree of linear polarization of Phaethon in the V band is Pmax = (45 ± 1) per cent at the phase angle αmax = 124.0° ± 0.4°, whereas the inversion angle αinv = 21.4° ± 1.2° and polarimetric slope is h = (0.326 ± 0.027) per cent per degree. Using the dependence ‘polarimetric slope – albedo,’ we have found the geometric albedo of asteroid Phaethon to be pv = 0.060 ± 0.005. This value falls into the lower range of albedo values for asteroids determined by different methods. The mean colour indices U–B = 0.207 m ± 0.053 m and B–V = 0.639 m ± 0.054 m of the asteroid are derived at heliocentric and geocentric distances 1.077 au and 0.102 au, respectively, and phase angle α = 23.78°. The absolute magnitude of Phaethon is V(1,1,0) = 14.505 m ± 0.059 m. The effective diameter of Phaethon is estimated from obtained absolute magnitude and geometrical albedo, it is equal to 6.8 ± 0.3 km. The best fit to the observed polarimetric data was obtained with the Sh-matrix model of conjugated random Gaussian particles composed of Mg-rich silicate (90 per cent) and amorphous carbon (10 per cent).

Uncertainty estimation for ensemble particle image velocimetry

We present a novel approach to estimate the uncertainty in ensemble particle image velocimetry (PIV) measurements. The ensemble PIV technique is widely used when the cross-correlation signal-to-noise ratio is insufficient to perform a reliable instantaneous velocity measurement. Despite the utility of ensemble PIV, uncertainty quantification for this type of measurement has not been studied. Here, we propose a method for estimating the uncertainty directly from the probability density function of displacements found by deconvolving the ensemble cross-correlation from the ensemble autocorrelation. We then find the second moment of the probability density function and apply a scaling factor to report the uncertainty in the velocity measurement. We call this method the moment of probability of displacement (MPD). We assess MPD’s performance with synthetic and experimental images. We show that predicted uncertainties agree well with the expected root mean square (RMS) of the error in the velocity measurements over a wide range of image and flow conditions. MPD shows good sensitivity to various PIV error sources with around 86% accuracy in matching the RMS of the error in the baseline data sets. So, MPD establishes itself as a reliable uncertainty quantification algorithm for ensemble PIV. We compared the results of MPD against one of the existing instantaneous PIV uncertainty approaches, moment of correlation (MC). We adapted the MC approach for ensemble PIV, however, its primary limitations remain the assumption of the Gaussian probability density function of displacements and the Gaussian particles’ intensity profile. In addition, our analysis shows that ensemble MC consistently underestimates the uncertainty, while MPD outperforms that and removes the limiting Gaussian assumption for the particle and probability density function, thus overcoming the limitations of MC.

Comet 2P/Encke in apparition of 2017: II. Polarization and color

We present results of imaging polarimetry of comet 2P/Encke performed on January 23, 2017 at the heliocentric (1.052 au) and geocentric (1.336 au) distances and phase angle 46.8°, 46 days before perihelion. Observations were made through the medium-band SED500 (λ5019/246 Å) and broadband r-sdss (λ6200/1200 Å) filters with the multimode focal reducer SCORPIO-2 at the 6-m BTA telescope of the Special Astrophysical Observatory (Russia). Dust in comet 2P/Encke was mainly concentrated in the near-nucleus region of the coma: the maximum dust/gas to leave Fem/Fcont ratios were 1.5 and 2.9 in the SED500 and the r-sdss filters near the nucleus but dropped sharply to ~0.2 and ~1 at the distance ~2.500 km, respectively. Then these ratios began to increase at distances ~12,000 km from the nucleus, the ratio was ~0.3 (SED500) and ~ 1.3 (r-sdds). There were significant variations of polarization over the coma, which correlated with the variations in the dust color and dust/gas ratio. The maximum degree of polarization, ~8% in the r-sdss filter, was observed in the dust shell which was shifted by ~1.000 km towards the Sun. Polarization sharply dropped to ~4% at the distance ~3.000 km and then gradually increased with wave-like fluctuations with the distance from the nucleus, reaching ~8% at the distance ~12,000 km. A similar change in polarization was observed in the SED500 filter. After correction for gas contamination, using the dust/gas ratios from spectroscopy made on the same night, the values of polarization appeared to be ~4% in the near-nucleus region (~1.000 km), and reached 11–12% at the distance ~12,000 km in both filters. We also found an effect of nucleus polarization on the polarization of the dust coma in comet Encke in the r-sdss filter. The maximum value of the nucleus contamination was ~0.7%. Changes in polarization and color across the 2P/Encke coma indicate changes in physical properties of the dust particles with the distance from the nucleus. Our Sh-matrix computer simulations of light scattering by Gaussian particles allow us to suggest that the observed trends in color and polarization are mainly result from changing particle size.

