Average Distribution Function Research Articles

High Accuracy Localization Scheme Using 1-Bit Side Information: Achievability from a GDoP Perspective

In this paper, we provide a novel methodology for high-precision positioning that utilizes 1-bit additional information, which applies to various positioning techniques. The proposed approach leverages binary information to indicate if a user is within a specified space of interest and refines the estimated location information outside this area. By matching the estimated locations outside the area of interest with the valid location information within, this methodology corrects the positional data obtained through any arbitrary positioning technique, aligning the estimated positions with the intended spatial boundaries. Performance analysis metrics, such as Average Positioning Error (APE) and Cumulative Distribution Function for positioning coverage, were employed to assess the effectiveness of the proposed methods. Numerical simulations demonstrate how the proposed method enhances the averaged positioning accuracy, significantly outperforming the conventional time of arrival method. Furthermore, the proposed positioning correction methodology demonstrates validated feasibility applicable to an arbitrary existing positioning method.

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocity v 0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case of v 0 polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

Molecular Dynamics Simulation of Silane Inserted CSH Nanostructure.

Herein, the toughening mechanism and effects of 3-(aminopropyl)triethoxysilane (3-APTES) intercalation in calcium-silicate-hydrate (CSH) structures were investigated through molecular dynamics simulations. CSH established a model using 11 Å-tobermorite to simulate the tensile properties, toughness, adsorption energy, average orientation displacement and radial distribution function of 3-APTES intercalation at different Ca/Si ratios under conditions of a CVFF force field, an NVT system, and 298 K temperature. Simulation results demonstrate that 3-APTES alters the fracture process of CSH and effectively enhances its tensile properties and toughness. The presence of 3-APTES molecules increases the energy required to destroy CSH, thereby increasing the adsorption energy of CSH crystals. Furthermore, 3-APTES molecules effectively increase the atom density within the CSH structure. As the Ca/Si ratio increases, Ca-O bond formation is enhanced, with noticeable aggregation occurring because of modification by 3-APTES within the CSH structure. This study found that 3-APTES organic compounds can effectively improve the tensile, toughness, adsorption and other properties of the CSH structure, and further improve the microstructure of CSH.

A study on the approximated angular averaging of distribution functions obtained from the Ornstein–Zernike theory for diatomic solutes consisting of fused Lennard-Jones particles immersed in a Lennard–Jones monatomic solvent

We propose an approximate method to obtain an angular averaged distribution function around an atom of a diatomic solute molecule consisting of fused Lennard–Jones (LJ) particles solvated in an LJ monatomic solvent. Our method employs the Ornstein–Zernike and closure equations for the correlation function between a single-centered solute and solvent by assuming spherical symmetry for the potential interaction. In setting the potential along the radial direction, the interaction between the solvent and solute atom that is covalently bonded to the atom located at the origin is also considered, as is typical in interaction site models. The proposed method accurately describes the angular averaged distribution function between a solvent and a solute atom that is completely buried inside the other atom in the solute, where the term “buried” indicates that the sum of the radius of one atom and the bond length is less than the radius of the other atom. The obtained angular-dependent one-dimensional distribution function is also reasonable for buried solute atoms. Thus, the proposed method is superior to the reference interaction site model (RISM) theory. However, our method failed to correctly describe the distribution function for an unburied atom of the solute, for which the RISM theory would be better than the proposed method. Furthermore, we demonstrated that sigma enlarging bridge (SEB) correction [T. Miyata, Bull. Chem. Soc. Japan, 90 (2017) 1095] is applicable to the proposed method. The combination of the method proposed in this study and SEB correction improves both the first rising region of the angular averaged distribution function and the solvation free energy.