Conjugated Gaussian Random Particle Model and Its Applications for Interpreting Cometary Polarimetric Observations

This article presents a model of conjugated Gaussian random particles, which are convenient for simulation of irregular particles that constitute cometary dust. Computer simulation is conducted for the polarimetric properties of these particles; phase dependences are calculated for the linear polarization degree. The calculated results are used to interpret cometary polarimetric observations and determine possible physical and chemical characteristics of comets as well as the variation range within which the model adequately describes the observed data. The model calculations are used to refine the empirical formula that describes the phase dependence of the linear polarization degree for the cometary continuum.

Cardinality-Consensus-Based PHD Filtering for Distributed Multitarget Tracking

We present a distributed probability hypothesis density (PHD) filter for multitarget tracking in decentralized sensor networks with severely constrained communication. The proposed “cardinality consensus” (CC) scheme uses communication only to estimate the number of targets (or, the cardinality of the target set) in a distributed way. The CC scheme allows for different implementations—e.g., using Gaussian mixtures or particles—of the local PHD filters. Although the CC scheme requires only a small amount of communication and of fusion computation, our simulation results demonstrate large performance gains compared with noncooperative local PHD filters.

Computer simulation of position and maximum of linear polarization of asteroids

The ground-based observations of near-Earth asteroids at large phase angles have shown some feature: the linear polarization maximum position of the high-albedo E-type asteroids shifted markedly towards smaller phase angles (αmax ≈ 70°) with respect to that for the moderate-albedo S-type asteroids (αmax ≈ 110°), weakly depending on the wavelength. To study this phenomenon, the theoretical approach and the modified T-matrix method (the so-called Sh-matrices method) were used. Theoretical approach was devoted to finding the values of αmax, corresponding to maximal values of positive polarization Pmax. Computer simulations were performed for an ensemble of random Gaussian particles, whose scattering properties were averaged over with different particle orientations and size parameters in the range X = 2.0 ... 21.0, with the power law distribution X − k, where k = 3.6. The real parts of the refractive index mr were 1.5, 1.6 and 1.7. Imaginary part of refractive index varied from mi = 0.0 to mi = 0.5. Both theoretical approach and computer simulation showed that the value of αmax strongly depends on the refractive index. The increase of mi leads to increased αmax and Pmax. In addition, computer simulation shows that the increase of the real part of the refractive index reduces Pmax. Whereas E-type high-albedo asteroids have smaller values of mi, than S -type asteroids, we can conclude, that value of αmax of E-type asteroids should be smaller than for S –type ones. This is in qualitative agreement with the observed effect in asteroids.

Positive branch of asteroid polarization: Observational data and computer modeling

Observations of near-Earth asteroids at large phase angles made it possible to obtain a more complete (for ground-based observations) phase dependence of the polarization of the E-type asteroids’ radiation including the maximum of the positive branch of the linear polarization degree. It is shown that the position of the polarization maximum of high-albedo asteroids is noticeably shifted to the decrease of phase angles compared with S-type asteroids. Model calculations of polarimetric properties of random Gaussian particles that simulate dust particles on the regolith surface are carried out. Model calculations show a qualitatively similar behavior pattern of parameters of the positive polarization branch. The influence of the refractive index of individual scattering particles on the size and position of the maximum of the positive branch of the linear polarization degree is investigated within the considered model.