Numerical investigation on the effect of porosity distribution on the flame characteristics

The low velocity filtration combustion of a lean methane/air mixture in the fixed bed reactors is numerically investigated using the system scale method. The effect of porosity on the flame characteristics, such as temperature profile, flame displacement speed and flame shape is examined in this study. For comparison, porosity is considered in two forms, i.e., volumetric average porosity (VAP) and porosity spatial distribution function (PSDF). The simulation results show that, local distribution of porosity primarily affects the flame shape, while having minimal impact on the peak flame temperature and mean flame displacement velocity. Quantitative analysis indicates that the flame displacement velocity obtained using VAP is closer to the experimental data compared to the PSDF. However, the simulation with PSDF explicitly captures the flame front bending caused by local porosity variation. Velocity and temperature fields suggests that flame front bending predominantly depends on the local flame displacement speed (LFDS), which is the vector sum of local interstitial airflow speed and the laminar flame speed of the combustible gas. The radial difference in LFDS, which is associated with uniformity in velocity and temperature fields, serves as the main driving force for flame front instability. The inclusion of PSDF enables a more accurate prediction of flame front development by capturing the preferential flow near the wall.

RCM Modeling of Bubble Injections Into the Inner Magnetosphere: Spectral Properties of Plasma Sheet Particles

AbstractCollisionless astrophysical plasmas are correlated systems in which particles are often not in thermal equilibrium and can be characterized by power‐law distributions. The kappa distribution function, which is a more generalized form of the power‐law function, is often used to describe acceleration and production of high‐energy particles in different space plasma environments. The spectra of particles in the Earth's plasma sheet constructed using Time History of Events and Mesoscale Interactions during Substorms data show that the kappa index exhibits a strong dawn‐dusk asymmetry and a clear dependence on both geocentric distance and magnetic local time. Furthermore, statistics indicate that spectrum hardening, or softening is expected during geomagnetically disturbed periods. To understand how the shape of the particle distribution function evolves and what factors affect the kappa index, we simulate earthward plasma transport using a kinetic drift model. In the simulations, the plasma distribution is initially considered to be a kappa function with . However, with time, both protons and electrons' distribution functions evolve and deviate from their initial shapes. We demonstrate that by implementing transient low‐entropy plasma injections, the Rice Convection Model average distribution functions can reasonably agree with observations. We also discuss the relative impact of gradient/curvature drift, particle loss, and bubble injections, based on controlled numerical experiments.

Global linear stability analysis of kinetic trapped ion mode (TIM) in tokamak plasma using the spectral method

Trapped ion modes (TIMs) belong to the family of ion temperature gradient (ITG) modes, which are one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis by considering the magnetic flux ψ dependency of the equilibrium Hamiltonian in both the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function . Using this spectral method, linear growth rates of TIM instability in the presence of different temperature profiles and precession frequencies of trapped ions, with an approximated constant Hamiltonian and the exact ψ dependent equilibrium Hamiltonian, are investigated. The growth rate depends on the logarithmic gradient of temperature κ T , density κ n and equilibrium Hamiltonian . With the exact ψ dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with an approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with good accuracy. This spectral method is very fast and requires much less computation resources compared to a linear version of the Vlasov-solver based on a semi-Lagrangian scheme.

Could network structures generated with simple rules imposed on a cubic lattice reproduce the structural descriptors of globular proteins?

Abstract A direct way to spot structural features that are universally shared among proteins is to find analogues from simpler condensed matter systems. In the current study, the feasibility of creating ensembles of artificial structures that can automatically reproduce a large number of geometrical and topological descriptors of globular proteins is investigated. Towards this aim, a simple cubic (SC) arrangement is shown to provide the best background lattice after a careful analysis of the residue packing trends from 210 globular proteins. It is shown that a minimalistic set of rules imposed on this lattice is sufficient to generate structures that can mimic real proteins. In the proposed method, 210 such structures are generated by randomly removing residues (beads) from clusters that have a SC lattice arrangement such that all the generated structures have single connected components. Two additional sets are prepared from the initial structures via random relaxation and a reverse Monte Carlo simulated annealing algorithm, which targets the average radial distribution function (RDF) of 210 globular proteins. The initial and relaxed structures are compared to real proteins via RDF, bond orientational order parameters and several descriptors of network topology. Based on these features, results indicate that the structures generated with 40% occupancy closely resemble real residue networks. The structure generation mechanism automatically produces networks that are in the same topological class as globular proteins and reproduce small-world characteristics of high clustering and small shortest path lengths. Most notably, the established correspondence rules out icosahedral order as a relevant structural feature for residue networks in contrast to other amorphous systems where it is an inherent characteristic. The close correspondence is also observed in the vibrational characteristics as computed from the Anisotropic Network Model, therefore hinting at a non-superficial link between the proteins and the defect laden cubic crystalline order.