Orthogonal Simulation Experiment for Flow Characteristics of Ore in Ore Drawing and Influencing Factors in a Single Funnel Under a Flexible Isolation Layer

A study on the flow characteristics of ore and factors that influence these characteristics is important to master ore flow laws. An orthogonal ore-drawing numerical model was established and the flow characteristics were explored. A weight matrix was obtained and the effect of the factors was determined. It was found that (1) the entire isolation–layer interface presents a Gaussian curve morphology and marked particles in each layer show a funnel morphology; (2) the drawing amount, Q, and the isolation layer half-width, W, are correlated positively with the fall depth, H, of the isolation layer; (3) factors that affect the characteristics sequentially include the particle friction coefficient, the interface friction coefficient, the isolation layer thickness, and the particle radius, and (4) the optimal combination is an isolation layer thickness of 0.005 m, an interface friction coefficient of 0.8, a particle friction coefficient of 0.2, and a particle radius of 0.007 m.

An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures.

The formation of microphases in systems of particles interacting by repulsive, bounded potentials is studied by means of density-functional theory (DFT) using a simple, mean-field-like form for the free energy which has already been proven accurate for this class of soft interactions. In an effort not to constrain the configurations available to the system, we do not make any assumption on the functional form of the density profile ρ(r), save for its being periodic. We sample ρ(r) at a large number of points in the unit cell and minimize the free energy with respect to both the values assumed by ρ(r) at these points and the lattice vectors which identify the Bravais lattice. After checking the accuracy of the method by applying it to a one-component generalized exponential model (GEM) fluid with pair potential ϵexp[ - (r/R)(4)], for which extensive DFT and simulation results are already available, we turn to a binary mixture of Gaussian particles which some time ago was shown to support microphase formation [A. J. Archer, C. N. Likos, and R. Evans, J. Phys.: Condens. Matter 16, L297 (2004)], but has not yet been investigated in detail. The phase diagram which we obtain, that supersedes the tentative one proposed by us in a former study [M. Carta, D. Pini, A. Parola, and L. Reatto, J. Phys.: Condens. Matter 24, 284106 (2012)], displays cluster, tubular, and bicontinuous phases similar to those observed in block copolymers or oil/water/surfactant mixtures. Remarkably, bicontinuous phases occupy a rather large portion of the phase diagram. We also find two non-cubic phases, in both of which one species is preferentially located inside the channels left available by the other, forming helices of alternating chirality. The features of cluster formation in this mixture and in GEM potentials are also compared.

Gaussian Random Particles with Flexible Hausdorff Dimension

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an isotropic random field on the sphere. If the kernel is a von Mises-Fisher density, or uniform on a spherical cap, the correlation function of the associated random field admits a closed form expression. The Hausdorff dimension of the surface of the Gaussian particle reflects the decay of the correlation function at the origin, as quantified by the fractal index. Under power kernels we obtain particles with boundaries of any Hausdorff dimension between 2 and 3.

Gaussian Random Particles with Flexible Hausdorff Dimension

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an isotropic random field on the sphere. If the kernel is a von Mises-Fisher density, or uniform on a spherical cap, the correlation function of the associated random field admits a closed form expression. The Hausdorff dimension of the surface of the Gaussian particle reflects the decay of the correlation function at the origin, as quantified by the fractal index. Under power kernels we obtain particles with boundaries of any Hausdorff dimension between 2 and 3.

Analytical theory of effective interactions in binary colloidal systems of soft particles.

While density functional theory with integral equations techniques are very efficient tools in the numerical analysis of complex fluids, analytical insight into the phenomenon of effective interactions is still limited. In this paper, we propose a theory of binary systems that results in a relatively simple analytical expression combining arbitrary microscopic potentials into effective interaction. The derivation is based on translating a many-particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language, which turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. As a result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the following: the effective attraction as a demixing factor in the binary systems of Gaussian particles, the screening of charged spheres by ions, which proves equivalent to Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, effective interactions in the binary mixtures of Yukawa particles, and the system of particles consisting of both a repulsive core and an attractive/repulsive Yukawa interaction tail. For this last case, we reproduce the "attraction-through-repulsion" and "repulsion-through-attraction" effects previously observed in simulations.