XAFS studies of glass structure

X-ray absorption fine structure (XAFS) spectroscopy has become one of the most important techniques to characterise the local coordination of specific atomic species present in condensed matter. The possibility of investigating the structure of noncrystalline materials has made XAFS very attractive for the study of the short range structure of the glassy state. The XAFS acronym denotes the structure present above the x-ray absorption edges; such a structure is distinguished as x-ray absorption near edge structure (XANES) and extended x-ray absorption fine structure (EXAFS). XANES carries information on the atomic arrangement around the absorbing species: distances and bonding angles. XANES also provides information on the electronic states in the proximity of the conduction band: different chemical environments may be identified from known features in the spectrum. EXAFS provides information on the average distance and radial distribution function of the nearest neighbours of the absorbing species. In the last decade, the enormous progress of experimental techniques and the excellent quality of experimental spectra, consequent to the development of the synchrotron radiation facilities, have stimulated the evolution of the XAFS theory and analysis procedures. This paper is a survey on the theoretical development of XAFS and on the methods for determining the short range information in disordered materials. Applications of XAFS to some vitreous systems are reported.

Comparison between pseudohomogeneous and resolved-particle models for liquid hydrodynamics in packed-bed reactors

Despite the advances in the modelling of Packed-Bed Reactors (PBR) it is common to find in literature works where resolved-particle models are implemented considering small-scale domains; or works where large-scale models are implemented with a pseudohomogeneous approach. In order to quantify the differences in the prediction of the local velocity between these two approaches, a CFD study was conducted for the modelling of the single-phase flow in a PBR. Six different cases, two resolved-particle and four pseudohomogeneous, were implemented and compared. The resolved-particle cases incorporated the explicit description of the solids bed distribution, considering an ordered and a randomly distributed bed of spheres, in which the punctual momentum balance was solved in the interstitial void space left by the solids. The pseudohomogeneous cases considered Darcy’s law (DL) and the Navier-Stokes-Darcy-Forchheimer (NSDF) equation, and the bed porosity as an overall average value εB=εB and as a function of the radial position of the bed εB=εBr, in order to include the effects of the solids bed without the explicit description of the solids distribution. The results show that there are significant local differences in the textural characteristics between the random packing and ordered packing for the resolved-particle cases. It was observed that the pseudohomogeneous models allow to predict the macroscopic behaviours indicated in the resolved-particle case, but fail to capture the local behaviours inside the bed. Furthermore, the inclusion of an average porosity distribution function does not improve the prediction of the local scale phenomena.

Estimating buildup factor of alloys based on combination of Monte Carlo method and multilayer feed-forward neural network

Up to now, different methods have been developed for estimation of buildup factor (BF). However, either expensive estimation or time-consuming estimation are major restrictions/challenges of these methods. In this study a new technique utilizing combination of Monte Carlo method and the Bayesian regularization (BR) learning algorithm of multilayer feed-forward neural network (FFNN) is employed for estimation of BFs. First, the BFs of the different elements (i.e. Al, Cu, and Fe) at different energies and different mean free paths (MFPs) are modeled by the MCNP code. The results show that the calculated BFs by MCNP code are in good agreement with the reported values of American nuclear society (ANS). Afterwards, the appropriate architecture of FFNN (i.e. the appropriate number of hidden neurons and hidden layers) and the appropriate input patterns features are investigated. The resulted FFNN is trained using the modeled BFs and the selected category of features. In the test process, the BFs of the master alloys (i.e. Fe-Al%50, Cu-Fe50%, Al-Cu50%) are estimated. To evaluate the performance of the proposed FFNN for training/estimation of the new elements/alloys, Si is added to the training process and the BFs of the Al-Si35% is estimated. Average mean relative error (AMRE) and cumulative distribution function (CDF) of the errors show the acceptable accuracy of the estimating the BFs of the alloys. The noticeable advantages of the proposed technique are: 1- The BFs of the different alloys are estimated only by using the BFs of the constituent elements of the alloys. 2- The time needed to estimate the new BFs by the proposed technique can be neglected versus the time needed to model the new BFs by Monte Carlo. 3- The proposed technique can generalize its ability for estimating the BFs of the new alloys. 4- Monte Carlo codes need the trained person to model the BFs of the alloys while the FFNN generates the new BFs easily.

Bayesian regularization of multilayer perceptron neural network for estimation of mass attenuation coefficient of gamma radiation in comparison with different supervised model-free methods

Multilayer perceptron (MLP) neural networks have been used extensively for estimation/regression of parameters. Moreover, recent studies have shown that learning algorithms of MLP which are based on Gaussian function are more accurate. In this paper, the mass attenuation coefficient (MAC) of gamma radiation for light-weight materials (e.g. O-8), mid-weight materials (e.g. Al-13), and heavy-weight materials (e.g. Pb-82) is modelled using Gaussian function based regularization of MLP (i.e. Bayesian regularization (BR)) and by a modular estimator. The results are compared with the Reference results. To show better performance of the utilized algorithm, the results of the different supervised methods including support vector machine (SVM) with different kernel functions, decision tree (DT), and radial basis network (RBN) are given. Average mean relative error (AMRE) and cumulative distribution function (CDF) of errors of MACs estimation are calculated. Comparison of the results indicates that MLP-BR gives more accurate results (e.g. AMREO−8=0.0014, CDFO−8(0.0069) = 0.99, AMREAl−13=0.0015, CDFAl−13(0.0048) = 0.99, AMREPb−82=0.0117, CDFPb−82(0.0523) = 0.99).

Kinetics of field-induced phase separation of a magnetic colloid under rotating magnetic fields.

This paper is focused on the experimental and theoretical study of the phase separation of a magnetic nanoparticle suspension under rotating magnetic fields in a frequency range, 5 Hz ≤ ν ≤ 25 Hz, relevant for several biomedical applications. The phase separation is manifested through the appearance of needle-like dense particle aggregates synchronously rotating with the field. Their size progressively increases with time due to the absorption of individual nanoparticles (aggregate growth) and coalescence with neighboring aggregates. The aggregate growth is enhanced by the convection of nanoparticles toward rotating aggregates. The maximal aggregate length, Lmax ∝ ν-2, is limited by fragmentation arising as a result of their collisions. Experimentally, the aggregate growth and coalescence occur at a similar timescale, ∼1 min, weakly dependent on the field frequency. The proposed theoretical model provides a semi-quantitative agreement with the experiments on the average aggregate size, aggregation timescale, and size distribution function without any adjustable parameter.

Fourth-order moment of the light field in atmosphere

The quasiclassical distribution function for photon density in the phase space is obtained from solution of the kinetic equation. This equation describes propagation of paraxial laser beams in the Earth atmosphere where ‘collision integral’ embodies the influence of turbulence. The anisotropy of photon distribution is shown and explained. For long propagation path, the explicit expression for fourth-order moment of light is obtained as a sum of linear and quadratic forms of the average distribution function. This moment describes a spatial correlation of four light waves, giving the information about the photon distribution in the cross-section of the beam. The fourth moment can be measured using two small detectors outside the central part of the beam. The linear form describes the shot noise (quantum fluctuations) of photons. The range where the shot noise exceeds the classical noise is found analytically. Derived photon fluctuations are the valuable source of information about statistical properties and local structure of the laser radiation that can be used for applications.

Phase space mixing in an external gravitational central potential

This article is devoted to the study of the dynamical behavior of a collisionless kinetic gas in d = 1, 2, 3 space dimensions which is trapped in a rotationally symmetric potential well. Although at the microscopic level the trajectories of individual gas particles are quasi-periodic and characterized by their d fundamental frequencies, at the macroscopic level the gas relaxes in time to a stationary state, provided the potential satisfies a certain non-degeneracy condition. In this article, we provide a mathematically precise formulation for this relaxation process which is due to phase space mixing. In particular, we prove that a physically relevant class of macroscopic observables computed from the one-particle distribution function, such as particle and energy densities, pressure and stress tensors, converge in time to the corresponding observables associated with an averaged distribution function. The latter can be determined from the initial datum and depends only on integrals of motion. Thus, the final state of the gas is described by an effective distribution function depending only on integrals of motion, which considerably reduces the degrees of freedom of the gas configuration. We discuss some applications to gravitational physics, including the propagation of a collisionless gas in typical potentials arising in stellar dynamics and the modeling of dark matter halos, and we also generalize our results to a relativistic gas whose individual particles follow bound timelike trajectories in the exterior region of a static, spherically symmetric black hole spacetime.

Performance study of bayesian regularization based multilayer feed-forward neural network for estimation of the uranium price in comparison with the different supervised learning algorithms

In this study, the estimation of the uranium price as one of the most important factors affecting the fuel cost of nuclear power plants (NPPs) is investigated. Supervised learning algorithms, especially, multilayer feed-forward neural network (FFNN) are used extensively for parameters estimation. Similar to other supervised methods, FFNN can suffer from overfitting (i.e. imbalance between memorization and generalization). In this study, different regularization techniques of FFNN are discussed and the most appropriate regularization technique (i.e. Bayesian regularization) is selected for estimation of the uranium price. The different methods including different learning algorithms of FFNN, support vector machine (SVM) with different kernel functions, radial basis network (RBN), and decision tree (DT) are utilized for the prediction of the uranium price and are compared with FFNN-BR. Average mean relative error (AMRE) and cumulative distribution function (CDF) of the results indicate that FFNN-BR method is more accurate for the uranium price estimation (i.e. CDF (0.0720) = 0.99 and AMRE = 0.0533).

A theoretical analysis of the hydrodynamic influence on the growth of microalgae in the photobioreactors with simple growth kinetics

This work presents a theoretical analysis for understanding the influence of hydrodynamics on the growth of microalgae in the photobioreactor (PBR). In the analysis, it is assumed that the growth rate is determined by the instantaneous light intensity and the light distribution is not influenced by the hydrodynamics. It is proved that the average growth rate over the tracked particles and the volume-averaged growth rate are the same if the average spatial distribution function (SDF) of the particles is included. In addition, the fluid kinematics shows that the SDF is related to the Jacobian or volumetric change ratio of the particle trajectories. For single-phase flows, the SDF should be uniform. The analysis justifies the conclusion that if the PBR is well-mixed and the dynamic growth kinetics are not included, the growth rate is only influenced by the light condition and the geometry of the PBR, but is not influenced by the hydrodynamics. The theoretical analysis is validated by the CFD simulations of the average growth rates of Taylor vortex PBR with single-phase flows, bubble column PBR and airlift PBRs with two-phase flows. It is also found that the particles tend to accumulate near the wall or boundary regions in the Lagrangian particle tracking method. This artificial effect is contrary to the theoretical analysis and can generate errors when predicting the growth rate. Therefore, further validations and examinations are needed for the numerical models.

Suppressing cosmic variance with paired-and-fixed cosmological simulations: average properties and covariances of dark matter clustering statistics

ABSTRACT Making cosmological inferences from the observed galaxy clustering requires accurate predictions for the mean clustering statistics and their covariances. Those are affected by cosmic variance – the statistical noise due to the finite number of harmonics. The cosmic variance can be suppressed by fixing the amplitudes of the harmonics instead of drawing them from a Gaussian distribution predicted by the inflation models. Initial realizations also can be generated in pairs with 180○ flipped phases to further reduce the variance. Here, we compare the consequences of using paired-and-fixed versus Gaussian initial conditions on the average dark matter clustering and covariance matrices predicted from N-body simulations. As in previous studies, we find no measurable differences between paired-and-fixed and Gaussian simulations for the average density distribution function, power spectrum, and bispectrum. Yet, the covariances from paired-and-fixed simulations are suppressed in a complicated scale- and redshift-dependent way. The situation is particularly problematic on the scales of Baryon acoustic oscillations where the covariance matrix of the power spectrum is lower by only $\sim 20{{\ \rm per\ cent}}$ compared to the Gaussian realizations, implying that there is not much of a reduction of the cosmic variance. The non-trivial suppression, combined with the fact that paired-and-fixed covariances are noisier than from Gaussian simulations, suggests that there is no path towards obtaining accurate covariance matrices from paired-and-fixed simulations – result, that is theoretically expected and accepted in the field. Because the covariances are crucial for the observational estimates of galaxy clustering statistics and cosmological parameters, paired-and-fixed simulations, though useful for some applications, cannot be used for the production of mock galaxy catalogues.

Randomly branching θ-polymers in two and three dimensions: Average properties and distribution functions.

Motivated by renewed interest in the physics of branched polymers, we present here a detailed characterization of the connectivity and spatial properties of 2- and 3-dimensional single-chain conformations of randomly branching polymers under θ-solvent conditions obtained by Monte Carlo computer simulations. The first part of the work focuses on polymer average properties, such as the average polymer spatial size as a function of the total tree mass and the typical length of the average path length on the polymer backbone. In the second part, we move beyond average chain behavior and we discuss the complete distribution functions for tree paths and tree spatial distances, which are shown to obey the classical Redner-des Cloizeaux functional form. Our results were rationalized first by the systematic comparison to a Flory theory for branching polymers and next by generalized Fisher-Pincus relationships between scaling exponents of distribution functions. For completeness, the properties of θ-polymers were compared to their ideal (i.e., no volume interactions) as well as good-solvent (i.e., above the θ-point) counterparts. The results presented here complement the recent work performed in our group [A. Rosa and R. Everaers, J. Phys. A: Math. Theor. 49, 345001 (2016); J. Chem. Phys. 145, 164906 (2016); and Phys. Rev. E 95, 012117 (2017)] in the context of the scaling properties of branching polymers.

Particle emissions from a HD SI gas engine fueled with LPG and CNG

An extensive experimental campaign was addressed to study the emissive behavior of a heavy-duty (HD) spark ignition (SI) gas engine fueled with LPG and CNG, mainly focusing on particle emissions analysis. The engine was tested in transient condition, along the World Harmonized Transient Cycle (WHTC), also analyzing the engine response in correspondence of cold- and hot-start WHTCs. Overall, for both CNG and LPG, regulated emissions are within the Euro VI homologation limits. The average particle size distribution function indicates that particles with diameters below 23 nm contribute to about 20% of total PN for both the fuels. The results reveal that the particles are emitted in the first part of tests, highlighting a correlation of soot and PN emissions with some specific phases of the test cycle, namely in correspondence to the passage from long engine idle periods to speed/load increments, in both cold- and hot-start WHTCs. No significant variation in the distribution of primary particles dimension is discernible in the particles sampled along the different WHTC versions, indicating that cold- and hot-start WHTCs negligible affect the formation of the nuclei cores at the early stage of the particles formation. The thermal reactivity of both LPG and CNG-derived soot is in line with typical engine particulate matter: the soot is completely burnt in the temperatures range between 550 and 680 °C and a moderately higher reactivity in case of soot from cold-start CNG tests was detected. Such difference was related to the larger presence of oxygen functional groups.